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-46.9306 262.5 358 ClipEllips 34.5509 -23.4197 -70.4415 241 381 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 232 351 ClipEllips 71.1018 35.5509 73.3008 223 321 ClipBox 14.0451 89.1872 -0.0791957 -45.6437 245 298.5 ClipEllips 71.1018 35.5509 -45.6437 223 321 ClipBox 14.3358 88.8452 -0.0954306 12.926 253.5 328 ClipEllips 34.5509 36.8576 -11.0056 223 321 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.875 89.9691 -0.0160334 74.1808 214.5 291 ClipEllips 71.1018 35.5509 74.1808 206 261 ClipBox 14.0095 89.1855 -0.0791559 -46.9306 227.5 238 ClipEllips 71.1018 35.5509 -46.9306 206 261 ClipBox 14.0806 88.8286 -0.0950825 13.815 236.5 268.5 ClipEllips 34.5509 37.2739 -9.6438 206 261 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.1535 89.9659 -0.0156499 72.6995 196.5 230.5 ClipEllips 71.1018 35.5509 72.6995 187 200 ClipBox 13.2104 89.1457 -0.0783068 -46.273 209 177 ClipEllips 71.1018 35.5509 -46.273 187 200 ClipBox 12.9427 88.7452 -0.0936472 13.6005 218 207.5 ClipEllips 34.5509 34.9654 -7.76434 187 200 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.911 88.8172 -0.0948565 -46.9306 201.5 344 ClipEllips 71.1018 35.5509 -46.9306 180 367 ClipBox 14.222 88.4129 -0.111153 12.926 210.5 374 ClipEllips 34.5509 36.4294 -10.5774 180 367 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 171 336.5 ClipEllips 71.1018 35.5509 73.5596 162 306 ClipBox 13.9469 88.8196 -0.0949039 -45.6437 184 283.5 ClipEllips 71.1018 35.5509 -45.6437 162 306 ClipBox 13.9648 88.3897 -0.110749 13.815 192.5 313.5 ClipEllips 34.5509 36.839 -9.20896 162 306 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 153 276 ClipEllips 71.1018 35.5509 73.3008 144 246 ClipBox 13.911 88.8172 -0.0948565 -46.9306 165.5 223 ClipEllips 71.1018 35.5509 -46.9306 144 246 ClipBox 12.8166 88.2724 -0.109082 13.6005 175 253.5 ClipEllips 34.5509 34.4967 -7.29559 144 246 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.911 88.8172 -0.0948565 -46.9306 140.5 329 ClipEllips 71.1018 35.5509 -46.9306 119 352 ClipBox 13.9648 88.3897 -0.110749 13.815 149.5 359.5 ClipEllips 34.5509 36.839 -9.20896 119 352 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 110 321.5 ClipEllips 71.1018 35.5509 73.5596 101 291 ClipBox 14.7059 88.868 -0.095954 -46.302 122.5 268.5 ClipEllips 71.1018 35.5509 -46.302 101 291 ClipBox 13.9648 88.3897 -0.110749 13.815 131.5 298.5 ClipEllips 34.5509 36.839 -9.20896 101 291 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.911 88.8172 -0.0948565 -46.9306 79.5 314 ClipEllips 71.1018 35.5509 -46.9306 58 337 ClipBox 13.9648 88.3897 -0.110749 13.815 88.5 344.5 ClipEllips 34.5509 36.839 -9.20896 58 337 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore 0.411765 0.411765 0.411765 34.5509 447 354 Sphere gsave %% 1 1 13.5005 89.9666 -0.0157212 73.5596 438 323.5 ClipEllips 34.5509 96.5437 50.5755 429 293 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 14.5779 89.9686 -0.0159617 73.3008 420 263 ClipEllips 34.5509 98.2412 48.3603 411 233 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 14.5779 89.9686 -0.0159617 73.3008 402 203 ClipEllips 34.5509 98.2412 48.3603 393 173 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.5005 89.9666 -0.0157212 73.5596 384 142.5 ClipEllips 34.5509 96.5437 50.5755 375 112 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.5005 89.9666 -0.0157212 73.5596 366 81.5 ClipEllips 34.5509 96.5437 50.5755 357 51 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.911 88.8172 -0.0948565 -46.9306 425.5 377 ClipEllips 34.5509 -23.7855 -70.0757 404 400 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 395 369.5 ClipEllips 71.1018 35.5509 73.5596 386 339 ClipBox 13.911 88.8172 -0.0948565 -46.9306 407.5 316 ClipEllips 71.1018 35.5509 -46.9306 386 339 ClipBox 13.9648 88.3897 -0.110749 13.815 416.5 346.5 ClipEllips 34.5509 36.839 -9.20896 386 339 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 377 309 ClipEllips 71.1018 35.5509 73.3008 368 279 ClipBox 13.911 88.8172 -0.0948565 -46.9306 389.5 256 ClipEllips 71.1018 35.5509 -46.9306 368 279 ClipBox 14.222 88.4129 -0.111153 12.926 398.5 286 ClipEllips 34.5509 36.4294 -10.5774 368 279 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 359 248.5 ClipEllips 71.1018 35.5509 73.5596 350 218 ClipBox 14.7059 88.868 -0.095954 -46.302 371.5 195.5 ClipEllips 71.1018 35.5509 -46.302 350 218 ClipBox 13.9648 88.3897 -0.110749 13.815 380.5 225.5 ClipEllips 34.5509 36.839 -9.20896 350 218 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 341 188 ClipEllips 71.1018 35.5509 73.3008 332 158 ClipBox 13.911 88.8172 -0.0948565 -46.9306 353.5 135 ClipEllips 71.1018 35.5509 -46.9306 332 158 ClipBox 13.9648 88.3897 -0.110749 13.815 362.5 165.5 ClipEllips 34.5509 36.839 -9.20896 332 158 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 323 127.5 ClipEllips 71.1018 35.5509 73.5596 314 97 ClipBox 13.911 88.8172 -0.0948565 -46.9306 335.5 74 ClipEllips 71.1018 35.5509 -46.9306 314 97 ClipBox 13.9648 88.3897 -0.110749 13.815 344.5 104.5 ClipEllips 34.5509 36.839 -9.20896 314 97 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.1059 88.7582 -0.0938417 -46.273 364 362 ClipEllips 71.1018 35.5509 -46.273 342 385 ClipBox 12.8166 88.2724 -0.109082 13.6005 373 392.5 ClipEllips 34.5509 34.4967 -7.29559 342 385 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 333 354.5 ClipEllips 71.1018 35.5509 73.5596 324 324 ClipBox 13.9469 88.8196 -0.0949039 -45.6437 346 301.5 ClipEllips 71.1018 35.5509 -45.6437 324 324 ClipBox 12.8166 88.2724 -0.109082 13.6005 355 331.5 ClipEllips 34.5509 34.4967 -7.29559 324 324 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 315 294 ClipEllips 71.1018 35.5509 73.3008 306 264 ClipBox 13.1059 88.7582 -0.0938417 -46.273 328 241 ClipEllips 71.1018 35.5509 -46.273 306 264 ClipBox 12.8166 88.2724 -0.109082 13.6005 337 271.5 ClipEllips 34.5509 34.4967 -7.29559 306 264 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 297 234 ClipEllips 71.1018 35.5509 73.3008 288 204 ClipBox 13.1059 88.7582 -0.0938417 -46.273 310 181 ClipEllips 71.1018 35.5509 -46.273 288 204 ClipBox 13.0964 88.3032 -0.109469 12.7244 319 211 ClipEllips 34.5509 34.1374 -8.68865 288 204 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.8208 89.9673 -0.0157897 74.4275 279.5 173.5 ClipEllips 71.1018 35.5509 74.4275 271 143 ClipBox 13.911 88.8172 -0.0948565 -46.9306 292.5 120 ClipEllips 71.1018 35.5509 -46.9306 271 143 ClipBox 13.9648 88.3897 -0.110749 13.815 301.5 150.5 ClipEllips 34.5509 36.839 -9.20896 271 143 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.5005 89.9666 -0.0157212 73.5596 262 112.5 ClipEllips 71.1018 35.5509 73.5596 253 82 ClipBox 13.9648 88.3897 -0.110749 13.815 283.5 89.5 ClipEllips 34.5509 36.839 -9.20896 253 82 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.911 88.8172 -0.0948565 -46.9306 320.5 408 ClipEllips 34.5509 -23.7855 -70.0757 299 431 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 15.5005 89.2469 -0.0809617 -46.9749 285 286.5 ClipEllips 71.1018 35.5509 -46.9749 264 309 ClipBox 15.1167 88.8916 -0.0965609 14.0362 294 316.5 ClipEllips 34.5509 39.4235 -11.351 264 309 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 4 4 13.8298 90 -0 -105.573 272.5 339.5 ClipEllips 71.1018 35.5509 -105.573 281 370 ClipBox 13.5005 89.9666 -0.0157212 73.5596 290 400.5 ClipEllips 71.1018 35.5509 73.5596 281 370 ClipBox 13.911 88.8172 -0.0948565 -46.9306 302.5 347 ClipEllips 71.1018 35.5509 -46.9306 281 370 ClipBox 13.9648 88.3897 -0.110749 13.815 311.5 377.5 ClipEllips 34.5509 36.839 -9.20896 281 370 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 14.0095 89.1855 -0.0791559 -46.9306 249.5 166 ClipEllips 71.1018 35.5509 -46.9306 228 189 ClipBox 15.1167 88.8916 -0.0965609 14.0362 258 196.5 ClipEllips 34.5509 39.4235 -11.351 228 189 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 4 4 13.5098 90 -0 -106.44 237 219.5 ClipEllips 71.1018 35.5509 -106.44 246 250 ClipBox 15.5407 89.8804 -0.0324059 73.0339 255 279.5 ClipEllips 71.1018 35.5509 73.0339 246 250 ClipBox 14.6549 88.8649 -0.0958804 -47.6026 267 227 ClipEllips 71.1018 35.5509 -47.6026 246 250 ClipBox 15.2484 88.496 -0.112889 13.134 276 257 ClipEllips 34.5509 38.5632 -12.2952 246 250 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 219 158.5 ClipEllips 71.1018 35.5509 73.5596 210 128 ClipBox 14.0095 89.1855 -0.0791559 -46.9306 231.5 105 ClipEllips 71.1018 35.5509 -46.9306 210 128 ClipBox 14.0806 88.8286 -0.0950825 13.815 240.5 135.5 ClipEllips 34.5509 37.2739 -9.6438 210 128 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 14.7484 89.2179 -0.0800128 -47.6026 260 393 ClipEllips 71.1018 35.5509 -47.6026 239 416 ClipBox 15.1167 88.8916 -0.0965609 14.0362 269 423.5 ClipEllips 34.5509 39.4235 -11.351 239 416 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 230 385.5 ClipEllips 71.1018 35.5509 73.5596 221 355 ClipBox 15.1167 88.8916 -0.0965609 14.0362 251 362.5 ClipEllips 71.1018 35.5509 14.0362 221 355 ClipBox 13.911 88.8172 -0.0948565 -46.9306 242.5 332 ClipEllips 34.5509 -23.7855 -70.0757 221 355 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 212 324.5 ClipEllips 71.1018 35.5509 73.5596 203 294 ClipBox 15.5327 89.248 -0.0810042 -45.6585 224.5 272 ClipEllips 71.1018 35.5509 -45.6585 203 294 ClipBox 13.9648 88.3897 -0.110749 13.815 233.5 301.5 ClipEllips 34.5509 36.839 -9.20896 203 294 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 15.5649 89.9702 -0.0162094 73.0339 194 264.5 ClipEllips 71.1018 35.5509 73.0339 185 235 ClipBox 14.0806 88.8286 -0.0950825 13.815 215.5 242.5 ClipEllips 71.1018 35.5509 13.815 185 235 ClipBox 13.911 88.8172 -0.0948565 -46.9306 206.5 212 ClipEllips 34.5509 -23.7855 -70.0757 185 235 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 176 204.5 ClipEllips 71.1018 35.5509 73.5596 167 174 ClipBox 13.911 88.8172 -0.0948565 -46.9306 188.5 151 ClipEllips 71.1018 35.5509 -46.9306 167 174 ClipBox 13.9648 88.3897 -0.110749 13.815 197.5 181.5 ClipEllips 34.5509 36.839 -9.20896 167 174 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.911 88.8172 -0.0948565 -46.9306 199.5 378 ClipEllips 71.1018 35.5509 -46.9306 178 401 ClipBox 13.9648 88.3897 -0.110749 13.815 208.5 408.5 ClipEllips 34.5509 36.839 -9.20896 178 401 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 169 371 ClipEllips 71.1018 35.5509 73.3008 160 341 ClipBox 13.0486 88.7537 -0.0937729 -47.5448 181.5 317.5 ClipEllips 71.1018 35.5509 -47.5448 160 341 ClipBox 14.222 88.4129 -0.111153 12.926 190.5 348 ClipEllips 34.5509 36.4294 -10.5774 160 341 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 151 311 ClipEllips 71.1018 35.5509 73.3008 142 281 ClipBox 13.911 88.8172 -0.0948565 -46.9306 163.5 258 ClipEllips 71.1018 35.5509 -46.9306 142 281 ClipBox 14.4573 88.4333 -0.111533 12.0306 172.5 287.5 ClipEllips 34.5509 35.9737 -11.9125 142 281 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 133 250.5 ClipEllips 71.1018 35.5509 73.5596 124 220 ClipBox 13.911 88.8172 -0.0948565 -46.9306 145.5 197 ClipEllips 71.1018 35.5509 -46.9306 124 220 ClipBox 13.9648 88.3897 -0.110749 13.815 154.5 227.5 ClipEllips 34.5509 36.839 -9.20896 124 220 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.9469 88.8196 -0.0949039 -45.6437 138 363.5 ClipEllips 71.1018 35.5509 -45.6437 116 386 ClipBox 12.8166 88.2724 -0.109082 13.6005 147 393.5 ClipEllips 34.5509 34.4967 -7.29559 116 386 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 107 356 ClipEllips 71.1018 35.5509 73.3008 98 326 ClipBox 13.9469 88.8196 -0.0949039 -45.6437 120 303.5 ClipEllips 71.1018 35.5509 -45.6437 98 326 ClipBox 12.8166 88.2724 -0.109082 13.6005 129 333.5 ClipEllips 34.5509 34.4967 -7.29559 98 326 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.875 89.9691 -0.0160334 74.1808 89.5 296 ClipEllips 71.1018 35.5509 74.1808 81 266 ClipBox 13.911 88.8172 -0.0948565 -46.9306 102.5 243 ClipEllips 71.1018 35.5509 -46.9306 81 266 ClipBox 13.9648 88.3897 -0.110749 13.815 111.5 273.5 ClipEllips 34.5509 36.839 -9.20896 81 266 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.911 88.8172 -0.0948565 -46.9306 76.5 349 ClipEllips 71.1018 35.5509 -46.9306 55 372 ClipBox 14.222 88.4129 -0.111153 12.926 85.5 379 ClipEllips 34.5509 36.4294 -10.5774 55 372 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 46 341.5 ClipEllips 71.1018 35.5509 73.5596 37 311 ClipBox 13.9469 88.8196 -0.0949039 -45.6437 59 288.5 ClipEllips 71.1018 35.5509 -45.6437 37 311 ClipBox 13.9648 88.3897 -0.110749 13.815 67.5 318.5 ClipEllips 34.5509 36.839 -9.20896 37 311 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore 0.411765 0.411765 0.411765 34.5509 487 342 Sphere gsave %% 1 1 15.8434 89.9705 -0.0162844 73.9264 478.5 312.5 ClipEllips 34.5509 101.206 46.6473 470 283 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.5005 89.9666 -0.0157212 73.5596 461 252.5 ClipEllips 34.5509 96.5437 50.5755 452 222 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.5005 89.9666 -0.0157212 73.5596 443 191.5 ClipEllips 34.5509 96.5437 50.5755 434 161 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 14.5779 89.9686 -0.0159617 73.3008 425 131 ClipEllips 34.5509 98.2412 48.3603 416 101 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore 0.901961 0.901961 0.901961 18.4271 178 138 Sphere gsave %% 1 1 13.911 88.8172 -0.0948565 -46.9306 465.5 365 ClipEllips 34.5509 -23.7855 -70.0757 444 388 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 435 358 ClipEllips 71.1018 35.5509 73.3008 426 328 ClipBox 13.9469 88.8196 -0.0949039 -45.6437 448 305.5 ClipEllips 71.1018 35.5509 -45.6437 426 328 ClipBox 14.222 88.4129 -0.111153 12.926 456.5 335 ClipEllips 34.5509 36.4294 -10.5774 426 328 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 417 298 ClipEllips 71.1018 35.5509 73.3008 408 268 ClipBox 13.1059 88.7582 -0.0938417 -46.273 430 245 ClipEllips 71.1018 35.5509 -46.273 408 268 ClipBox 12.8166 88.2724 -0.109082 13.6005 439 275.5 ClipEllips 34.5509 34.4967 -7.29559 408 268 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 399 237.5 ClipEllips 71.1018 35.5509 73.5596 390 207 ClipBox 13.1059 88.7582 -0.0938417 -46.273 412 184 ClipEllips 71.1018 35.5509 -46.273 390 207 ClipBox 12.8166 88.2724 -0.109082 13.6005 421 214.5 ClipEllips 34.5509 34.4967 -7.29559 390 207 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 381 176.5 ClipEllips 71.1018 35.5509 73.5596 372 146 ClipBox 13.9469 88.8196 -0.0949039 -45.6437 394 123.5 ClipEllips 71.1018 35.5509 -45.6437 372 146 ClipBox 12.8166 88.2724 -0.109082 13.6005 403 153.5 ClipEllips 34.5509 34.4967 -7.29559 372 146 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.911 88.8172 -0.0948565 -46.9306 422.5 411 ClipEllips 34.5509 -23.7855 -70.0757 401 434 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 392 404 ClipEllips 71.1018 35.5509 73.3008 383 374 ClipBox 13.911 88.8172 -0.0948565 -46.9306 404.5 351 ClipEllips 71.1018 35.5509 -46.9306 383 374 ClipBox 14.222 88.4129 -0.111153 12.926 413.5 381 ClipEllips 34.5509 36.4294 -10.5774 383 374 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 374 343.5 ClipEllips 71.1018 35.5509 73.5596 365 313 ClipBox 14.7059 88.868 -0.095954 -46.302 386.5 290.5 ClipEllips 71.1018 35.5509 -46.302 365 313 ClipBox 13.9648 88.3897 -0.110749 13.815 395.5 320.5 ClipEllips 34.5509 36.839 -9.20896 365 313 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 356 283 ClipEllips 71.1018 35.5509 73.3008 347 253 ClipBox 13.911 88.8172 -0.0948565 -46.9306 368.5 230 ClipEllips 71.1018 35.5509 -46.9306 347 253 ClipBox 13.9648 88.3897 -0.110749 13.815 377.5 260.5 ClipEllips 34.5509 36.839 -9.20896 347 253 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 338 222.5 ClipEllips 71.1018 35.5509 73.5596 329 192 ClipBox 13.911 88.8172 -0.0948565 -46.9306 350.5 169 ClipEllips 71.1018 35.5509 -46.9306 329 192 ClipBox 13.9648 88.3897 -0.110749 13.815 359.5 199.5 ClipEllips 34.5509 36.839 -9.20896 329 192 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 14.5779 89.9686 -0.0159617 73.3008 320 162 ClipEllips 71.1018 35.5509 73.3008 311 132 ClipBox 14.222 88.4129 -0.111153 12.926 341.5 139 ClipEllips 34.5509 36.4294 -10.5774 311 132 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.911 88.8172 -0.0948565 -46.9306 379.5 457 ClipEllips 34.5509 -23.7855 -70.0757 358 480 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 349 449.5 ClipEllips 71.1018 35.5509 73.5596 340 419 ClipBox 14.7059 88.868 -0.095954 -46.302 361.5 396.5 ClipEllips 71.1018 35.5509 -46.302 340 419 ClipBox 13.9648 88.3897 -0.110749 13.815 370.5 426.5 ClipEllips 34.5509 36.839 -9.20896 340 419 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 331 389 ClipEllips 71.1018 35.5509 73.3008 322 359 ClipBox 13.911 88.8172 -0.0948565 -46.9306 343.5 336 ClipEllips 71.1018 35.5509 -46.9306 322 359 ClipBox 13.9648 88.3897 -0.110749 13.815 352.5 366.5 ClipEllips 34.5509 36.839 -9.20896 322 359 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 313 328.5 ClipEllips 71.1018 35.5509 73.5596 304 298 ClipBox 14.7059 88.868 -0.095954 -46.302 325.5 275.5 ClipEllips 71.1018 35.5509 -46.302 304 298 ClipBox 13.9648 88.3897 -0.110749 13.815 334.5 305.5 ClipEllips 34.5509 36.839 -9.20896 304 298 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 14.7484 89.2179 -0.0800128 -47.6026 290 155 ClipEllips 71.1018 35.5509 -47.6026 269 178 ClipBox 15.3546 88.9046 -0.0969256 13.134 299 185 ClipEllips 34.5509 38.9676 -12.6996 269 178 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 4 4 14.8834 90 -0 -105.819 277.5 208 ClipEllips 71.1018 35.5509 -105.819 286 238 ClipBox 14.5779 89.9686 -0.0159617 73.3008 295 268 ClipEllips 71.1018 35.5509 73.3008 286 238 ClipBox 13.911 88.8172 -0.0948565 -46.9306 307.5 215 ClipEllips 71.1018 35.5509 -46.9306 286 238 ClipBox 13.9648 88.3897 -0.110749 13.815 316.5 245.5 ClipEllips 34.5509 36.839 -9.20896 286 238 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 14.0095 89.1855 -0.0791559 -46.9306 318.5 442 ClipEllips 71.1018 35.5509 -46.9306 297 465 ClipBox 14.0806 88.8286 -0.0950825 13.815 327.5 472.5 ClipEllips 34.5509 37.2739 -9.6438 297 465 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.875 89.9691 -0.0160334 74.1808 288.5 435 ClipEllips 71.1018 35.5509 74.1808 280 405 ClipBox 14.7484 89.2179 -0.0800128 -47.6026 301 382 ClipEllips 71.1018 35.5509 -47.6026 280 405 ClipBox 15.3546 88.9046 -0.0969256 13.134 310 412 ClipEllips 34.5509 38.9676 -12.6996 280 405 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 271 374.5 ClipEllips 71.1018 35.5509 73.5596 262 344 ClipBox 14.7484 89.2179 -0.0800128 -47.6026 283 321 ClipEllips 71.1018 35.5509 -47.6026 262 344 ClipBox 15.1167 88.8916 -0.0965609 14.0362 292 351.5 ClipEllips 34.5509 39.4235 -11.351 262 344 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 15.4439 89.2448 -0.0808875 13.134 256 231 ClipEllips 71.1018 35.5509 13.134 226 224 ClipBox 14.0095 89.1855 -0.0791559 -46.9306 247.5 201 ClipEllips 34.5509 -23.4197 -70.4415 226 224 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 4 4 14.5865 90 -0 -106.699 235 254 ClipEllips 71.1018 35.5509 -106.699 244 284 ClipBox 14.5779 89.9686 -0.0159617 73.3008 253 314 ClipEllips 71.1018 35.5509 73.3008 244 284 ClipBox 14.7484 89.2179 -0.0800128 -47.6026 265 261 ClipEllips 71.1018 35.5509 -47.6026 244 284 ClipBox 15.3546 88.9046 -0.0969256 13.134 274 291 ClipEllips 34.5509 38.9676 -12.6996 244 284 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.5005 89.9666 -0.0157212 73.5596 217 193.5 ClipEllips 71.1018 35.5509 73.5596 208 163 ClipBox 14.0806 88.8286 -0.0950825 13.815 238.5 170.5 ClipEllips 34.5509 37.2739 -9.6438 208 163 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.2104 89.1457 -0.0783068 -46.273 258 428 ClipEllips 71.1018 35.5509 -46.273 236 451 ClipBox 14.3358 88.8452 -0.0954306 12.926 266.5 458 ClipEllips 34.5509 36.8576 -11.0056 236 451 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 227 420.5 ClipEllips 71.1018 35.5509 73.5596 218 390 ClipBox 13.2104 89.1457 -0.0783068 -46.273 240 367 ClipEllips 71.1018 35.5509 -46.273 218 390 ClipBox 12.9427 88.7452 -0.0936472 13.6005 249 397.5 ClipEllips 34.5509 34.9654 -7.76434 218 390 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 209 359.5 ClipEllips 71.1018 35.5509 73.5596 200 329 ClipBox 14.0451 89.1872 -0.0791957 -45.6437 222 306.5 ClipEllips 71.1018 35.5509 -45.6437 200 329 ClipBox 12.9427 88.7452 -0.0936472 13.6005 231 336.5 ClipEllips 34.5509 34.9654 -7.76434 200 329 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 15.5649 89.9702 -0.0162094 73.0339 191 299.5 ClipEllips 71.1018 35.5509 73.0339 182 270 ClipBox 13.2199 88.7671 -0.0939797 12.7244 213 277 ClipEllips 71.1018 35.5509 12.7244 182 270 ClipBox 13.1059 88.7582 -0.0938417 -46.273 204 247 ClipEllips 34.5509 -24.6092 -67.9368 182 270 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 173 239.5 ClipEllips 71.1018 35.5509 73.5596 164 209 ClipBox 13.1059 88.7582 -0.0938417 -46.273 186 186 ClipEllips 71.1018 35.5509 -46.273 164 209 ClipBox 12.8166 88.2724 -0.109082 13.6005 195 216.5 ClipEllips 34.5509 34.4967 -7.29559 164 209 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.911 88.8172 -0.0948565 -46.9306 196.5 413 ClipEllips 71.1018 35.5509 -46.9306 175 436 ClipBox 13.9648 88.3897 -0.110749 13.815 205.5 443.5 ClipEllips 34.5509 36.839 -9.20896 175 436 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 166 405.5 ClipEllips 71.1018 35.5509 73.5596 157 375 ClipBox 13.911 88.8172 -0.0948565 -46.9306 178.5 352 ClipEllips 71.1018 35.5509 -46.9306 157 375 ClipBox 13.9648 88.3897 -0.110749 13.815 187.5 382.5 ClipEllips 34.5509 36.839 -9.20896 157 375 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 148 344.5 ClipEllips 71.1018 35.5509 73.5596 139 314 ClipBox 15.4439 88.9093 -0.097065 -45.6585 160.5 292 ClipEllips 71.1018 35.5509 -45.6585 139 314 ClipBox 13.9648 88.3897 -0.110749 13.815 169.5 321.5 ClipEllips 34.5509 36.839 -9.20896 139 314 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 15.5649 89.9702 -0.0162094 73.0339 130 284.5 ClipEllips 71.1018 35.5509 73.0339 121 255 ClipBox 13.911 88.8172 -0.0948565 -46.9306 142.5 232 ClipEllips 71.1018 35.5509 -46.9306 121 255 ClipBox 13.9648 88.3897 -0.110749 13.815 151.5 262.5 ClipEllips 34.5509 36.839 -9.20896 121 255 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.5005 89.9666 -0.0157212 73.5596 112 224.5 ClipEllips 71.1018 35.5509 73.5596 103 194 ClipBox 13.9648 88.3897 -0.110749 13.815 133.5 201.5 ClipEllips 34.5509 36.839 -9.20896 103 194 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.911 88.8172 -0.0948565 -46.9306 135.5 398 ClipEllips 71.1018 35.5509 -46.9306 114 421 ClipBox 13.9648 88.3897 -0.110749 13.815 144.5 428.5 ClipEllips 34.5509 36.839 -9.20896 114 421 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 105 390.5 ClipEllips 71.1018 35.5509 73.5596 96 360 ClipBox 13.911 88.8172 -0.0948565 -46.9306 117.5 337 ClipEllips 71.1018 35.5509 -46.9306 96 360 ClipBox 13.9648 88.3897 -0.110749 13.815 126.5 367.5 ClipEllips 34.5509 36.839 -9.20896 96 360 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 87 330 ClipEllips 71.1018 35.5509 73.3008 78 300 ClipBox 14.7059 88.868 -0.095954 -46.302 99.5 277.5 ClipEllips 71.1018 35.5509 -46.302 78 300 ClipBox 14.222 88.4129 -0.111153 12.926 108.5 307 ClipEllips 34.5509 36.4294 -10.5774 78 300 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 69 270 ClipEllips 71.1018 35.5509 73.3008 60 240 ClipBox 13.911 88.8172 -0.0948565 -46.9306 81.5 217 ClipEllips 71.1018 35.5509 -46.9306 60 240 ClipBox 13.9648 88.3897 -0.110749 13.815 90.5 247.5 ClipEllips 34.5509 36.839 -9.20896 60 240 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore 0.411765 0.411765 0.411765 34.5509 510 271 Sphere gsave %% 1 1 14.5779 89.9686 -0.0159617 73.3008 501 241 ClipEllips 34.5509 98.2412 48.3603 492 211 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.5005 89.9666 -0.0157212 73.5596 483 180.5 ClipEllips 34.5509 96.5437 50.5755 474 150 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore 0.901961 0.901961 0.901961 18.4271 237 188 Sphere gsave %% 1 1 14.7991 89.2199 -0.0800743 -46.302 488.5 293.5 ClipEllips 34.5509 -21.3326 -71.2713 467 316 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 15.5649 89.9702 -0.0162094 73.0339 458 286.5 ClipEllips 71.1018 35.5509 73.0339 449 257 ClipBox 14.0095 89.1855 -0.0791559 -46.9306 470.5 234 ClipEllips 71.1018 35.5509 -46.9306 449 257 ClipBox 14.3358 88.8452 -0.0954306 12.926 479.5 264 ClipEllips 34.5509 36.8576 -11.0056 449 257 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 440 226.5 ClipEllips 71.1018 35.5509 73.5596 431 196 ClipBox 14.0095 89.1855 -0.0791559 -46.9306 452.5 173 ClipEllips 71.1018 35.5509 -46.9306 431 196 ClipBox 14.0806 88.8286 -0.0950825 13.815 461.5 203.5 ClipEllips 34.5509 37.2739 -9.6438 431 196 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.911 88.8172 -0.0948565 -46.9306 445.5 339 ClipEllips 34.5509 -23.7855 -70.0757 424 362 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 415 331.5 ClipEllips 71.1018 35.5509 73.5596 406 301 ClipBox 15.4439 88.9093 -0.097065 -45.6585 427.5 279 ClipEllips 71.1018 35.5509 -45.6585 406 301 ClipBox 13.9648 88.3897 -0.110749 13.815 436.5 308.5 ClipEllips 34.5509 36.839 -9.20896 406 301 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 15.5649 89.9702 -0.0162094 73.0339 397 271.5 ClipEllips 71.1018 35.5509 73.0339 388 242 ClipBox 13.911 88.8172 -0.0948565 -46.9306 409.5 219 ClipEllips 71.1018 35.5509 -46.9306 388 242 ClipBox 13.9648 88.3897 -0.110749 13.815 418.5 249.5 ClipEllips 34.5509 36.839 -9.20896 388 242 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.5005 89.9666 -0.0157212 73.5596 379 211.5 ClipEllips 71.1018 35.5509 73.5596 370 181 ClipBox 13.9648 88.3897 -0.110749 13.815 400.5 188.5 ClipEllips 34.5509 36.839 -9.20896 370 181 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.911 88.8172 -0.0948565 -46.9306 402.5 385 ClipEllips 34.5509 -23.7855 -70.0757 381 408 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.1535 89.9659 -0.0156499 72.6995 371.5 377.5 ClipEllips 71.1018 35.5509 72.6995 362 347 ClipBox 13.1059 88.7582 -0.0938417 -46.273 384 324 ClipEllips 71.1018 35.5509 -46.273 362 347 ClipBox 12.8166 88.2724 -0.109082 13.6005 393 354.5 ClipEllips 34.5509 34.4967 -7.29559 362 347 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.875 89.9691 -0.0160334 74.1808 353.5 317 ClipEllips 71.1018 35.5509 74.1808 345 287 ClipBox 14.7059 88.868 -0.095954 -46.302 366.5 264.5 ClipEllips 71.1018 35.5509 -46.302 345 287 ClipBox 14.222 88.4129 -0.111153 12.926 375.5 294 ClipEllips 34.5509 36.4294 -10.5774 345 287 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 336 257 ClipEllips 71.1018 35.5509 73.3008 327 227 ClipBox 13.911 88.8172 -0.0948565 -46.9306 348.5 204 ClipEllips 71.1018 35.5509 -46.9306 327 227 ClipBox 13.9648 88.3897 -0.110749 13.815 357.5 234.5 ClipEllips 34.5509 36.839 -9.20896 327 227 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 1 1 13.1059 88.7582 -0.0938417 -46.273 359 431 ClipEllips 34.5509 -24.6092 -67.9368 337 454 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 13.5005 89.9666 -0.0157212 73.5596 328 423.5 ClipEllips 71.1018 35.5509 73.5596 319 393 ClipBox 13.911 88.8172 -0.0948565 -46.9306 340.5 370 ClipEllips 71.1018 35.5509 -46.9306 319 393 ClipBox 12.8166 88.2724 -0.109082 13.6005 350 400.5 ClipEllips 34.5509 34.4967 -7.29559 319 393 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 310 363 ClipEllips 71.1018 35.5509 73.3008 301 333 ClipBox 13.1059 88.7582 -0.0938417 -46.273 323 310 ClipEllips 71.1018 35.5509 -46.273 301 333 ClipBox 14.222 88.4129 -0.111153 12.926 331.5 340 ClipEllips 34.5509 36.4294 -10.5774 301 333 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 3 3 14.5779 89.9686 -0.0159617 73.3008 292 303 ClipEllips 71.1018 35.5509 73.3008 283 273 ClipBox 13.1059 88.7582 -0.0938417 -46.273 305 250 ClipEllips 71.1018 35.5509 -46.273 283 273 ClipBox 13.0964 88.3032 -0.109469 12.7244 314 280 ClipEllips 34.5509 34.1374 -8.68865 283 273 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 13.8208 89.9673 -0.0157897 74.4275 274.5 242.5 ClipEllips 71.1018 35.5509 74.4275 266 212 ClipBox 13.9648 88.3897 -0.110749 13.815 296.5 219.5 ClipEllips 34.5509 36.839 -9.20896 266 212 ClipSphere 0.411765 0.411765 0.411765 34.5509 Shade grestore gsave %% 2 2 14.7484 89.2179 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y(these)k(states)f([6])g(so)g(that)h(their)g(in\015uence)g(on) f(surface)g(pro)r(cesses)f(is)h(often)h(limited.)290 2076 y(On)21 b(the)g(other)g(hand,)g(there)g(are)f(v)n(ery)g(in)n (teresting)g(pro)r(cesses)g(in)h(whic)n(h)g(electronic)165 2175 y(nonadiabatic)31 b(pro)r(cesses)g(are)g(induced,)h(as)g(w)n(e)f (will)i(see)e(in)i(Chap.)13 b(9.)32 b(The)g(theoret-)165 2275 y(ical)f(treatmen)n(t)f(of)h(these)f(systems)g(requires)g(sp)r (ecial)g(tec)n(hniques)g(that)h(will)g(also)f(b)r(e)165 2374 y(discussed)d(later)g(in)h(this)g(b)r(o)r(ok.)165 2683 y Fy(2.3)42 b(Structure)37 b(of)h(the)f(Hamiltonian)165 2871 y FE(Emplo)n(ying)e(the)i(Born{Opp)r(enheimer)e(appro)n(ximation)f (means)i(\014rst)g(to)h(solv)n(e)e(the)165 2970 y(electronic)i (structure)f(problem)h(for)g(\014xed)g(atomic)g(co)r(ordinates.)f(The)h (atomic)g(p)r(o-)165 3070 y(sitions)32 b(determine)g(the)g(external)g (electrostatic)f(p)r(oten)n(tial)h(in)g(whic)n(h)g(the)g(electrons)165 3169 y(mo)n(v)n(e.)f(F)-7 b(urthermore,)32 b(they)g(determine)g(the)h (symmetry)e(prop)r(erties)h(of)g(the)g(Hamil-)165 3269 y(tonian.)290 3369 y(Surface)25 b(science)g(studies)h(are)f(concerned)g (with)h(the)g(structure)f(and)h(dynamics)f(of)165 3468 y(surfaces)f(and)g(the)h(in)n(teraction)e(of)i(atoms)f(and)g(molecules) g(with)h(surfaces.)e(If)i(not)g(just)165 3568 y(ordered)i(surface)g (structures)f(are)h(considered,)g(then)h(the)g(theoretical)f(surface)g (scien-)165 3668 y(tists)32 b(has)e(to)i(deal)e(with)i(a)f(system)g (with)h(only)f(few)g(degrees)f(of)h(freedom,)g(the)h(atom)165 3767 y(or)24 b(molecule,)h(in)n(teracting)f(with)h(a)f(system,)h(the)g (surface)f(or)g(semi-in\014nite)h(substrate,)165 3867 y(that)h(has)f(in)h(principle)f(an)h(in\014nite)g(n)n(um)n(b)r(er)f(of) h(degrees)e(of)h(freedom.)g(Th)n(us)h(the)f(sub-)165 3966 y(strate)i(exhibits)h(a)f(quasi-con)n(tin)n(uum)g(of)g(states.)g (One)h(faces)f(no)n(w)g(the)h(problem)f(that)165 4066 y(usually)h(di\013eren)n(t)h(metho)r(ds)f(are)g(used)g(to)g(treat)g 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(electronic)h(structure)f(metho)r(ds)h(for)f(the)h(determi-)165 1378 y(nation)32 b(of)f(total)g(energies)g(of)g(surface)g(systems.)g (The)h(ev)-5 b(aluation)31 b(of)g(total)g(energies)165 1478 y(is)k(a)e(prerequisite)h(for)g(the)g(theoretical)g(treatmen)n(t)g (of)g(man)n(y)g(prop)r(erties)f(and)h(pro-)165 1577 y(cesses)18 b(at)h(surfaces.)f(There)h(are)f(t)n(w)n(o)g(main)h(tec)n(hniques,)g(w) n(a)n(v)n(e-function)e(and)i(electron-)165 1677 y(densit)n(y)h(based)f (metho)r(ds)h(that)g(originate)e(from)h(quan)n(tum)h(c)n(hemistry)f (and)g(solid-state)165 1777 y(ph)n(ysics,)j(resp)r(ectiv)n(ely)-7 b(.)22 b(Both)g(t)n(yp)r(es)h(of)f(metho)r(ds)h(will)g(b)r(e)g(in)n (tro)r(duced)f(and)h(discussed)165 1876 y(in)31 b(some)f(detail.)h(Sp)r (ecial)g(atten)n(tion)f(will)h(b)r(e)g(paid)f(to)h(the)g(discussion)e (of)i(electronic)165 1976 y(exc)n(hange)c(and)g(correlation)f (e\013ects.)290 2076 y(Electronic)33 b(structure)g(calculations)g(for)h (surface)f(science)g(problems)h(are)f(domi-)165 2175 y(nated)e(b)n(y)g(densit)n(y)g(functional)g(theory)f(\(DFT\))i(metho)r (ds.)g(Therefore)e(w)n(e)g(will)h(ha)n(v)n(e)165 2275 y(a)j(closer)e(lo)r(ok)h(at)g(some)g(sp)r(eci\014c)h(implemen)n (tations)f(of)h(electronic)f(structure)g(algo-)165 2374 y(rithms)28 b(based)f(on)h(DFT.)g(This)g(c)n(hapter)f(will)g(b)r(e)i (concluded)e(b)n(y)h(an)f(in)n(tro)r(duction)g(to)165 2474 y(the)j(tigh)n(t-binding)g(metho)r(d)g(whic)n(h)f(is)h(w)n (ell-suited)f(for)g(a)g(qualitativ)n(e)g(discussion)f(of)165 2574 y(band)g(structure)f(e\013ects.)165 2887 y Fy(3.1)42 b(Hartree{F)-9 b(o)s(c)m(k)37 b(Theory)165 3080 y FE(W)-7 b(e)31 b(start)e(the)i(sections)e(ab)r(out)h(electronic)g(structure)f (metho)r(ds)i(with)f(the)h(so-called)165 3180 y(Hartree)e(and)g (Hartree-F)-7 b(o)r(c)n(k)28 b(metho)r(ds.)i(This)g(do)r(es)f(not)g (only)h(follo)n(w)e(the)i(historical)165 3279 y(dev)n(elopmen)n(t)25 b([15,)9 b(16],)24 b(but)i(it)g(also)e(allo)n(ws)g(to)h(in)n(tro)r (duce)g(imp)r(ortan)n(t)h(concepts)f(suc)n(h)165 3379 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b(the)h(n)n(um)n(b)r (er)f(of)g(electrons)g(in)g(the)h(system,)f(then)h(w)n(e)f(ha)n(v)n(e)f (to)i(deal)165 482 y(with)e(a)f(partial)g(di\013eren)n(tial)g(equation) g(in)h(3)p FA(N)31 b FE(unkno)n(wns)23 b(with)h FA(N)32 b FE(commonly)23 b(larger)165 581 y(than)30 b(100.)e(This)i(is)g (completely)f(in)n(tractable)g(to)g(solv)n(e.)g(The)g(w)n(a)n(y)g(out)g (is)h(to)g(expand)165 681 y(the)e(electronic)f(w)n(a)n(v)n(e)e (function)j(in)g(some)f(suitable,)g(but)h(necessarily)e(\014nite)i (basis)e(set)165 780 y(whose)33 b(matrix)g(elemen)n(ts)g(deriv)n(ed)g (from)g(\(3.1\))g(can)g(b)r(e)h(con)n(v)n(enien)n(tly)e(determined.)165 880 y(This)27 b(will)f(then)h(con)n(v)n(ert)e(the)i(partial)e (di\013eren)n(tial)h(equation)g(in)n(to)g(a)g(set)h(of)f(algebraic)165 980 y(equations)35 b(that)g(are)f(m)n(uc)n(h)h(easier)f(to)h(handle.)g (Of)g(course,)f(w)n(e)h(ha)n(v)n(e)f(to)h(b)r(e)g(a)n(w)n(are)165 1079 y(that)e(b)n(y)f(using)g(a)g(\014nite)h(basis)f(set)h(w)n(e)f 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b({)g(that)g(pro)n(vides)f(a)h(route)g(to)165 1976 y(\014nd)j(appro)n(ximativ)n(e)d(solutions)h(for)g(the)i(ground)e (state)h(energy)-7 b(.)31 b(It)h(states)g(that)g(the)165 2076 y(exp)r(ectation)f(v)-5 b(alue)30 b(of)h(the)g(Hamiltonian)f(in)h (an)n(y)f(state)g Fs(j)p FA(\011)9 b Fs(i)31 b FE(is)g(alw)n(a)n(ys)d (larger)h(than)165 2175 y(or)e(equal)g(to)h(the)g(ground)e(state)i (energy)e FA(E)1542 2187 y Fx(0)1580 2175 y FE(,)h(i.e.)313 2366 y FA(E)374 2378 y Fx(0)435 2366 y Fs(\024)532 2309 y(h)p FA(\011)9 b Fs(j)p FA(H)e Fs(j)p FA(\011)i Fs(i)p 532 2346 307 4 v 582 2423 a(h)p FA(\011)g Fs(j)p FA(\011)g Fs(i)862 2366 y FA(:)1873 b FE(\(3.2\))165 2561 y(Hence)41 b(w)n(e)f(can)g(just)h(pic)n(k)f(some)g(suitable)g(guess)g(for)g Fs(j)p FA(\011)9 b Fs(i)p FE(.)41 b(Then)f(w)n(e)g(kno)n(w)g(that)165 2661 y Fs(h)p FA(\011)9 b Fs(j)p FA(H)e Fs(j)p FA(\011)i Fs(i)p FA(=)p Fs(h)p FA(\011)g Fs(j)p FA(\011)g Fs(i)41 b FE(will)f(alw)n(a)n(ys)d(b)r(e)j(an)g(upp)r(er)g(b)r(ound)g(for)f (the)h(true)g(ground)e(state)165 2761 y(energy)-7 b(.)26 b(By)h(impro)n(ving)f(our)g(guesses)g(for)g Fs(j)p FA(\011)9 b Fs(i)p FE(,)28 b(preferen)n(tially)e(in)h(a)g(systematic)f(w)n(a)n(y) -7 b(,)165 2860 y(w)n(e)28 b(will)f(come)h(closer)e(to)h(the)h(true)g (ground)e(state)i(energy)-7 b(.)290 2960 y(Before)27 b(w)n(e)h(pro)r(ceed,)f(w)n(e)h(note)f(that)i(the)f(p)r(oten)n(tial)g (term)g FA(V)2232 2972 y Fx(n)n(ucl)p Fw(\000)p Fx(el)2485 2960 y FE(\(2.5\))f(acts)h(as)165 3060 y(an)e(e\013ectiv)n(e)g (external)f(one-particle)g(p)r(oten)n(tial)h(for)f(the)h(electrons.)f (Hence)h(w)n(e)g(de\014ne)165 3159 y(the)i(external)f(p)r(oten)n(tial)h (for)f(the)h(electrons)e(as)313 3355 y FA(v)353 3367 y Fv(ext)452 3355 y FE(\()p Ft(r)r FE(\))e(=)e Fs(\000)752 3276 y Fu(X)800 3454 y Fx(I)963 3299 y FA(Z)1020 3311 y Fx(I)1047 3299 y FA(e)1086 3269 y Fx(2)p 896 3336 296 4 v 896 3412 a Fs(j)p Ft(r)f Fs(\000)d Ft(R)1139 3424 y Fx(I)1167 3412 y Fs(j)1214 3355 y FA(:)1521 b FE(\(3.3\))165 3576 y(No)n(w)38 b(let)h(us)g(assume)f(that)h(the)g(n)n(um)n(b)r(er)f (of)h(electrons)e(in)i(our)f(system)g(is)h FA(N)47 b FE(and)165 3676 y(that)40 b(w)n(e)f(ha)n(v)n(e)f(already)g(determined)i (the)g FA(N)48 b FE(lo)n(w)n(est)39 b(eigenfunctions)g Fs(j)p FA( )2608 3688 y Fv(i)2636 3676 y Fs(i)g FE(of)h(the)165 3775 y(one-particle)27 b(Sc)n(hr\177)-42 b(odinger)25 b(equation)313 3861 y Fu(\032)375 3978 y Fs(\000)464 3922 y FE(\026)-42 b FA(h)512 3885 y Fx(2)p 450 3959 115 4 v 450 4035 a FE(2)p FA(m)574 3978 y Fs(r)643 3944 y Fx(2)699 3978 y FE(+)18 b FA(v)822 3990 y Fv(ext)921 3978 y FE(\()p Ft(r)r FE(\))1031 3861 y Fu(\033)1108 3978 y FA( )1162 3990 y Fv(i)1190 3978 y FE(\()p Ft(r)r FE(\))24 b(=)e FA(")1450 3944 y Fv(o)1450 3998 y(i)1487 3978 y FA( )1541 3990 y Fv(i)1569 3978 y FE(\()p Ft(r)s FE(\))14 b FA(:)1041 b FE(\(3.4\))165 4170 y(Here)24 b(w)n(e)g(ha)n(v)n(e)f(completely)g(neglected)h(the)h (electron-electron)d(in)n(teraction.)h(Still,)i(w)n(e)165 4270 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y(Th)n(us)28 b(w)n(e)f(obtain)313 592 y Fs(h)p FA(\011)396 604 y Fx(H)449 592 y Fs(j)p FA(H)7 b Fs(j)p FA(\011)622 604 y Fx(H)675 592 y Fs(i)23 b FE(=)849 488 y Fv(N)818 513 y Fu(X)824 690 y Fv(i)p Fx(=1)952 479 y Fu(Z)1049 592 y FA(d)1092 558 y Fx(3)1129 592 y FA(r)r( )1225 558 y Fw(\003)1222 612 y Fv(i)1264 592 y FE(\()p Ft(r)s FE(\))1389 475 y Fu(\022)1450 592 y Fs(\000)1539 536 y FE(\026)-42 b FA(h)1587 499 y Fx(2)p 1525 573 115 4 v 1525 649 a FE(2)p FA(m)1649 592 y Fs(r)1718 558 y Fx(2)1774 592 y FE(+)18 b FA(v)1897 604 y Fv(ext)1996 592 y FE(\()p Ft(r)r FE(\))2106 475 y Fu(\023)2182 592 y FA( )2236 604 y Fv(i)2263 592 y FE(\()p Ft(r)s FE(\))363 930 y(+)438 874 y(1)p 438 911 42 4 v 438 987 a(2)552 827 y Fv(N)522 851 y Fu(X)503 1028 y Fv(i;j)s Fx(=1)675 817 y Fu(Z)771 930 y FA(d)814 896 y Fx(3)852 930 y FA(r)r(d)934 896 y Fx(3)972 930 y FA(r)1011 896 y Fw(0)1139 874 y FA(e)1178 844 y Fx(2)p 1045 911 264 4 v 1045 987 a Fs(j)p Ft(r)j Fs(\000)d Ft(r)1263 963 y Fw(0)1286 987 y Fs(j)1319 930 y(j)p FA( )1396 942 y Fv(i)1424 930 y FE(\()p Ft(r)s FE(\))p Fs(j)1558 896 y Fx(2)1595 930 y Fs(j)p FA( )1672 942 y Fv(j)1707 930 y FE(\()p Ft(r)1786 896 y Fw(0)1809 930 y FE(\))p Fs(j)1864 896 y Fx(2)1921 930 y FE(+)g FA(V)2052 942 y Fx(n)n(ucl)p Fw(\000)p Fx(n)n(ucl)2362 930 y FA(:)373 b FE(\(3.6\))165 1168 y(No)n(w)32 b(w)n(e)f(w)n(ould)h (lik)n(e)f(to)h(minimize)g(the)g(exp)r(ectation)g(v)-5 b(alue)32 b(\(3.6\))f(with)i(resp)r(ect)e(to)165 1268 y(more)k(suitable)h(single-particle)e(functions)i FA( )1658 1280 y Fv(i)1686 1268 y FE(\()p Ft(r)s FE(\))g(under)f(the)h(constrain) n(t)f(that)h(the)165 1368 y(w)n(a)n(v)n(e)23 b(functions)h(are)f (normalized.)h(This)g(is)g(a)f(t)n(ypical)h(v)-5 b(ariational)23 b(problem)g(with)i(the)165 1467 y(constrain)n(t)36 b(tak)n(en)h(in)n (to)f(accoun)n(t)h(via)f(Lagrange)f(m)n(ultipliers.)i(If)g(w)n(e)g (consider)f(the)165 1567 y(w)n(a)n(v)n(e)26 b(functions)j FA( )781 1579 y Fv(i)808 1567 y FE(\()p Ft(r)s FE(\))f(and)g FA( )1166 1537 y Fw(\003)1163 1588 y Fv(i)1204 1567 y FE(\()p Ft(r)s FE(\))g(as)f(indep)r(enden)n(t,)i(w)n(e)e(can)h (minimize)g(\(3.6\))g(with)165 1666 y(resp)r(ect)g(to)f(the)h FA( )751 1636 y Fw(\003)748 1688 y Fv(i)817 1666 y FE(under)g(the)g (constrain)n(t)e(of)h(normalization)g(via)371 1842 y FA(\016)p 323 1879 136 4 v 323 1955 a(\016)s( )420 1926 y Fw(\003)417 1978 y Fv(i)482 1756 y Fu(")530 1898 y Fs(h)p FA(\011)613 1910 y Fx(H)667 1898 y Fs(j)p FA(H)7 b Fs(j)p FA(\011)840 1910 y Fx(H)893 1898 y Fs(i)18 b(\000)1057 1794 y Fv(N)1026 1819 y Fu(X)1032 1996 y Fv(i)p Fx(=1)1146 1898 y Fs(f)p FA(")1227 1910 y Fv(i)1254 1898 y FE(\(1)g Fs(\000)g(h)p FA( )1515 1910 y Fv(i)1543 1898 y Fs(j)p FA( )1620 1910 y Fv(i)1648 1898 y Fs(i)p FE(\))p Fs(g)1754 1756 y Fu(#)1826 1898 y FE(=)k(0)14 b FA(:)766 b FE(\(3.7\))165 2120 y(The)31 b FA(")378 2132 y Fv(i)436 2120 y FE(act)f(as)g(Lagrange) e(m)n(ultipliers)j(ensuring)f(the)g(normalization)f(of)i(the)g(eigen-) 165 2220 y(functions.)d(This)g(minimization)g(leads)f(to)g(the)h (so-called)e FD(Hartr)l(e)l(e)k(e)l(quations)k FE([15]:)313 2298 y Fu(8)313 2373 y(<)313 2523 y(:)387 2469 y Fs(\000)476 2412 y FE(\026)-42 b FA(h)524 2375 y Fx(2)p 461 2450 115 4 v 461 2526 a FE(2)p FA(m)586 2469 y Fs(r)655 2434 y Fx(2)711 2469 y FE(+)18 b FA(v)834 2481 y Fv(ext)932 2469 y FE(\()p Ft(r)s FE(\))h(+)1175 2365 y Fv(N)1145 2390 y Fu(X)1147 2567 y Fv(j)s Fx(=1)1279 2356 y Fu(Z)1375 2469 y FA(d)1418 2434 y Fx(3)1456 2469 y FA(r)1495 2434 y Fw(0)1623 2412 y FA(e)1662 2382 y Fx(2)p 1529 2450 264 4 v 1529 2526 a Fs(j)p Ft(r)i Fs(\000)d Ft(r)1746 2502 y Fw(0)1770 2526 y Fs(j)1803 2469 y(j)p FA( )1880 2481 y Fv(j)1915 2469 y FE(\()p Ft(r)1994 2434 y Fw(0)2017 2469 y FE(\))p Fs(j)2072 2434 y Fx(2)2110 2298 y Fu(9)2110 2373 y(=)2110 2523 y(;)2197 2469 y FA( )2251 2481 y Fv(i)2279 2469 y FE(\()p Ft(r)s FE(\))25 b(=)f FA(")2543 2481 y Fv(i)2571 2469 y FA( )2625 2481 y Fv(i)2653 2469 y FE(\()p Ft(r)r FE(\))15 b FA(:)2758 2693 y FE(\(3.8\))165 2842 y(The)44 b(Hartree)f(equations)h(corresp)r(ond)e(to)i(a)g(mean-\014eld) f(appro)n(ximation.)g(Equa-)165 2942 y(tion)27 b(\(3.8\))f(sho)n(ws)g (that)g(an)h(e\013ectiv)n(e)f(one-particle)f(Sc)n(hr\177)-42 b(odinger)25 b(equation)h(is)g(solv)n(ed)165 3041 y(for)32 b(an)f(electron)g(em)n(b)r(edded)h(in)g(the)g(electrostatic)f(\014eld)h (of)f FD(al)t(l)k(ele)l(ctr)l(ons)e(including)165 3141 y(the)e(p)l(articular)g(ele)l(ctr)l(on)g(itself)p FE(.)e(This)f(causes) f(the)i(so-called)e FD(self)k(inter)l(action)k FE(whic)n(h)165 3241 y(is)28 b(erroneously)d(con)n(tained)i(in)h(the)g(Hartree)f (equations.)290 3340 y(Using)g(the)h(electron)f(densit)n(y)313 3566 y FA(n)p FE(\()p Ft(r)s FE(\))c(=)615 3463 y Fv(N)585 3488 y Fu(X)591 3664 y Fv(i)p Fx(=1)718 3566 y Fs(j)p FA( )795 3578 y Fv(i)823 3566 y FE(\()p Ft(r)s FE(\))p Fs(j)957 3532 y Fx(2)1008 3566 y FA(;)1727 b FE(\(3.9\))165 3788 y(the)28 b FD(Hartr)l(e)l(e)i(p)l(otential)37 b FA(v)994 3800 y Fx(H)1075 3788 y FE(can)27 b(b)r(e)h(de\014ned:)313 3986 y FA(v)353 3998 y Fx(H)406 3986 y FE(\()p Ft(r)s FE(\))c(=)628 3873 y Fu(Z)725 3986 y FA(d)768 3952 y Fx(3)805 3986 y FA(r)844 3952 y Fw(0)869 3986 y FA(n)p FE(\()p Ft(r)997 3952 y Fw(0)1020 3986 y FE(\))1157 3930 y FA(e)1196 3900 y Fx(2)p 1063 3967 V 1063 4043 a Fs(j)p Ft(r)d Fs(\000)d Ft(r)1280 4019 y Fw(0)1304 4043 y Fs(j)1351 3986 y FA(:)1343 b FE(\(3.10\))165 4180 y(It)26 b(corresp)r(onds)d(to)j (the)f(electrostatic)f(p)r(oten)n(tial)i(of)f(all)g(electrons.)f(With)j (this)e(de\014ni-)165 4280 y(tion)j(the)g(Hartree)f(equations)f(can)i (b)r(e)g(written)f(in)h(a)f(more)g(compact)g(form)h(as)313 4367 y Fu(\032)375 4485 y Fs(\000)464 4428 y FE(\026)-42 b FA(h)512 4391 y Fx(2)p 450 4465 115 4 v 450 4541 a FE(2)p FA(m)574 4485 y Fs(r)643 4450 y Fx(2)699 4485 y FE(+)18 b FA(v)822 4497 y Fv(ext)921 4485 y FE(\()p Ft(r)r FE(\))h(+)f FA(v)1173 4497 y Fx(H)1227 4485 y FE(\()p Ft(r)r FE(\))1337 4367 y Fu(\033)1414 4485 y FA( )1468 4497 y Fv(i)1496 4485 y FE(\()p 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.1985 .21706 L .2148 .22992 L .21624 .2311 L .22757 .24739 L .2311 .25364 L .23422 .26369 L .23716 .27999 L .23798 .29628 L .23653 .31258 L .23297 .32888 L .2311 .33425 L .22468 .34518 L .2148 .35849 L .21171 .36147 L .1985 .37024 L .18442 .37777 L .1822 .37843 L .16591 .38157 L .14961 .38257 L .13331 .38153 L .11701 .37836 L .11505 .37777 L .10072 .37008 L .08777 .36147 L .08442 .35822 L .07483 .34518 L .06812 .33369 L .06646 .32888 L .0629 .31258 L .06147 .29628 L .06228 .27999 L .06521 .26369 L .06812 .25423 L .07196 .24739 L .08322 .2311 L .08442 .23012 L .10072 .21723 L .10478 .2148 L .11701 .21049 L s .67112 .10785 m .68742 .11549 L .68773 .11701 L .68742 .12304 L .67112 .13103 L .66427 .11701 L .67112 .10785 L s .31258 .11549 m .32888 .10785 L .33573 .11701 L .32888 .13103 L .31258 .12304 L .31227 .11701 L .31258 .11549 L s .65482 .03141 m .67112 .03085 L .68742 .03097 L .70372 .03288 L .71051 .03553 L .72001 .04059 L .73631 .05114 L .73691 .05183 L .75067 .06812 L .75261 .07125 L .75774 .08442 L .76171 .10072 L .76353 .11701 L .76246 .13331 L .75901 .14961 L .75332 .16591 L .75261 .16718 L .74112 .1822 L .73631 .18674 L .72001 .19817 L .71943 .1985 L .70372 .20347 L .68742 .20631 L .67112 .20694 L .65482 .20515 L .63853 .20131 L .63113 .1985 L .62223 .19294 L .60892 .1822 L .60593 .17837 L .59788 .16591 L .58983 .14961 L .58963 .14933 L .58693 .13331 L .58623 .11701 L .58747 .10072 L .58963 .08885 L .5918 .08442 L .60026 .06812 L .60593 .06041 L .61319 .05183 L .62223 .04531 L .63853 .03605 L .63956 .03553 L .65482 .03141 L s .29628 .03288 m .31258 .03097 L .32888 .03085 L .34518 .03141 L .36044 .03553 L .36147 .03605 L .37777 .04531 L .38681 .05183 L .39407 .06041 L .39974 .06812 L .4082 .08442 L .41037 .08885 L .41253 .10072 L .41377 .11701 L .41307 .13331 L .41037 .14933 L .41017 .14961 L .40212 .16591 L .39407 .17837 L .39108 .1822 L .37777 .19294 L .36887 .1985 L .36147 .20131 L .34518 .20515 L .32888 .20694 L .31258 .20631 L .29628 .20347 L .28057 .1985 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L s .91276 .01923 m .89928 .03176 L .88299 .0346 L .87994 .03553 L .86669 .0373 L .85039 .03807 L .83409 .03732 L .82056 .03553 L .8178 .03467 L .8015 .03181 L .78774 .01923 L s .56194 .01923 m .55704 .02977 L .54074 .03329 L .52882 .03553 L .52445 .03628 L .50815 .03788 L .49185 .03788 L .47555 .03628 L .47118 .03553 L .45926 .03329 L .44296 .02977 L .43806 .01923 L s .21226 .01923 m .1985 .03181 L .1822 .03467 L .17944 .03553 L .16591 .03732 L .14961 .03807 L .13331 .0373 L .12006 .03553 L .11701 .0346 L .10072 .03176 L .08724 .01923 L s .85039 .63362 m .86117 .63853 L .85576 .65482 L .85039 .65574 L .84466 .65482 L .83925 .63853 L .85039 .63362 L s .49185 .63482 m .50815 .63482 L .51094 .63853 L .50815 .65472 L .49185 .65472 L .48906 .63853 L .49185 .63482 L s .14961 .63362 m .16075 .63853 L .15534 .65482 L .14961 .65574 L .14424 .65482 L .13883 .63853 L .14961 .63362 L s .8015 .55673 m .8178 .55198 L .83409 .54987 L .85039 .54923 L .86669 .5499 L .88299 .55203 L .89928 .55682 L .89978 .55704 L .91558 .56766 L .92184 .57334 L .93188 .58563 L .93401 .58963 L .93969 .60593 L .94306 .62223 L .94489 .63853 L .94313 .65482 L .93934 .67112 L .93376 .68742 L .93188 .69133 L .92219 .70372 L .91558 .71083 L .90423 .72001 L .89928 .72279 L .88299 .7293 L .86669 .73425 L .8533 .73631 L .85039 .73636 L .84727 .73631 L .83409 .73432 L .8178 .72939 L .8015 .72292 L .7963 .72001 L .7852 .71106 L .77834 .70372 L .7689 .69176 L .76681 .68742 L .76122 .67112 L .75734 .65482 L .75545 .63853 L .75741 .62223 L .76087 .60593 L .76655 .58963 L .7689 .58523 L .77866 .57334 L .7852 .56745 L .80079 .55704 L .8015 .55673 L s .45926 .5539 m .47555 .55073 L .49185 .54939 L .50815 .54939 L .52445 .55073 L .54074 .5539 L .54931 .55704 L .55704 .56203 L .57239 .57334 L .57334 .57431 L .58333 .58963 L .58963 .60086 L .59117 .60593 L .59383 .62223 L .59451 .63853 L .59368 .65482 L .59096 .67112 L .58963 .676 L .58267 .68742 L .57334 .70267 L .5724 .70372 L .55704 .71775 L .55399 .72001 L .54074 .72641 L .52445 .732 L .50815 .73587 L .49185 .73587 L .47555 .732 L .45926 .72641 L .44601 .72001 L .44296 .71775 L .4276 .70372 L .42666 .70267 L .41733 .68742 L .41037 .676 L .40904 .67112 L .40632 .65482 L .40549 .63853 L .40617 .62223 L .40883 .60593 L .41037 .60086 L .41667 .58963 L .42666 .57431 L .42761 .57334 L .44296 .56203 L .45069 .55704 L .45926 .5539 L s .10072 .55682 m .11701 .55203 L .13331 .5499 L .14961 .54923 L .16591 .54987 L .1822 .55198 L .1985 .55673 L .19921 .55704 L .2148 .56745 L .22134 .57334 L .2311 .58523 L .23345 .58963 L .23913 .60593 L .24259 .62223 L .24455 .63853 L .24266 .65482 L .23878 .67112 L .23319 .68742 L .2311 .69176 L .22166 .70372 L .2148 .71106 L .2037 .72001 L .1985 .72292 L .1822 .72939 L .16591 .73432 L .15273 .73631 L .14961 .73636 L .1467 .73631 L .13331 .73425 L .11701 .7293 L .10072 .72279 L .09577 .72001 L .08442 .71083 L .07781 .70372 L .06812 .69133 L .06624 .68742 L .06066 .67112 L .05687 .65482 L .05511 .63853 L .05694 .62223 L .06031 .60593 L .06599 .58963 L .06812 .58563 L .07816 .57334 L .08442 .56766 L .10022 .55704 L .10072 .55682 L s .67112 .45814 m .68341 .45926 L .68591 .47555 L .67112 .47894 L .66639 .47555 L .6687 .45926 L .67112 .45814 L s .32888 .45814 m .3313 .45926 L .33361 .47555 L .32888 .47894 L .31409 .47555 L .31659 .45926 L .32888 .45814 L s .63853 .37726 m .65482 .37453 L .67112 .3736 L .68742 .3739 L .70372 .37562 L .71367 .37777 L .72001 .38138 L .73631 .38968 L .74226 .39407 L .75261 .40494 L .75617 .41037 L .76328 .42666 L .7689 .43969 L .76945 .44296 L .77104 .45926 L .7711 .47555 L .76968 .49185 L .7689 .49685 L .76376 .50815 L .75751 .52445 L .75261 .53205 L .74495 .54074 L .73631 .5478 L .72144 .55704 L .72001 .55769 L .70372 .56173 L .68742 .56343 L .67112 .56375 L .65482 .5628 L .63853 .56015 L .62877 .55704 L .62223 .55277 L .60593 .54153 L .60512 .54074 L .5929 .52445 L .58963 .51961 L .58565 .50815 L .58261 .49185 L .58118 .47555 L .58123 .45926 L .58276 .44296 L .58605 .42666 L .58963 .41713 L .5941 .41037 L .60593 .39519 L .60718 .39407 L .62223 .38502 L .63671 .37777 L .63853 .37726 L s .29628 .37562 m .31258 .3739 L .32888 .3736 L .34518 .37453 L .36147 .37726 L .36329 .37777 L .37777 .38502 L .39282 .39407 L .39407 .39519 L .4059 .41037 L .41037 .41713 L .41395 .42666 L .41724 .44296 L .41877 .45926 L .41882 .47555 L .41739 .49185 L .41435 .50815 L .41037 .51961 L .4071 .52445 L .39488 .54074 L .39407 .54153 L .37777 .55277 L .37123 .55704 L .36147 .56015 L .34518 .5628 L .32888 .56375 L .31258 .56343 L .29628 .56173 L .27999 .55769 L .27856 .55704 L .26369 .5478 L .25505 .54074 L .24739 .53205 L .24249 .52445 L .23624 .50815 L .2311 .49685 L .23032 .49185 L .2289 .47555 L .22896 .45926 L .23055 .44296 L .2311 .43969 L .23672 .42666 L .24383 .41037 L .24739 .40494 L .25774 .39407 L .26369 .38968 L .27999 .38138 L .28633 .37777 L .29628 .37562 L s .85039 .28214 m .86113 .29628 L .85039 .30409 L .83928 .29628 L .85039 .28214 L s .49185 .28398 m .50815 .28398 L .51084 .29628 L .50815 .30245 L .49185 .30245 L .48916 .29628 L .49185 .28398 L s .14961 .28214 m .16072 .29628 L .14961 .30409 L .13887 .29628 L .14961 .28214 L s .83409 .19788 m .85039 .19713 L .86669 .1979 L .8733 .1985 L .88299 .20309 L .89928 .20819 L .91264 .2148 L .91558 .21706 L .92866 .2311 L .93188 .23543 L .93718 .24739 L .94147 .26369 L .94492 .27999 L .9467 .29628 L .94397 .31258 L .9404 .32888 L .93551 .34518 L .93188 .35213 L .92484 .36147 L .91558 .3703 L .90478 .37777 L .89928 .38029 L .88299 .38488 L .86669 .38743 L .85039 .38848 L .83409 .38746 L .8178 .38493 L .8015 .38054 L .79573 .37777 L .7852 .37053 L .77565 .36147 L .7689 .35258 L .76505 .34518 L .76015 .32888 L .75645 .31258 L .7532 .29628 L .75542 .27999 L .75906 .26369 L .76338 .24739 L .7689 .23498 L .77182 .2311 L .7852 .21684 L .78786 .2148 L .8015 .20809 L .8178 .20301 L .82707 .1985 L .83409 .19788 L s .49185 .19731 m .50815 .19731 L .5215 .1985 L .52445 .20014 L .54074 .20547 L .55704 .21196 L .56162 .2148 L .57334 .22524 L .57799 .2311 L .58733 .24739 L .58963 .25092 L .59278 .26369 L .59462 .27999 L .59504 .29628 L .59427 .31258 L .59187 .32888 L .58963 .33686 L .58479 .34518 L .57466 .36147 L .57334 .36293 L .55704 .37633 L .55507 .37777 L .54074 .38306 L .52445 .38634 L .50815 .3882 L .49185 .3882 L .47555 .38634 L .45926 .38306 L .44493 .37777 L .44296 .37633 L .42666 .36293 L .42534 .36147 L .41521 .34518 L .41037 .33686 L .40813 .32888 L .40573 .31258 L .40496 .29628 L .40538 .27999 L .40722 .26369 L .41037 .25092 L .41267 .24739 L .42201 .2311 L .42666 .22524 L .43838 .2148 L .44296 .21196 L .45926 .20547 L .47555 .20014 L .4785 .1985 L .49185 .19731 L s .13331 .1979 m .14961 .19713 L .16591 .19788 L .17293 .1985 L .1822 .20301 L .1985 .20809 L .21214 .2148 L .2148 .21684 L .22818 .2311 L .2311 .23498 L .23662 .24739 L .24094 .26369 L .24458 .27999 L .2468 .29628 L .24355 .31258 L .23985 .32888 L .23495 .34518 L .2311 .35258 L .22435 .36147 L .2148 .37053 L .20427 .37777 L .1985 .38054 L .1822 .38493 L .16591 .38746 L .14961 .38848 L .13331 .38743 L .11701 .38488 L .10072 .38029 L .09522 .37777 L .08442 .3703 L .07516 .36147 L .06812 .35213 L .06449 .34518 L .0596 .32888 L .05603 .31258 L .0533 .29628 L .05508 .27999 L .05853 .26369 L .06282 .24739 L .06812 .23543 L .07134 .2311 L .08442 .21706 L .08736 .2148 L .10072 .20819 L .11701 .20309 L .1267 .1985 L .13331 .1979 L s .67112 .1089 m .68711 .11701 L .67112 .13014 L .66527 .11701 L .67112 .1089 L s .32888 .1089 m .33473 .11701 L .32888 .13014 L .31289 .11701 L .32888 .1089 L s .62223 .03361 m .63853 .02355 L .65482 .02311 L .67112 .02583 L .68742 .02477 L .70372 .0227 L .72001 .02664 L .72986 .03553 L .73631 .04011 L .74977 .05183 L .75261 .05531 L .75953 .06812 L .76544 .08442 L .7689 .09048 L .77026 .10072 L .77122 .11701 L .77077 .13331 L .7689 .1491 L .76798 .14961 L .76164 .16591 L .75351 .1822 L .75261 .18333 L .73689 .1985 L .73631 .19894 L .72001 .20619 L .70372 .21091 L .69426 .2148 L .68742 .21545 L .67112 .21583 L .65603 .2148 L .65482 .21405 L .63853 .20861 L .62223 .2033 L .61362 .1985 L .60593 .19224 L .59713 .1822 L .58963 .17059 L .58752 .16591 L .58347 .14961 L .58152 .13331 L .58103 .11701 L .58206 .10072 L .58457 .08442 L .58962 .06812 L .58963 .06809 L .6013 .05183 L .60593 .04697 L .62052 .03553 L .62223 .03361 L s .27999 .02664 m .29628 .0227 L .31258 .02477 L .32888 .02583 L .34518 .02311 L .36147 .02355 L .37777 .03361 L .37948 .03553 L .39407 .04697 L .3987 .05183 L .41037 .06809 L .41038 .06812 L .41543 .08442 L .41794 .10072 L .41897 .11701 L .41848 .13331 L .41653 .14961 L .41248 .16591 L .41037 .17059 L .40287 .1822 L .39407 .19224 L .38638 .1985 L .37777 .2033 L .36147 .20861 L .34518 .21405 L .34397 .2148 L .32888 .21583 L .31258 .21545 L .30574 .2148 L .29628 .21091 L .27999 .20619 L .26369 .19894 L .26311 .1985 L .24739 .18333 L .24649 .1822 L .23836 .16591 L .23202 .14961 L .2311 .1491 L .22923 .13331 L .22878 .11701 L .22974 .10072 L .2311 .09048 L .23456 .08442 L .24047 .06812 L .24739 .05531 L .25023 .05183 L .26369 .04011 L .27014 .03553 L .27999 .02664 L s .01923 .55779 m .0212 .55704 L .03553 .54796 L .04446 .54074 L .05183 .53243 L .05697 .52445 L .06331 .50815 L .06812 .49797 L .06909 .49185 L .0705 .47555 L .07045 .45926 L .06887 .44296 L .06812 .43857 L .0628 .42666 L .05564 .41037 L .05183 .40459 L .04176 .39407 L .03553 .3895 L .01923 .38125 L s .01923 .20627 m .03553 .19906 L .03629 .1985 L .05183 .18359 L .05293 .1822 L .06112 .16591 L .06786 .14961 L .06812 .14948 L .07018 .13331 L .07062 .11701 L .06967 .10072 L .06812 .08947 L .06507 .08442 L .05899 .06812 L .05183 .05492 L .04929 .05183 L .03553 .03992 L .02981 .03553 L .01923 .02648 L s .98077 .55779 m .9788 .55704 L .96447 .54796 L .95554 .54074 L .94817 .53243 L .94303 .52445 L .93669 .50815 L .93188 .49797 L .93091 .49185 L .9295 .47555 L .92955 .45926 L .93113 .44296 L .93188 .43857 L .9372 .42666 L .94436 .41037 L .94817 .40459 L .95824 .39407 L .96447 .3895 L .98077 .38125 L s .98077 .20627 m .96447 .19906 L .96371 .1985 L .94817 .18359 L .94707 .1822 L .93888 .16591 L .93214 .14961 L .93188 .14948 L .92982 .13331 L .92938 .11701 L .93033 .10072 L .93188 .08947 L .93493 .08442 L .94101 .06812 L .94817 .05492 L .95071 .05183 L .96447 .03992 L .97019 .03553 L .98077 .02648 L s .91716 .01923 m .91558 .02124 L .89928 .03304 L .88789 .03553 L .88299 .03674 L .86669 .03903 L .85039 .03968 L .83409 .03905 L .8178 .03679 L .81262 .03553 L .8015 .03309 L .7852 .02145 L .78341 .01923 L s .56703 .01923 m .55704 .03241 L .54074 .03484 L .53784 .03553 L .52445 .03817 L .50815 .03952 L .49185 .03952 L .47555 .03817 L .46216 .03553 L .45926 .03484 L .44296 .03241 L .43297 .01923 L s .21659 .01923 m .2148 .02145 L .1985 .03309 L .18738 .03553 L .1822 .03679 L .16591 .03905 L .14961 .03968 L .13331 .03903 L .11701 .03674 L .11211 .03553 L .10072 .03304 L .08442 .02124 L .08284 .01923 L s .85039 .63383 m .86093 .63853 L .85533 .65482 L .85039 .6556 L .84509 .65482 L .83949 .63853 L .85039 .63383 L s .49185 .63501 m .50815 .63501 L .51079 .63853 L .50815 .65453 L .49185 .65453 L .48921 .63853 L .49185 .63501 L s .14961 .63383 m .16051 .63853 L .15491 .65482 L .14961 .6556 L .14467 .65482 L .13907 .63853 L .14961 .63383 L s .8015 .55368 m .8178 .54931 L .83409 .54738 L .85039 .54674 L .86669 .5474 L .88299 .54935 L .89928 .55378 L .90683 .55704 L .91558 .56238 L .92793 .57334 L .93188 .57831 L .93797 .58963 L .94322 .60593 L .94817 .61785 L .94859 .62223 L .94936 .63853 L .94821 .65482 L .94817 .65524 L .94142 .67112 L .93564 .68742 L .93188 .69492 L .92451 .70372 L .91558 .71329 L .90723 .72001 L .89928 .72444 L .88299 .73097 L .86893 .73631 L .86669 .73652 L .85039 .73751 L .83409 .73656 L .83145 .73631 L .8178 .73107 L .8015 .72456 L .79329 .72001 L .7852 .71351 L .776 .70372 L .7689 .69531 L .76493 .68742 L .75911 .67112 L .75261 .65701 L .7524 .65482 L .75127 .63853 L .75202 .62223 L .75261 .61631 L .75727 .60593 L .76254 .58963 L .7689 .57789 L .77254 .57334 L .7852 .56217 L .79365 .55704 L Mistroke .8015 .55368 L Mfstroke .44296 .55685 m .45926 .55097 L .47555 .54819 L .49185 .54691 L .50815 .54691 L .52445 .54819 L .54074 .55097 L .55704 .55685 L .55759 .55704 L .57334 .56969 L .57668 .57334 L .58834 .58963 L .58963 .59168 L .59399 .60593 L .59606 .62223 L .5964 .63853 L .5954 .65482 L .59271 .67112 L .58963 .68132 L .58507 .68742 L .57471 .70372 L .57334 .70546 L .55712 .72001 L .55704 .72006 L .54074 .72798 L .52445 .73402 L .51803 .73631 L .50815 .73728 L .49185 .73728 L .48197 .73631 L .47555 .73402 L .45926 .72798 L .44296 .72006 L .44288 .72001 L .42666 .70546 L .42529 .70372 L .41493 .68742 L .41037 .68132 L .40729 .67112 L .4046 .65482 L .4036 .63853 L .40394 .62223 L .40601 .60593 L .41037 .59168 L .41166 .58963 L .42332 .57334 L .42666 .56969 L .44241 .55704 L .44296 .55685 L s .10072 .55378 m .11701 .54935 L .13331 .5474 L .14961 .54674 L .16591 .54738 L .1822 .54931 L .1985 .55368 L .20635 .55704 L .2148 .56217 L .22746 .57334 L .2311 .57789 L .23746 .58963 L .24273 .60593 L .24739 .61631 L .24798 .62223 L .24873 .63853 L .2476 .65482 L .24739 .65701 L .24089 .67112 L .23507 .68742 L .2311 .69531 L .224 .70372 L .2148 .71351 L .20671 .72001 L .1985 .72456 L .1822 .73107 L .16855 .73631 L .16591 .73656 L .14961 .73751 L .13331 .73652 L .13107 .73631 L .11701 .73097 L .10072 .72444 L .09277 .72001 L .08442 .71329 L .07549 .70372 L .06812 .69492 L .06436 .68742 L .05858 .67112 L .05183 .65524 L .05179 .65482 L .05064 .63853 L .05141 .62223 L .05183 .61785 L .05678 .60593 L .06203 .58963 L .06812 .57831 L .07207 .57334 L .08442 .56238 L .09317 .55704 L Mistroke .10072 .55378 L Mfstroke .67112 .45829 m .68313 .45926 L .68569 .47555 L .67112 .47873 L .66664 .47555 L .66899 .45926 L .67112 .45829 L s .32888 .45829 m .33101 .45926 L .33336 .47555 L .32888 .47873 L .31431 .47555 L .31687 .45926 L .32888 .45829 L s .63853 .37449 m .65482 .3723 L .67112 .37157 L .68742 .3718 L .70372 .37316 L .72001 .37679 L .7228 .37777 L .73631 .38479 L .74901 .39407 L .75261 .3979 L .76066 .41037 L .76811 .42666 L .7689 .42793 L .77183 .44296 L .77307 .45926 L .77308 .47555 L .7719 .49185 L .7689 .50796 L .76877 .50815 L .76134 .52445 L .75261 .53906 L .75116 .54074 L .73631 .55258 L .72913 .55704 L .72001 .56083 L .70372 .56422 L .68742 .56569 L .67112 .56597 L .65482 .56514 L .63853 .56289 L .62223 .55765 L .62149 .55704 L .60593 .54608 L .6004 .54074 L .58963 .52585 L .58852 .52445 L .58287 .50815 L .58006 .49185 L .57845 .47555 L .57846 .45926 L .58006 .44296 L .58299 .42666 L .58906 .41037 L .58963 .40877 L .60254 .39407 L .60593 .3909 L .62223 .38042 L .62693 .37777 L .63853 .37449 L s .27999 .37679 m .29628 .37316 L .31258 .3718 L .32888 .37157 L .34518 .3723 L .36147 .37449 L .37307 .37777 L .37777 .38042 L .39407 .3909 L .39746 .39407 L .41037 .40877 L .41094 .41037 L .41701 .42666 L .41994 .44296 L .42154 .45926 L .42155 .47555 L .41994 .49185 L .41713 .50815 L .41148 .52445 L .41037 .52585 L .3996 .54074 L .39407 .54608 L .37851 .55704 L .37777 .55765 L .36147 .56289 L .34518 .56514 L .32888 .56597 L .31258 .56569 L .29628 .56422 L .27999 .56083 L .27087 .55704 L .26369 .55258 L .24884 .54074 L .24739 .53906 L .23866 .52445 L .23123 .50815 L .2311 .50796 L .2281 .49185 L .22692 .47555 L .22693 .45926 L .22817 .44296 L .2311 .42793 L .23189 .42666 L .23934 .41037 L .24739 .3979 L .25099 .39407 L .26369 .38479 L .2772 .37777 L .27999 .37679 L s .85039 .28237 m .86085 .29628 L .85039 .30379 L .83955 .29628 L .85039 .28237 L s .49185 .28423 m .50815 .28423 L .51067 .29628 L .50815 .30217 L .49185 .30217 L .48933 .29628 L .49185 .28423 L s .14961 .28237 m .16045 .29628 L .14961 .30379 L .13915 .29628 L .14961 .28237 L s .8178 .19795 m .83409 .19568 L .85039 .19509 L .86669 .1957 L .88299 .198 L .88557 .1985 L .89928 .20442 L .91558 .21276 L .91765 .2148 L .93188 .22977 L .93328 .2311 L .94064 .24739 L .94568 .26369 L .94817 .2654 L .94959 .27999 L .9501 .29628 L .94917 .31258 L .94817 .3209 L .94407 .32888 L .93913 .34518 L .93188 .35998 L .93079 .36147 L .91558 .37597 L .91284 .37777 L .89928 .38401 L .88299 .38796 L .86669 .39149 L .85983 .39407 L .85039 .39436 L .84068 .39407 L .83409 .39156 L .8178 .38801 L .8015 .38395 L .78765 .37777 L .7852 .37617 L .76969 .36147 L .7689 .3604 L .76142 .34518 L .75638 .32888 L .75261 .322 L .75145 .31258 L .75053 .29628 L .75103 .27999 L .75261 .26485 L .75462 .26369 L .7599 .24739 L .7673 .2311 L .7689 .22943 L .78287 .2148 L .7852 .2126 L Mistroke .8015 .20433 L .81495 .1985 L .8178 .19795 L Mfstroke .47555 .19653 m .49185 .19523 L .50815 .19523 L .52445 .19653 L .5356 .1985 L .54074 .20132 L .55704 .2077 L .5688 .2148 L .57334 .21872 L .58309 .2311 L .58963 .24293 L .59133 .24739 L .59528 .26369 L .59676 .27999 L .59709 .29628 L .59648 .31258 L .59454 .32888 L .58991 .34518 L .58963 .34552 L .57942 .36147 L .57334 .36841 L .5611 .37777 L .55704 .38031 L .54074 .38617 L .52445 .38966 L .50989 .39407 L .50815 .39417 L .49185 .39417 L .49011 .39407 L .47555 .38966 L .45926 .38617 L .44296 .38031 L .4389 .37777 L .42666 .36841 L .42058 .36147 L .41037 .34552 L .41009 .34518 L .40546 .32888 L .40352 .31258 L .40291 .29628 L .40324 .27999 L .40472 .26369 L .40867 .24739 L .41037 .24293 L .41691 .2311 L .42666 .21872 L .4312 .2148 L .44296 .2077 L .45926 .20132 L .4644 .1985 L Mistroke .47555 .19653 L Mfstroke .11701 .198 m .13331 .1957 L .14961 .19509 L .16591 .19568 L .1822 .19795 L .18505 .1985 L .1985 .20433 L .2148 .2126 L .21713 .2148 L .2311 .22943 L .2327 .2311 L .2401 .24739 L .24538 .26369 L .24739 .26485 L .24897 .27999 L .24947 .29628 L .24855 .31258 L .24739 .322 L .24362 .32888 L .23858 .34518 L .2311 .3604 L .23031 .36147 L .2148 .37617 L .21235 .37777 L .1985 .38395 L .1822 .38801 L .16591 .39156 L .15932 .39407 L .14961 .39436 L .14017 .39407 L .13331 .39149 L .11701 .38796 L .10072 .38401 L .08716 .37777 L .08442 .37597 L .06921 .36147 L .06812 .35998 L .06087 .34518 L .05593 .32888 L .05183 .3209 L .05083 .31258 L .0499 .29628 L .05041 .27999 L .05183 .2654 L .05432 .26369 L .05936 .24739 L .06672 .2311 L .06812 .22977 L .08235 .2148 L .08442 .21276 L Mistroke .10072 .20442 L .11443 .1985 L .11701 .198 L Mfstroke .67112 .10918 m .68691 .11701 L .67112 .12991 L .66553 .11701 L .67112 .10918 L s .32888 .10918 m .33447 .11701 L .32888 .12991 L .31309 .11701 L .32888 .10918 L s .01923 .56091 m .02932 .55704 L .03553 .55275 L .05069 .54074 L .05183 .53943 L .06082 .52445 L .06812 .50868 L .06826 .50815 L .07131 .49185 L .07248 .47555 L .07247 .45926 L .07124 .44296 L .06812 .42712 L .06782 .42666 L .06017 .41037 L .05183 .39755 L .04853 .39407 L .03553 .38462 L .02299 .37777 L .01923 .37671 L s .01923 .21008 m .03553 .203 L .04226 .1985 L .05183 .18949 L .05717 .1822 L .06541 .16591 L .06812 .16072 L .07058 .14961 L .07227 .13331 L .07259 .11701 L .07178 .10072 L .06941 .08442 L .06812 .07945 L .06276 .06812 L .05349 .05183 L .05183 .0484 L .03707 .03553 L .03553 .0342 L .01923 .02272 L s .98077 .56091 m .97068 .55704 L .96447 .55275 L .94931 .54074 L .94817 .53943 L .93918 .52445 L .93188 .50868 L .93174 .50815 L .92869 .49185 L .92752 .47555 L .92753 .45926 L .92876 .44296 L .93188 .42712 L .93218 .42666 L .93983 .41037 L .94817 .39755 L .95147 .39407 L .96447 .38462 L .97701 .37777 L .98077 .37671 L s .98077 .21008 m .96447 .203 L .95774 .1985 L .94817 .18949 L .94283 .1822 L .93459 .16591 L .93188 .16072 L .92942 .14961 L .92773 .13331 L .92741 .11701 L .92822 .10072 L .93059 .08442 L .93188 .07945 L .93724 .06812 L .94651 .05183 L .94817 .0484 L .96293 .03553 L .96447 .0342 L .98077 .02272 L s .92275 .01923 m .91558 .02626 L .89928 .0351 L .89765 .03553 L .88299 .03932 L .86669 .04118 L .85039 .0417 L .83409 .0412 L .8178 .03936 L .80286 .03553 L .8015 .03517 L .7852 .02645 L .77772 .01923 L s .68926 .01923 m .70372 .02044 L .72001 .02279 L .73631 .03443 L .73759 .03553 L .75261 .04871 L .75406 .05183 L .76326 .06812 L .7689 .08026 L .76998 .08442 L .77238 .10072 L .77319 .11701 L .77287 .13331 L .77115 .14961 L .7689 .15989 L .76583 .16591 L .75768 .1822 L .75261 .18913 L .74273 .1985 L .73631 .20284 L .72001 .20998 L .70929 .2148 L .70372 .21588 L .68742 .21763 L .67112 .21793 L .65482 .21699 L .64068 .2148 L .63853 .21328 L .62223 .20715 L .60603 .1985 L .60593 .19842 L .59169 .1822 L .58963 .17882 L .58424 .16591 L .58073 .14961 L .57878 .13331 L .57825 .11701 L .57948 .10072 L .58191 .08442 L .58663 .06812 L .58963 .06171 L .59599 .05183 L .60593 .04122 L .61363 .03553 L .62223 .0269 L .63853 .02116 L .65482 .01993 L .66117 .01923 L s .57379 .01923 m .57334 .01967 L .55704 .03371 L .54687 .03553 L .54074 .03737 L .52445 .04048 L .50815 .04158 L .49185 .04158 L .47555 .04048 L .45926 .03737 L .45313 .03553 L .44296 .03371 L .42666 .01967 L .42621 .01923 L s .33883 .01923 m .34518 .01993 L .36147 .02116 L .37777 .0269 L .38637 .03553 L .39407 .04122 L .40401 .05183 L .41037 .06171 L .41337 .06812 L .41809 .08442 L .42052 .10072 L .42175 .11701 L .42122 .13331 L .41927 .14961 L .41576 .16591 L .41037 .17882 L .40831 .1822 L .39407 .19842 L .39397 .1985 L .37777 .20715 L .36147 .21328 L .35932 .2148 L .34518 .21699 L .32888 .21793 L .31258 .21763 L .29628 .21588 L .29071 .2148 L .27999 .20998 L .26369 .20284 L .25727 .1985 L .24739 .18913 L .24232 .1822 L .23417 .16591 L .2311 .15989 L .22885 .14961 L .22713 .13331 L .22681 .11701 L .22762 .10072 L .23002 .08442 L .2311 .08026 L .23674 .06812 L .24594 .05183 L .24739 .04871 L .26241 .03553 L .26369 .03443 L .27999 .02279 L .29628 .02044 L .31074 .01923 L s .22228 .01923 m .2148 .02645 L .1985 .03517 L .19714 .03553 L .1822 .03936 L .16591 .0412 L .14961 .0417 L .13331 .04118 L .11701 .03932 L .10235 .03553 L .10072 .0351 L .08442 .02626 L .07725 .01923 L s .85039 .63405 m .86067 .63853 L .85485 .65482 L .85039 .65546 L .84557 .65482 L .83974 .63853 L .85039 .63405 L s .49185 .63521 m .50815 .63521 L .51063 .63853 L .50815 .65433 L .49185 .65433 L .48937 .63853 L .49185 .63521 L s .14961 .63405 m .16026 .63853 L .15443 .65482 L .14961 .65546 L .14515 .65482 L .13933 .63853 L .14961 .63405 L s .85039 .54047 m .86127 .54074 L .86669 .54229 L .88299 .54541 L .89928 .54926 L .91558 .55554 L .91828 .55704 L .93188 .56822 L .93573 .57334 L .94361 .58963 L .94817 .60254 L .94897 .60593 L .95153 .62223 L .95184 .63853 L .95052 .65482 L .94817 .66895 L .94485 .67112 L .93792 .68742 L .93188 .69881 L .9274 .70372 L .91558 .71608 L .91066 .72001 L .89928 .72637 L .88299 .73325 L .87835 .73631 L .86669 .73791 L .85039 .73882 L .83409 .73794 L .82209 .73631 L .8178 .73337 L .8015 .72649 L .78986 .72001 L .7852 .7163 L .77309 .70372 L .7689 .69917 L .76264 .68742 L .75553 .67112 L .75261 .66943 L .75011 .65482 L .7488 .63853 L .74909 .62223 L .75163 .60593 L .75261 .60171 L .75688 .58963 L .7648 .57334 L .7689 .56792 L .78224 .55704 L .7852 .5554 L .8015 .54916 L .8178 .54536 L Mistroke .83409 .54223 L .83925 .54074 L .85039 .54047 L Mfstroke .49185 .54061 m .50815 .54061 L .51117 .54074 L .52445 .54392 L .54074 .54701 L .55704 .55263 L .56802 .55704 L .57334 .56143 L .58454 .57334 L .58963 .58017 L .59285 .58963 L .5977 .60593 L .59923 .62223 L .5991 .63853 L .59768 .65482 L .59484 .67112 L .58963 .68656 L .58878 .68742 L .57735 .70372 L .57334 .70853 L .56033 .72001 L .55704 .72222 L .54074 .72992 L .52662 .73631 L .52445 .73671 L .50815 .73861 L .49185 .73861 L .47555 .73671 L .47338 .73631 L .45926 .72992 L .44296 .72222 L .43967 .72001 L .42666 .70853 L .42265 .70372 L .41122 .68742 L .41037 .68656 L .40516 .67112 L .40232 .65482 L .4009 .63853 L .40077 .62223 L .4023 .60593 L .40715 .58963 L .41037 .58017 L .41546 .57334 L .42666 .56143 L .43198 .55704 L .44296 .55263 L .45926 .54701 L .47555 .54392 L .48883 .54074 L Mistroke .49185 .54061 L Mfstroke .14961 .54047 m .16075 .54074 L .16591 .54223 L .1822 .54536 L .1985 .54916 L .2148 .5554 L .21776 .55704 L .2311 .56792 L .2352 .57334 L .24312 .58963 L .24739 .60171 L .24837 .60593 L .25091 .62223 L .2512 .63853 L .24989 .65482 L .24739 .66943 L .24447 .67112 L .23736 .68742 L .2311 .69917 L .22691 .70372 L .2148 .7163 L .21014 .72001 L .1985 .72649 L .1822 .73337 L .17791 .73631 L .16591 .73794 L .14961 .73882 L .13331 .73791 L .12165 .73631 L .11701 .73325 L .10072 .72637 L .08934 .72001 L .08442 .71608 L .0726 .70372 L .06812 .69881 L .06208 .68742 L .05515 .67112 L .05183 .66895 L .04948 .65482 L .04816 .63853 L .04847 .62223 L .05103 .60593 L .05183 .60254 L .05639 .58963 L .06427 .57334 L .06812 .56822 L .08172 .55704 L .08442 .55554 L .10072 .54926 L .11701 .54541 L Mistroke .13331 .54229 L .13873 .54074 L .14961 .54047 L Mfstroke .67112 .45844 m .68284 .45926 L .68547 .47555 L .67112 .47852 L .66691 .47555 L .66929 .45926 L .67112 .45844 L s .32888 .45844 m .33071 .45926 L .33309 .47555 L .32888 .47852 L .31453 .47555 L .31716 .45926 L .32888 .45844 L s .62223 .37543 m .63853 .37091 L .65482 .3692 L .67112 .36864 L .68742 .36882 L .70372 .36987 L .72001 .37283 L .73565 .37777 L .73631 .37805 L .75261 .38846 L .75781 .39407 L .76694 .41037 L .7689 .41564 L .77203 .42666 L .77487 .44296 L .77574 .45926 L .77568 .47555 L .77474 .49185 L .77208 .50815 L .7689 .51987 L .76692 .52445 L .75854 .54074 L .75261 .54785 L .74049 .55704 L .73631 .55819 L .72001 .56492 L .70372 .5679 L .68742 .56971 L .67112 .57023 L .65482 .56893 L .63853 .56665 L .62223 .56188 L .61149 .55704 L .60593 .55412 L .59208 .54074 L .58963 .53645 L .58405 .52445 L .57889 .50815 L .57464 .49185 L .57334 .48941 L .57222 .47555 L .57222 .45926 L .57334 .44565 L .57455 .44296 L .57868 .42666 L .58433 .41037 L .58963 .39794 L .59322 .39407 L .60593 .38329 L .61443 .37777 L Mistroke .62223 .37543 L Mfstroke .27999 .37283 m .29628 .36987 L .31258 .36882 L .32888 .36864 L .34518 .3692 L .36147 .37091 L .37777 .37543 L .38557 .37777 L .39407 .38329 L .40678 .39407 L .41037 .39794 L .41567 .41037 L .42132 .42666 L .42545 .44296 L .42666 .44565 L .42778 .45926 L .42778 .47555 L .42666 .48941 L .42536 .49185 L .42111 .50815 L .41595 .52445 L .41037 .53645 L .40792 .54074 L .39407 .55412 L .38851 .55704 L .37777 .56188 L .36147 .56665 L .34518 .56893 L .32888 .57023 L .31258 .56971 L .29628 .5679 L .27999 .56492 L .26369 .55819 L .25951 .55704 L .24739 .54785 L .24146 .54074 L .23308 .52445 L .2311 .51987 L .22792 .50815 L .22526 .49185 L .22432 .47555 L .22426 .45926 L .22513 .44296 L .22797 .42666 L .2311 .41564 L .23306 .41037 L .24219 .39407 L .24739 .38846 L .26369 .37805 L .26435 .37777 L Mistroke .27999 .37283 L Mfstroke .85039 .28261 m .86056 .29628 L .85039 .30347 L .83983 .29628 L .85039 .28261 L s .49185 .28448 m .50815 .28448 L .5105 .29628 L .50815 .30189 L .49185 .30189 L .4895 .29628 L .49185 .28448 L s .14961 .28261 m .16017 .29628 L .14961 .30347 L .13944 .29628 L .14961 .28261 L s .8015 .19832 m .8178 .19465 L .83409 .19289 L .85039 .19246 L .86669 .1929 L .88299 .1947 L .89928 .19838 L .89982 .1985 L .91558 .20646 L .92794 .2148 L .93188 .21921 L .93897 .2311 L .94607 .24739 L .94817 .25219 L .95028 .26369 L .9524 .27999 L .95277 .29628 L .95207 .31258 L .9495 .32888 L .94817 .33513 L .94435 .34518 L .93769 .36147 L .93188 .3701 L .92361 .37777 L .91558 .38089 L .89928 .38915 L .8837 .39407 L .88299 .3942 L .86669 .39646 L .85039 .39708 L .83409 .39648 L .8178 .39424 L .81685 .39407 L .8015 .3887 L .7852 .38107 L .77691 .37777 L .7689 .3704 L .76284 .36147 L .75614 .34518 L .75261 .33602 L .75109 .32888 L .74855 .31258 L .74787 .29628 L .74824 .27999 L .7503 .26369 L .75261 .2513 L .75436 .24739 L .76151 .2311 L .7689 .2187 L .77244 .2148 L Mistroke .7852 .20628 L .8007 .1985 L .8015 .19832 L Mfstroke .45926 .19642 m .47555 .19352 L .49185 .19256 L .50815 .19256 L .52445 .19352 L .54074 .19642 L .54801 .1985 L .55704 .20169 L .57334 .21021 L .57878 .2148 L .58963 .2302 L .59006 .2311 L .59552 .24739 L .59872 .26369 L .59999 .27999 L .6003 .29628 L .59974 .31258 L .59811 .32888 L .59392 .34518 L .58963 .35601 L .58723 .36147 L .57334 .37777 L .57334 .37777 L .55704 .38566 L .54074 .39111 L .53371 .39407 L .52445 .39533 L .50815 .39694 L .49185 .39694 L .47555 .39533 L .46629 .39407 L .45926 .39111 L .44296 .38566 L .42666 .37777 L .42666 .37777 L .41277 .36147 L .41037 .35601 L .40608 .34518 L .40189 .32888 L .40026 .31258 L .3997 .29628 L .40001 .27999 L .40128 .26369 L .40448 .24739 L .40994 .2311 L .41037 .2302 L .42122 .2148 L .42666 .21021 L .44296 .20169 L .45199 .1985 L Mistroke .45926 .19642 L Mfstroke .10072 .19838 m .11701 .1947 L .13331 .1929 L .14961 .19246 L .16591 .19289 L .1822 .19465 L .1985 .19832 L .1993 .1985 L .2148 .20628 L .22756 .2148 L .2311 .2187 L .23849 .2311 L .24564 .24739 L .24739 .2513 L .2497 .26369 L .25176 .27999 L .25213 .29628 L .25145 .31258 L .24891 .32888 L .24739 .33602 L .24386 .34518 L .23716 .36147 L .2311 .3704 L .22309 .37777 L .2148 .38107 L .1985 .3887 L .18315 .39407 L .1822 .39424 L .16591 .39648 L .14961 .39708 L .13331 .39646 L .11701 .3942 L .1163 .39407 L .10072 .38915 L .08442 .38089 L .07639 .37777 L .06812 .3701 L .06231 .36147 L .05565 .34518 L .05183 .33513 L .0505 .32888 L .04793 .31258 L .04723 .29628 L .0476 .27999 L .04972 .26369 L .05183 .25219 L .05393 .24739 L .06103 .2311 L .06812 .21921 L .07206 .2148 L Mistroke .08442 .20646 L .10018 .1985 L .10072 .19838 L Mfstroke .67112 .10947 m .6867 .11701 L .67112 .12966 L .66581 .11701 L .67112 .10947 L s .32888 .10947 m .33419 .11701 L .32888 .12966 L .3133 .11701 L .32888 .10947 L s .01923 .56498 m .03553 .55831 L .03997 .55704 L .05183 .5481 L .05801 .54074 L .06647 .52445 L .06812 .52069 L .07154 .50815 L .07415 .49185 L .07509 .47555 L .07515 .45926 L .07428 .44296 L .07149 .42666 L .06812 .41477 L .06646 .41037 L .05729 .39407 L .05183 .38823 L .03553 .37791 L .03526 .37777 L .01923 .37275 L s .01923 .21572 m .02325 .2148 L .03553 .2093 L .05183 .19975 L .05318 .1985 L .06393 .1822 L .06812 .17052 L .07025 .16591 L .07379 .14961 L .07502 .13331 L .07519 .11701 L .07453 .10072 L .07266 .08442 L .06845 .06812 L .06812 .06671 L .05957 .05183 L .05183 .03987 L .04685 .03553 L .03553 .02614 L .01923 .02026 L s .98077 .56498 m .96447 .55831 L .96003 .55704 L .94817 .5481 L .94199 .54074 L .93353 .52445 L .93188 .52069 L .92846 .50815 L .92585 .49185 L .92491 .47555 L .92485 .45926 L .92572 .44296 L .92851 .42666 L .93188 .41477 L .93354 .41037 L .94271 .39407 L .94817 .38823 L .96447 .37791 L .96474 .37777 L .98077 .37275 L s .98077 .21572 m .97675 .2148 L .96447 .2093 L .94817 .19975 L .94682 .1985 L .93607 .1822 L .93188 .17052 L .92975 .16591 L .92621 .14961 L .92498 .13331 L .92481 .11701 L .92547 .10072 L .92734 .08442 L .93155 .06812 L .93188 .06671 L .94043 .05183 L .94817 .03987 L .95315 .03553 L .96447 .02614 L .98077 .02026 L s .93228 .01923 m .93188 .0197 L .91558 .03247 L .90688 .03553 L .89928 .03866 L .88299 .04265 L .86669 .04416 L .85039 .04458 L .83409 .04417 L .8178 .04269 L .8015 .03874 L .79346 .03553 L .7852 .03261 L .7689 .02 L .76824 .01923 L s .70969 .01923 m .72001 .02029 L .73631 .02633 L .74737 .03553 L .75261 .04012 L .76003 .05183 L .7689 .06741 L .76907 .06812 L .77323 .08442 L .77512 .10072 L .77578 .11701 L .77561 .13331 L .77437 .14961 L .77081 .16591 L .7689 .16946 L .7644 .1822 L .7537 .1985 L .75261 .19952 L .73631 .20915 L .72386 .2148 L .72001 .21566 L .70372 .21909 L .68742 .22039 L .67112 .2206 L .65482 .21993 L .63853 .21751 L .62693 .2148 L .62223 .21286 L .60593 .20551 L .5966 .1985 L .58963 .19003 L .58683 .1822 L .5798 .16591 L .57596 .14961 L .57334 .14225 L .57265 .13331 L .57209 .11701 L .57314 .10072 L .57334 .09803 L .57785 .08442 L .582 .06812 L .58868 .05183 L .58963 .0502 L .60282 .03553 L .60593 .03297 L .62223 .02205 L .63853 .01939 L .64014 .01923 L s .58191 .01923 m .57334 .02736 L .55909 .03553 L .55704 .03605 L .54074 .0412 L .52445 .04359 L .50815 .04447 L .49185 .04447 L .47555 .04359 L .45926 .0412 L .44296 .03605 L .44091 .03553 L .42666 .02736 L .41809 .01923 L s .35986 .01923 m .36147 .01939 L .37777 .02205 L .39407 .03297 L .39718 .03553 L .41037 .0502 L .41132 .05183 L .418 .06812 L .42215 .08442 L .42666 .09803 L .42686 .10072 L .42791 .11701 L .42735 .13331 L .42666 .14225 L .42404 .14961 L .4202 .16591 L .41317 .1822 L .41037 .19003 L .4034 .1985 L .39407 .20551 L .37777 .21286 L .37307 .2148 L .36147 .21751 L .34518 .21993 L .32888 .2206 L .31258 .22039 L .29628 .21909 L .27999 .21566 L .27614 .2148 L .26369 .20915 L .24739 .19952 L .2463 .1985 L .2356 .1822 L .2311 .16946 L .22919 .16591 L .22563 .14961 L .22439 .13331 L .22422 .11701 L .22488 .10072 L .22677 .08442 L .23093 .06812 L .2311 .06741 L .23997 .05183 L .24739 .04012 L .25263 .03553 L .26369 .02633 L .27999 .02029 L .29031 .01923 L s .23176 .01923 m .2311 .02 L .2148 .03261 L .20654 .03553 L .1985 .03874 L .1822 .04269 L .16591 .04417 L .14961 .04458 L .13331 .04416 L .11701 .04265 L .10072 .03866 L .09312 .03553 L .08442 .03247 L .06812 .0197 L .06772 .01923 L s .85039 .63427 m .86041 .63853 L .85431 .65482 L .85039 .65531 L .84611 .65482 L .84 .63853 L .85039 .63427 L s .49185 .63541 m .50815 .63541 L .51047 .63853 L .50815 .65413 L .49185 .65413 L .48953 .63853 L .49185 .63541 L s .14961 .63427 m .16 .63853 L .15389 .65482 L .14961 .65531 L .14569 .65482 L .13959 .63853 L .14961 .63427 L s .67112 .45859 m .68253 .45926 L .68524 .47555 L .67112 .47831 L .66718 .47555 L .6696 .45926 L .67112 .45859 L s .32888 .45859 m .3304 .45926 L .33282 .47555 L .32888 .47831 L .31476 .47555 L .31747 .45926 L .32888 .45859 L s .7852 .39158 m .79412 .39407 L .8015 .39518 L .8178 .39812 L .83409 .40018 L .85039 .40059 L .86669 .40017 L .88299 .39808 L .89928 .39513 L .9064 .39407 L .91558 .39149 L .92715 .39407 L .92779 .41037 L .92309 .42666 L .92125 .44296 L .92052 .45926 L .9207 .47555 L .92167 .49185 L .92344 .50815 L .92812 .52445 L .93047 .54074 L .91558 .547 L .89928 .54293 L 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.14961 .30315 L .13974 .29628 L .14961 .28285 L s .60593 .21672 m .62223 .21861 L .63853 .22245 L .65482 .22402 L .67112 .2245 L .68742 .22434 L .70372 .22342 L .72001 .22069 L .73631 .21801 L .75159 .2311 L .74902 .24739 L .74586 .26369 L .7445 .27999 L .74426 .29628 L .74471 .31258 L .74664 .32888 L .75013 .34518 L .75236 .36147 L .73631 .37003 L .72001 .36686 L .70372 .36452 L .68742 .36203 L .68429 .36147 L .67112 .36135 L .66603 .36147 L .65482 .36335 L .63853 .36564 L .62223 .36901 L .60593 .37127 L .59781 .36147 L .60055 .34518 L .60384 .32888 L .60593 .32072 L .60648 .31258 L .6071 .29628 L .60675 .27999 L .60593 .2654 L .60479 .26369 L .60177 .24739 L .59854 .2311 L .60593 .21672 L s .26369 .21801 m .27999 .22069 L .29628 .22342 L .31258 .22434 L .32888 .2245 L .34518 .22402 L .36147 .22245 L .37777 .21861 L .39407 .21672 L .40146 .2311 L .39823 .24739 L .39521 .26369 L .39407 .2654 L .39325 .27999 L .3929 .29628 L .39352 .31258 L .39407 .32072 L .39616 .32888 L .39945 .34518 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.95974 .63853 L .96082 .62223 L .96031 .60593 L .95957 .58963 L .96447 .58124 L .98077 .57798 L Mfstroke .98077 .35965 m .96447 .35616 L .95947 .34518 L .96068 .32888 L .96173 .31258 L .96222 .29628 L .96194 .27999 L .96115 .26369 L .95963 .24739 L .96447 .23181 L .96554 .2311 L .98077 .22894 L s .85039 .63472 m .85986 .63853 L .85289 .65482 L .85039 .65502 L .84751 .65482 L .84054 .63853 L .85039 .63472 L s .49185 .63582 m .50815 .63582 L .51015 .63853 L .50815 .65371 L .49185 .65371 L .48985 .63853 L .49185 .63582 L s .14961 .63472 m .15946 .63853 L .15249 .65482 L .14961 .65502 L .14711 .65482 L .14014 .63853 L .14961 .63472 L s .67112 .4589 m .68187 .45926 L .68476 .47555 L .67112 .47787 L .66775 .47555 L .67028 .45926 L .67112 .4589 L s .32888 .4589 m .32972 .45926 L .33225 .47555 L .32888 .47787 L .31524 .47555 L .31813 .45926 L .32888 .4589 L s .8015 .41689 m .8178 .41251 L .83409 .41244 L .85039 .41252 L .86669 .41244 L .88299 .41251 L .89928 .41707 L .90613 .42666 L .90747 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.20791 .49185 L .20806 .50815 L .1985 .52328 L .19514 .52445 L .1822 .52575 L .16591 .52545 L .14961 .52522 L .13331 .52545 L .11701 .52575 L .10433 .52445 L .10072 .52316 L .09144 .50815 L .09159 .49185 L .09216 .47555 L .09245 .45926 L .09253 .44296 L .09387 .42666 L .10072 .41707 L s .85039 .28337 m .85962 .29628 L .85039 .30245 L .84076 .29628 L .85039 .28337 L s .49185 .28529 m .50815 .28529 L .50999 .29628 L .50815 .30096 L .49185 .30096 L .49001 .29628 L .49185 .28529 L s .14961 .28337 m .15924 .29628 L .14961 .30245 L .14038 .29628 L .14961 .28337 L s .63853 .23775 m .65482 .23739 L .67112 .23751 L .68742 .23747 L .70372 .23741 L .72001 .23923 L .72804 .24739 L .732 .26369 L .732 .27999 L .73195 .29628 L .73204 .31258 L .73182 .32888 L .72423 .34518 L .72001 .34781 L .70372 .35006 L .68742 .35003 L .67112 .34997 L .65482 .35009 L .63853 .34965 L .62602 .34518 L .62223 .3405 L .61929 .32888 L .61892 .31258 L .61902 .29628 L .61895 .27999 L .61902 .26369 L .62223 .24756 L .62232 .24739 L .63853 .23775 L s .27999 .23923 m .29628 .23741 L .31258 .23747 L .32888 .23751 L .34518 .23739 L .36147 .23775 L .37768 .24739 L .37777 .24756 L .38098 .26369 L .38105 .27999 L .38098 .29628 L .38108 .31258 L .38071 .32888 L .37777 .3405 L .37398 .34518 L .36147 .34965 L .34518 .35009 L .32888 .34997 L .31258 .35003 L .29628 .35006 L .27999 .34781 L .27577 .34518 L .26818 .32888 L .26796 .31258 L .26805 .29628 L .268 .27999 L .268 .26369 L .27196 .24739 L .27999 .23923 L s .67112 .11043 m .68604 .11701 L .67112 .12888 L .66668 .11701 L .67112 .11043 L s .32888 .11043 m .33332 .11701 L .32888 .12888 L .31396 .11701 L .32888 .11043 L s .8015 .06373 m .8178 .06147 L .83409 .0618 L .85039 .06202 L .86669 .06179 L .88299 .06147 L .89928 .06474 L .90363 .06812 L .90868 .08442 L .90824 .10072 L .90772 .11701 L .90753 .13331 L .90736 .14961 L .90443 .16591 L .89928 .17086 L .88299 .17569 L .86669 .17575 L .85039 .17565 L .83409 .17575 L .8178 .1757 L .8015 .1722 L .79603 .16591 L .79313 .14961 L .79297 .13331 L .79278 .11701 L .79227 .10072 L .79183 .08442 L .79689 .06812 L .8015 .06373 L s .45926 .06177 m .47555 .06159 L .49185 .06196 L .50815 .06196 L .52445 .06159 L .54074 .06177 L .55336 .06812 L .55704 .07941 L .55731 .08442 L .55704 .09914 L .557 .10072 L .5567 .11701 L .55658 .13331 L .55646 .14961 L .55322 .16591 L .54074 .17504 L .52445 .17581 L .50815 .17566 L .49185 .17566 L .47555 .17581 L .45926 .17504 L .44678 .16591 L .44354 .14961 L .44342 .13331 L .4433 .11701 L .443 .10072 L .44296 .09914 L .44269 .08442 L .44296 .07941 L .44664 .06812 L .45926 .06177 L s .10072 .06474 m .11701 .06147 L .13331 .06179 L .14961 .06202 L .16591 .0618 L .1822 .06147 L .1985 .06373 L .20311 .06812 L .20817 .08442 L .20773 .10072 L .20722 .11701 L .20703 .13331 L .20687 .14961 L .20397 .16591 L .1985 .1722 L .1822 .1757 L .16591 .17575 L .14961 .17565 L .13331 .17575 L .11701 .17569 L .10072 .17086 L .09557 .16591 L .09264 .14961 L .09247 .13331 L .09228 .11701 L .09176 .10072 L .09132 .08442 L .09637 .06812 L .10072 .06474 L s .01923 .34791 m .02273 .34518 L .0295 .32888 L .02793 .31258 L .02672 .29628 L .02745 .27999 L .02978 .26369 L .02654 .24739 L .01923 .23914 L s .01923 .59021 m .02944 .60593 L .02984 .62223 L .03134 .63853 L .03553 .6521 L .03647 .65482 L .04194 .67112 L .04951 .68742 L .05183 .69214 L .06067 .70372 L .06812 .7125 L .07631 .72001 L .08442 .72619 L .10072 .73595 L .10124 .73631 L .11701 .74172 L .13331 .74388 L .14961 .74464 L .16591 .7439 L .1822 .7418 L .19824 .73631 L .1985 .73613 L .2148 .72637 L .22317 .72001 L .2311 .71277 L .23882 .70372 L .24739 .69254 L .24993 .68742 L .25757 .67112 L .26312 .65482 L .26369 .65328 L .26566 .63853 L .267 .62223 L .26816 .60593 L .27999 .59029 L .28246 .58963 L .29628 .58828 L .31258 .58839 L .32888 .58847 L .34518 .5883 L .36147 .58867 L .36739 .58963 L .37777 .59682 L .38067 .60593 L .38229 .62223 L .3841 .63853 L .38736 .65482 L .39212 .67112 L .39407 .67727 L .39982 .68742 L Mistroke .41037 .70371 L .41037 .70372 L .42634 .72001 L .42666 .72029 L .44296 .73156 L .45155 .73631 L .45926 .73917 L .47555 .74291 L .49185 .74445 L .50815 .74445 L .52445 .74291 L .54074 .73917 L .54845 .73631 L .55704 .73156 L .57334 .72029 L .57366 .72001 L .58963 .70372 L .58963 .70371 L .60018 .68742 L .60593 .67727 L .60788 .67112 L .61264 .65482 L .6159 .63853 L .61771 .62223 L .61933 .60593 L .62223 .59682 L .63261 .58963 L .63853 .58867 L .65482 .5883 L .67112 .58847 L .68742 .58839 L .70372 .58828 L .71754 .58963 L .72001 .59029 L .73184 .60593 L .733 .62223 L .73434 .63853 L .73631 .65328 L .73688 .65482 L .74243 .67112 L .75007 .68742 L .75261 .69254 L .76118 .70372 L .7689 .71277 L .77683 .72001 L .7852 .72637 L .8015 .73613 L .80176 .73631 L .8178 .7418 L .83409 .7439 L Mistroke .85039 .74464 L .86669 .74388 L .88299 .74172 L .89876 .73631 L .89928 .73595 L .91558 .72619 L .92369 .72001 L .93188 .7125 L .93933 .70372 L .94817 .69214 L .95049 .68742 L .95806 .67112 L .96353 .65482 L .96447 .6521 L .96866 .63853 L .97016 .62223 L .97056 .60593 L .98077 .59021 L Mfstroke .98077 .34791 m .97727 .34518 L .9705 .32888 L .97207 .31258 L .97328 .29628 L .97255 .27999 L .97022 .26369 L .97346 .24739 L .98077 .23914 L s .85039 .63495 m .85957 .63853 L .85166 .65482 L .85039 .65487 L .8487 .65482 L .84083 .63853 L .85039 .63495 L s .49185 .63603 m .50815 .63603 L .50999 .63853 L .50815 .6535 L .49185 .6535 L .49001 .63853 L .49185 .63603 L s .14961 .63495 m .15917 .63853 L .1513 .65482 L .14961 .65487 L .14834 .65482 L .14043 .63853 L .14961 .63495 L s .67112 .45906 m .68151 .45926 L .68451 .47555 L .67112 .47764 L .66805 .47555 L .67065 .45926 L .67112 .45906 L s .32888 .45906 m .32935 .45926 L .33195 .47555 L .32888 .47764 L .31549 .47555 L .31849 .45926 L .32888 .45906 L s .8178 .42654 m .83409 .4227 L .85039 .42201 L .86669 .42273 L .88297 .42666 L .88299 .42667 L .89628 .44296 L .89796 .45926 L .89834 .47555 L .89785 .49185 L .89289 .50815 L .88299 .51438 L .86669 .51724 L .85039 .51773 L .83409 .51726 L .8178 .51448 L .80895 .50815 L .80273 .49185 L .80227 .47555 L .80263 .45926 L .80426 .44296 L .81753 .42666 L .8178 .42654 L s .47555 .42389 m .49185 .42222 L .50815 .42222 L .52445 .42389 L .53312 .42666 L .54074 .43153 L .54557 .44296 L .54792 .45926 L .54851 .47555 L .54777 .49185 L .5413 .50815 L .54074 .50867 L .52445 .51645 L .50815 .51756 L .49185 .51756 L .47555 .51645 L .45926 .50867 L .4587 .50815 L .45223 .49185 L .45149 .47555 L .45208 .45926 L .45443 .44296 L .45926 .43153 L .46688 .42666 L .47555 .42389 L s .13331 .42273 m .14961 .42201 L .16591 .4227 L .1822 .42654 L .18247 .42666 L .19574 .44296 L .19737 .45926 L .19773 .47555 L .19727 .49185 L .19105 .50815 L .1822 .51448 L .16591 .51726 L .14961 .51773 L .13331 .51724 L .11701 .51438 L .10711 .50815 L .10215 .49185 L .10166 .47555 L .10204 .45926 L .10372 .44296 L .11701 .42667 L .11703 .42666 L .13331 .42273 L s .85039 .28364 m .85928 .29628 L .85039 .30207 L .84109 .29628 L .85039 .28364 L s .49185 .28558 m .50815 .28558 L .50981 .29628 L .50815 .30062 L .49185 .30062 L .49019 .29628 L .49185 .28558 L s .14961 .28364 m .15891 .29628 L .14961 .30207 L .14072 .29628 L .14961 .28364 L s .63853 .25356 m .65482 .24858 L .67112 .24788 L .68742 .2481 L .70372 .24989 L .71869 .26369 L .72001 .27268 L .72087 .27999 L .72142 .29628 L .72037 .31258 L .72001 .31513 L .71694 .32888 L .70372 .33809 L .68742 .34057 L .67112 .34092 L .65482 .33987 L .63853 .33366 L .63417 .32888 L .6287 .31258 L .62772 .29628 L .62823 .27999 L .63152 .26369 L .63853 .25356 L s .29628 .24989 m .31258 .2481 L .32888 .24788 L .34518 .24858 L .36147 .25356 L .36848 .26369 L .37177 .27999 L .37228 .29628 L .3713 .31258 L .36583 .32888 L .36147 .33366 L .34518 .33987 L .32888 .34092 L .31258 .34057 L .29628 .33809 L .28306 .32888 L .27999 .31513 L .27963 .31258 L .27858 .29628 L .27913 .27999 L .27999 .27268 L .28131 .26369 L .29628 .24989 L s .67112 .11078 m .68581 .11701 L .67112 .1286 L .66699 .11701 L .67112 .11078 L s .32888 .11078 m .33301 .11701 L .32888 .1286 L .31419 .11701 L .32888 .11078 L s .8178 .0729 m .83409 .07069 L .85039 .07033 L .86669 .0707 L .88299 .07298 L .89563 .08442 L .89813 .10072 L .89831 .11701 L .8977 .13331 L .89501 .14961 L .88299 .16229 L .86669 .16512 L .85039 .16555 L .83409 .16514 L .8178 .1624 L .80551 .14961 L .80288 .13331 L .80229 .11701 L .80247 .10072 L .8049 .08442 L .8178 .0729 L s .45926 .0792 m .47555 .0713 L .49185 .07047 L .50815 .07047 L .52445 .0713 L .54074 .0792 L .54467 .08442 L .54819 .10072 L .54846 .11701 L .54753 .13331 L .54397 .14961 L .54074 .15587 L .52445 .16437 L .50815 .16543 L .49185 .16543 L .47555 .16437 L .45926 .15587 L .45603 .14961 L .45247 .13331 L .45154 .11701 L .45181 .10072 L .45533 .08442 L .45926 .0792 L s .11701 .07298 m .13331 .0707 L .14961 .07033 L .16591 .07069 L .1822 .0729 L .1951 .08442 L .19753 .10072 L .19771 .11701 L .19712 .13331 L .19449 .14961 L .1822 .1624 L .16591 .16514 L .14961 .16555 L .13331 .16512 L .11701 .16229 L .10499 .14961 L .1023 .13331 L .10169 .11701 L .10187 .10072 L .10437 .08442 L .11701 .07298 L s .01923 .31686 m .01947 .31258 L .01979 .29628 L .01964 .27999 L .01923 .27106 L s .01923 .61542 m .02036 .62223 L .02215 .63853 L .02608 .65482 L .03515 .67112 L .03553 .67193 L .04406 .68742 L .05183 .70014 L .05483 .70372 L .06812 .71809 L .0703 .72001 L .08442 .73064 L .09361 .73631 L .10072 .73948 L .11701 .74535 L .13331 .74742 L .14961 .74851 L .16591 .74746 L .1822 .74543 L .1985 .73959 L .20587 .73631 L .2148 .73081 L .2292 .72001 L .2311 .71834 L .24467 .70372 L .24739 .70048 L .25543 .68742 L .26369 .67256 L .26411 .67112 L .26909 .65482 L .2735 .63853 L .2777 .62223 L .27999 .6161 L .28581 .60593 L .29628 .60027 L .31258 .59788 L .32888 .59754 L .34518 .59859 L .36147 .60401 L .3642 .60593 L .37296 .62223 L .37618 .63853 L .37777 .64859 L .37985 .65482 L .38626 .67112 L .39374 .68742 L .39407 .68815 L .4054 .70372 L .41037 .71004 L .42077 .72001 L Mistroke .42666 .72493 L .44296 .73584 L .44378 .73631 L .45926 .74269 L .47555 .74627 L .49185 .74822 L .50815 .74822 L .52445 .74627 L .54074 .74269 L .55622 .73631 L .55704 .73584 L .57334 .72493 L .57923 .72001 L .58963 .71004 L .5946 .70372 L .60593 .68815 L .60626 .68742 L .61374 .67112 L .62015 .65482 L .62223 .64859 L .62382 .63853 L .62704 .62223 L .6358 .60593 L .63853 .60401 L .65482 .59859 L .67112 .59754 L .68742 .59788 L .70372 .60027 L .71419 .60593 L .72001 .6161 L .7223 .62223 L .7265 .63853 L .73091 .65482 L .73589 .67112 L .73631 .67256 L .74457 .68742 L .75261 .70048 L .75533 .70372 L .7689 .71834 L .7708 .72001 L .7852 .73081 L .79413 .73631 L .8015 .73959 L .8178 .74543 L .83409 .74746 L .85039 .74851 L .86669 .74742 L .88299 .74535 L .89928 .73948 L .90639 .73631 L Mistroke .91558 .73064 L .9297 .72001 L .93188 .71809 L .94517 .70372 L .94817 .70014 L .95594 .68742 L .96447 .67193 L .96485 .67112 L .97392 .65482 L .97785 .63853 L .97964 .62223 L .98077 .61542 L Mfstroke .98077 .31686 m .98053 .31258 L .98021 .29628 L .98036 .27999 L .98077 .27106 L s .85039 .63519 m .85927 .63853 L .85039 .65468 L .84113 .63853 L .85039 .63519 L s .49185 .63624 m .50815 .63624 L .50982 .63853 L .50815 .65328 L .49185 .65328 L .49018 .63853 L .49185 .63624 L s .14961 .63519 m .15887 .63853 L .14961 .65468 L .14073 .63853 L .14961 .63519 L s .67112 .45922 m .68112 .45926 L .68425 .47555 L .67112 .47741 L .66836 .47555 L .67104 .45926 L .67112 .45922 L s .32888 .45922 m .32896 .45926 L .33164 .47555 L .32888 .47741 L .31575 .47555 L .31888 .45926 L .32888 .45922 L s .83409 .44277 m .85039 .43894 L .86669 .44292 L .86677 .44296 L .87976 .45926 L .88119 .47555 L .87556 .49185 L .86669 .49817 L .85039 .50097 L .83409 .49827 L .82496 .49185 L .81933 .47555 L .82077 .45926 L .83373 .44296 L .83409 .44277 L s .49185 .43989 m .50815 .43989 L .51674 .44296 L .52445 .44898 L .52955 .45926 L .53104 .47555 L .52511 .49185 L .52445 .49261 L .50815 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y(are)e(mainly)h FA(d)p FE(-band)g(metals)f(where)h(the)g (magnetic)f(e\013ects)h(originate)f(from)g(the)i(ex-)165 4664 y(c)n(hange)38 b(coupling)g(b)r(et)n(w)n(een)g(the)h FA(d)g FE(electrons.)e(There)h(is)g(a)g(comp)r(etition)h(b)r(et)n(w)n (een)p eop end %%Page: 164 45 TeXDict begin 164 175 bop 165 100 a FC(164)153 b(6.)42 b(Surface)26 b(magnetism)165 282 y FE(these)h(exc)n(hange)d(e\013ects)j (and)f(the)g(smearing)f(of)h(the)h(densit)n(y)f(of)g(state.)g(Broad)f (bands)165 382 y(resulting)40 b(from)g(small)g(nearest-neigh)n(b)r(or)e (distances)i(are)f(usually)h(non-magnetic,)165 482 y(while)32 b(transition)f(metals)g(with)h(partially)e(\014lled)i FA(d)p FE(-bands)f(are)f(magnetic)h(for)g(larger)165 581 y(v)n(olumes)38 b(and)h(lo)n(w)n(er)e(densities.)i(As)f(a)h (consequence,)e(a)i(magnetic)f(material)g(suc)n(h)165 681 y(as)32 b(iron)g(b)r(ecomes)g(non-magnetic)f(when)i(it)g(is)f (compressed,)f(or)g(con)n(v)n(ersely)-7 b(,)31 b(a)h(non-)165 780 y(magnetic)25 b(material)f(suc)n(h)g(as)g(Pd)h(b)r(ecomes)f (magnetic)h(up)r(on)g(expansion)f([262].)f(With)165 880 y(the)33 b(same)e(argumen)n(ts,)f(surfaces)h(should)h(sho)n(w)f(larger) f(magnetic)h(momen)n(ts)h(as)f(the)165 980 y(bulk)d(b)r(ecause)f(of)h (the)g(lo)n(w)n(er)e(co)r(ordination)g(of)i(the)g(atoms.)290 1079 y(Although)c(the)h FA(d)p FE(-electrons)f(of)g(transition)g (metals)g(are)g(forming)f(bands,)i(they)f(are)165 1179 y(still)g(rather)e(lo)r(calized)h(compared)g(to)g FA(s)g FE(and)h FA(p)f FE(electrons.)g(Therefore)f(the)i(magnetism)165 1279 y(in)d(these)f(materials)f(is)h(con)n(trolled)f(b)n(y)h(the)h(h)n (ybridization)e(b)r(et)n(w)n(een)h(the)h FA(d)f FE(electrons)f(of)165 1378 y(nearest-neigh)n(b)r(or)i(sites.)h(The)h(basic)f(ph)n(ysics)g (underlying)g(the)h(exc)n(hange)e(in)n(teraction)165 1478 y(can)28 b(th)n(us)h(b)r(e)g(understo)r(o)r(d)f(using)g(the)g (simplest)h(molecule,)f(the)h(H)2308 1490 y Fx(2)2374 1478 y FE(molecule,)f(as)f(an)165 1577 y(example)38 b([11].)f(W)-7 b(e)38 b(will)g(sho)n(w)f(that)h(a)g(magnetic)f(solution)h(can)f(exist) h(ev)n(en)f(if)h(no)165 1677 y(magnetism)22 b(is)f(explicitly)h(tak)n (en)g(in)n(to)f(accoun)n(t)g(in)h(the)g(Hamiltonian.)g(The)g (electronic)165 1777 y(Hamiltonian)28 b(of)f(a)g(h)n(ydrogen)f (molecule)i(for)f(\014xed)g(n)n(uclei)h(can)f(b)r(e)h(written)g(as)313 1974 y FA(H)k FE(=)545 1918 y Ft(p)594 1930 y Fx(1)p 513 1955 151 4 v 513 2031 a FE(2)p FA(m)628 2043 y Fv(e)692 1974 y FE(+)814 1918 y Ft(p)864 1930 y Fq(1)p 784 1955 V 784 2031 a FE(2)p FA(m)899 2043 y Fv(e)963 1974 y Fs(\000)1189 1918 y FA(e)1228 1888 y Fx(2)p 1056 1955 342 4 v 1056 2031 a Fs(j)p Ft(r)1126 2043 y Fx(1)1181 2031 y Fs(\000)18 b Ft(R)1337 2043 y Fx(1)1374 2031 y Fs(j)1426 1974 y(\000)1652 1918 y FA(e)1691 1888 y Fx(2)p 1519 1955 V 1519 2031 a Fs(j)p Ft(r)1588 2043 y Fx(1)1644 2031 y Fs(\000)g Ft(R)1800 2043 y Fx(2)1837 2031 y Fs(j)503 2209 y(\000)710 2152 y FA(e)749 2122 y Fx(2)p 578 2190 V 578 2266 a Fs(j)p Ft(r)647 2278 y Fx(2)703 2266 y Fs(\000)g Ft(R)859 2278 y Fx(1)896 2266 y Fs(j)947 2209 y(\000)1173 2152 y FA(e)1212 2122 y Fx(2)p 1040 2190 V 1040 2266 a Fs(j)p Ft(r)1110 2278 y Fx(2)1166 2266 y Fs(\000)g Ft(R)1322 2278 y Fx(2)1359 2266 y Fs(j)1410 2209 y FE(+)1623 2152 y FA(e)1662 2122 y Fx(2)p 1503 2190 316 4 v 1503 2266 a Fs(j)p Ft(r)1573 2278 y Fx(1)1629 2266 y Fs(\000)g Ft(r)1758 2278 y Fx(2)1795 2266 y Fs(j)1847 2209 y FE(+)2086 2152 y FA(e)2125 2122 y Fx(2)p 1940 2190 368 4 v 1940 2266 a Fs(j)p Ft(R)2036 2278 y Fx(1)2091 2266 y Fs(\000)g Ft(R)2247 2278 y Fx(2)2284 2266 y Fs(j)2331 2209 y FA(;)404 b FE(\(6.1\))165 2401 y(where)39 b Ft(p)466 2413 y Fv(i)533 2401 y FE(and)f Ft(r)752 2413 y Fv(i)818 2401 y FE(are)g(the)h(momen)n(ta)f(and)h(the)g (co)r(ordinates)e(of)i(b)r(oth)g(electrons,)165 2501 y(resp)r(ectiv)n(ely)-7 b(,)36 b(and)f Ft(R)885 2513 y Fv(i)949 2501 y FE(are)g(the)h(lo)r(cations)g(of)g(the)g(n)n(uclei,)g (i.e.,)g(here)g(the)g(protons.)165 2601 y(Note)21 b(that)f(this)h 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y(an)n(tisymmetric)35 b(with)h(resp)r(ect)f (to)h(the)g(in)n(terc)n(hange)e(of)h(b)r(oth)h(electrons.)f(The)g(spin) 165 482 y(singlet)30 b(state)g(is)g(an)n(tisymmetric;)g(hence)g(it)g (has)g(to)g(b)r(e)g(coupled)g(with)h(a)f(symmetric)165 581 y(spatial)22 b(w)n(a)n(v)n(e)f(function.)i(The)g(triplet)f(state,)h (on)f(the)h(other)f(hand,)g(is)h(symmetric)f(with)165 681 y(resp)r(ect)j(to)g(the)g(in)n(terc)n(hange)e(of)i(the)h(t)n(w)n(o) e(electrons;)g(therefore)g(the)h(spatial)f(part)h(has)165 780 y(to)j(b)r(e)h(an)n(tisymmetric.)e(W)-7 b(e)29 b(will)f(denote)g(b) n(y)g FA(E)1695 792 y Fv(s)1758 780 y FE(and)g FA(E)1981 792 y Fv(t)2039 780 y FE(the)g(lo)n(w)n(est)f(eigen)n(v)-5 b(alues)27 b(of)165 880 y(the)21 b(singlet)f(\(symmetric\))g(and)g (triplet)h(\(an)n(tisymmetric\))f(solutions)f(of)h(the)h(electronic)165 980 y(t)n(w)n(o-particle)d(Hamiltonian)h(\(6.1\).)h(The)f(sign)g(of)h (the)g(singlet-triplet)f(splitting)h FA(E)2734 992 y Fv(s)2772 980 y Fs(\000)r FA(E)2900 992 y Fv(t)165 1079 y FE(will)26 b(determine)g(whether)g(the)g(ground)f(state)h(will)g(ha)n (v)n(e)e(spin)i(zero)f(or)g(spin)h(one.)f(It)h(is)165 1179 y(imp)r(ortan)n(t)f(to)h(recall)e(that)i(this)f(splitting)h(is)f (a)g(consequence)f(of)i(a)f(spin-indep)r(enden)n(t)165 1279 y(Sc)n(hr\177)-42 b(odinger)32 b(equation,)g(i.e.,)i(there)e(migh) n(t)i(b)r(e)f(a)g(magnetic)f(solution)h(although)f(no)165 1378 y(magnetic)c(e\013ects)f(are)g(explicitly)h(included.)290 1478 y(In)k(order)e(to)i(appro)n(ximately)e(solv)n(e)h(the)h (electronic)f(Sc)n(hr\177)-42 b(odinger)30 b(equation,)i(w)n(e)165 1577 y(follo)n(w)h(the)g(so-called)e FD(Heitler-L)l(ondon)40 b FE(ansatz)33 b(of)g(using)f(the)i(single-particle)d(solu-)165 1677 y(tions)25 b(of)g(the)g(isolated)f(h)n(ydrogen)f(atom.)i(If)g(w)n (e)f(denote)h(with)h FA(\036)2190 1689 y Fv(i)2243 1677 y FE(the)f(electronic)f(w)n(a)n(v)n(e)165 1777 y(function)i(of)f(the)h (h)n(ydrogen)e(atom)h FA(i)p FE(,)g(the)g(symmetric)g(and)g(an)n (tisymmetric)g(solutions)165 1876 y(are)i(giv)n(en)g(b)n(y)313 2060 y FA( )367 2072 y Fv(s;t)447 2060 y FE(\()p Ft(r)526 2072 y Fx(1)563 2060 y FA(;)14 b Ft(r)647 2072 y Fx(2)684 2060 y FE(\))23 b(=)872 2004 y(1)p 837 2041 111 4 v 837 2058 a Fs(p)p 906 2058 42 4 v 68 x FE(2)958 1993 y Fu(\000)996 2060 y FA(\036)1045 2072 y Fx(1)1082 2060 y FE(\()p Ft(r)1161 2072 y Fx(1)1199 2060 y FE(\))p FA(\036)1280 2072 y Fx(2)1318 2060 y FE(\()p Ft(r)1396 2072 y Fx(2)1434 2060 y FE(\))18 b Fs(\006)g FA(\036)1616 2072 y Fx(1)1654 2060 y FE(\()p Ft(r)1733 2072 y Fx(2)1770 2060 y FE(\))p FA(\036)1851 2072 y Fx(2)1889 2060 y FE(\()p Ft(r)1968 2072 y Fx(1)2005 2060 y FE(\))2037 1993 y Fu(\001)2089 2060 y FA(:)646 b FE(\(6.5\))165 2253 y(The)40 b(+)f(sign)g(is)h(for)f(the)h(spin)f (singlet,)h(the)g Fs(\000)f FE(sign)g(for)g(the)h(spin)f(triplet.)h (Using)165 2353 y(these)34 b(singlet)g(and)g(triplet)g(w)n(a)n(v)n(e)e (functions,)i(the)h(singlet-triplet)e(splitting)h(can)g(b)r(e)165 2452 y(ev)-5 b(aluated)28 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2205 m 8730 2205 l 8730 7965 l 2745 7965 l cp gs col0 s gr % Polyline n 2745 2790 m 2925 2790 l gs col0 s gr % Polyline n 2745 3960 m 2925 3960 l gs col0 s gr % Polyline n 2745 6255 m 2925 6255 l gs col0 s gr % Polyline n 2745 7380 m 2925 7380 l gs col0 s gr % Polyline n 8550 2790 m 8730 2790 l gs col0 s gr % Polyline n 8550 3960 m 8730 3960 l gs col0 s gr % Polyline n 8550 6255 m 8730 6255 l gs col0 s gr % Polyline n 8550 7380 m 8730 7380 l gs col0 s gr % Polyline n 2745 3375 m 2880 3375 l gs col0 s gr % Polyline n 2745 5670 m 2880 5670 l gs col0 s gr % Polyline n 2745 6795 m 2880 6795 l gs col0 s gr % Polyline n 8595 3375 m 8730 3375 l gs col0 s gr % Polyline n 8595 4545 m 8730 4545 l gs col0 s gr % Polyline n 8550 5670 m 8730 5670 l gs col0 s gr % Polyline n 8550 6795 m 8730 6795 l gs col0 s gr % Polyline n 3780 7965 m 3780 7785 l gs col0 s gr % Polyline n 4725 7965 m 4725 7785 l gs col0 s gr % Polyline n 5760 7965 m 5760 7785 l gs col0 s gr % Polyline n 7740 7965 m 7740 7785 l gs col0 s gr % Polyline n 3240 7965 m 3240 7830 l gs col0 s gr % Polyline n 4230 7965 m 4230 7830 l gs col0 s gr % Polyline n 5265 7965 m 5265 7830 l gs col0 s gr % Polyline n 6255 7965 m 6255 7830 l gs col0 s gr % Polyline n 7245 7965 m 7245 7830 l gs col0 s gr % Polyline n 8235 7965 m 8235 7830 l gs col0 s gr % Polyline n 6750 2205 m 6750 7965 l gs col0 s gr % Polyline n 2745 5130 m 8730 5130 l gs col0 s gr % Polyline n 2745 4545 m 2880 4545 l gs col0 s gr /Helvetica-iso ff 375.00 scf sf 3600 8370 m gs 1 -1 sc (-6) col0 sh gr /Helvetica-iso ff 375.00 scf sf 4590 8370 m gs 1 -1 sc (-4) col0 sh gr /Helvetica-iso ff 375.00 scf sf 5580 8370 m gs 1 -1 sc (-2) col0 sh gr /Helvetica-iso ff 375.00 scf sf 6660 8370 m gs 1 -1 sc (0) col0 sh gr /Helvetica-iso ff 375.00 scf sf 7650 8370 m gs 1 -1 sc (2) col0 sh gr /Helvetica-iso ff 375.00 scf sf 2430 5220 m gs 1 -1 sc (0) col0 sh gr /Helvetica-iso ff 375.00 scf sf 2430 4050 m gs 1 -1 sc (1) col0 sh gr /Helvetica-iso ff 375.00 scf sf 2430 2880 m gs 1 -1 sc (2) col0 sh gr /Helvetica-iso ff 375.00 scf sf 5040 8820 m gs 1 -1 sc (Energy \(eV\)) col0 sh gr /Helvetica-iso ff 375.00 scf sf 2160 6525 m gs 1 -1 sc 90.0 rot (LDOS \(states/eV\)) col0 sh gr /Helvetica-iso ff 330.00 scf sf 3285 2745 m gs 1 -1 sc (spin up) col0 sh gr /Helvetica-iso ff 330.00 scf sf 3150 7425 m gs 1 -1 sc (spin down) col0 sh gr /Helvetica-iso ff 330.00 scf sf 6930 2700 m gs 1 -1 sc (Ru/Ag\(100\)) col0 sh gr /Helvetica-Bold-iso ff 420.00 scf sf 3240 3735 m gs 1 -1 sc (b\)) col0 sh gr /Helvetica-iso ff 375.00 scf sf 2295 7470 m gs 1 -1 sc (-2) col0 sh gr /Helvetica-iso ff 375.00 scf sf 2295 6390 m gs 1 -1 sc (-1) col0 sh gr % here ends figure; $F2psEnd rs showpage %%EndDocument @endspecial 2718 1262 a currentpoint grestore moveto 2718 1262 a 165 1387 a Fz(Fig.)39 b(6.2.)74 b FC(a\))34 b(Lo)r(cal)i(magnetic)g(momen)n(ts)e(calculated)i (for)f(3)p Fk(d)g FC(and)f(4)p Fk(d)h FC(monola)n(y)n(ers)g(on)165 1470 y(Ag\(100\))42 b(from)f(scalar-relativistic)i(LSD)n(A)c (calculations,)k(i.e.)e(without)g(spin-orbit)f(cou-)165 1553 y(pling)c([270])h(and)e(from)h(fully)f(relativistic)i(LSD)n(A)d (calculations)j([271];)h(b\))c(Lo)r(cal)j(densit)n(y)165 1636 y(of)27 b(states)f(of)h(a)f(Ru)f(o)n(v)n(erla)n(y)n(er)g(on)h (Ag\(100\))g(\(after)h([270]\).)165 1904 y FE(surface)k(breaks)g(the)h (symmetry)f(p)r(erp)r(endicular)h(to)g(the)g(\014lm.)g(One)g(can)f(sho) n(w)g(that)165 2003 y(this)d(magnetic)f(anisotrop)n(y)f(stabilizes)h (the)h(long-range)d(order)h(in)i(thin)h(\014lms)e([269].)290 2103 y(Using)43 b(an)f(scalar-relativistic)e(LSD)n(A)k(approac)n(h,)d (the)i(magnetism)f(of)h(transi-)165 2202 y(tion)37 b(metal)g(o)n(v)n (erla)n(y)n(ers)c(on)j(the)h(\(100\))f(surfaces)f(of)i(Au)g(and)g(Ag)f (has)g(b)r(een)h(in)n(v)n(es-)165 2302 y(tigated)29 b([270].)f(The)g (lo)r(cal)h(magnetic)f(momen)n(ts)h(obtained)f(from)g(these)h (calculations)165 2402 y(are)f(plotted)i(in)f(Fig.)g(6.2a.)f(And)i (indeed,)g(according)d(to)i(these)g(calculations,)f(mono-)165 2501 y(la)n(y)n(ers)c(of)i(the)h(4)p FA(d)e FE(metals)h(Tc,)g(Ru)g(and) g(Rh)g(are)f(ferromagnetic)g(although)g(the)h(corre-)165 2601 y(sp)r(onding)h(bulk)f(materials)f(are)h(non-magnetic.)f(Ob)n (viously)-7 b(,)26 b(band)g(structure)g(e\013ects)165 2701 y(induced)k(b)n(y)f(the)h(lo)n(w)n(er)e(co)r(ordination)g (stabilize)h(the)g(o)n(v)n(erla)n(y)n(er)d(magnetism)j(for)g(the)165 2800 y(late)f(4)p FA(d)f FE(transition)g(metals.)290 2900 y(In)c(Fig.)g(6.2a,)f(additional)h(results)f(for)h(Ru)h(and)f(Rh)g (from)g(fully)h(relativistic)e(calcu-)165 2999 y(lations)e(are)f (included)i([271])e(whic)n(h)h(also)f(tak)n(e)g(the)i(spin-orbit)e (coupling)h(in)n(to)g(accoun)n(t.)165 3099 y(As)30 b(can)f(b)r(e)h (seen,)g(for)f(the)h(4)p FA(d)f FE(metals,)h(the)g(spin-orbit)f (coupling)g(hardly)g(has)g(an)g(in-)165 3199 y(\015uence)37 b(on)f(the)h(magnetic)f(momen)n(ts.)h(Ho)n(w)n(ev)n(er,)d(the)j (inclusion)f(of)h(this)g(coupling)165 3298 y(do)r(es)d(in)g(fact)h (matter)f(for)f(the)i(5)p FA(d)f FE(metals,)f(where)h (scalar-relativistic)d(calculations)165 3398 y(predict)d(the)g (Os/Ag\(100\))e(and)h(Ir/Ag\(100\))f(o)n(v)n(erla)n(y)n(ers)e(to)j(b)r (e)h(ferromagnetic)e([270])165 3498 y(while)f(the)g(ferromagnetism)e(v) -5 b(anishes)23 b(when)i(the)g(spin-orbit)e(coupling)h(is)h(tak)n(en)e (in)n(to)165 3597 y(accoun)n(t)k([271].)290 3697 y(In)i(addition,)f (Fig.)h(6.2b)f(displa)n(ys)g(the)h(lo)r(cal)f(densit)n(y)h(of)f(states) h(of)f(the)h(Ru)g(o)n(v)n(er-)165 3796 y(la)n(y)n(er)i(on)h(Ag\(100\).) g(The)g(ma)5 b(jorit)n(y)31 b(band,)h(i.e.,)h(the)g(band)f(with)h(the)g (larger)d(degree)165 3896 y(of)c(\014lling,)g(is)f(ab)r(out)h(1)g(eV)f (lo)n(w)n(er)g(in)h(energy)e(than)i(the)g(minorit)n(y)f(band)h(whic)n (h)g(means)165 3996 y(that)33 b(there)f(is)g(an)g(exc)n(hange)e (splitting)j(b)r(et)n(w)n(een)f(the)g(spin)h(up)f(and)g(the)g(spin)h (do)n(wn)165 4095 y(states)25 b(of)h(roughly)e(1)h(eV.)h(F)-7 b(or)25 b(the)h(3)p FA(d)f FE(metals)h(on)f(Ag\(100\),)f(ho)n(w)n(ev)n 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y(op)r(erator)26 b(exp)o(\()p Fs(\000)p FA(iH)7 b(t=)p FE(\026)-42 b FA(h)o FE(\))27 b(in)g(the)h(gas-surface)c (dynamics)i(comm)n(unit)n(y)h(are)f(the)h(split-)165 1639 y(op)r(erator)32 b([299,)12 b(300])32 b(and)h(the)h(Cheb)n(yc)n (hev)e([301])g(metho)r(ds.)h(In)h(the)f(split-op)r(erator)165 1739 y(metho)r(d,)c(the)f(time-ev)n(olution)e(op)r(erator)g(for)h (small)h(time)g(steps)f FA(\001t)h FE(is)f(written)h(as)313 1888 y(e)350 1854 y Fw(\000)p Fx(i)p Fv(H)t(\001t=)p Fx(\026)-34 b Fv(h)659 1888 y FE(=)23 b(e)784 1854 y Fw(\000)p Fx(i)p Fv(T)9 b(\001t=)p Fx(2\026)-34 b Fv(h)1120 1888 y FE(e)1157 1854 y Fw(\000)p Fx(i)p Fv(V)14 b(\001t=)p Fx(\026)-34 b Fv(h)1465 1888 y FE(e)1502 1854 y Fw(\000)p Fx(i)p Fv(T)9 b(\001t=)p Fx(2\026)-34 b Fv(h)1857 1888 y FE(+)46 b FA(O)r FE(\()p FA(\001t)2164 1854 y Fx(3)2202 1888 y FE(\))14 b FA(;)446 b FE(\(7.18\))165 2038 y(In)n(terestingly)37 b(enough,)h(the)g(split-op)r(erator)e(tec)n(hnique)i(for)g(a)f(certain) h(n)n(um)n(b)r(er)f(of)165 2137 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FE(=)22 b(tr)14 b(\()p FA(A\032)p FE(\))28 b FA(:)1854 b FE(\(7.21\))165 1696 y(The)30 b(time-ev)n(olution)g(of)g(the)g (reduced)g(densit)n(y)g(matrix)f(is)h(giv)n(en)f(b)n(y)h(the)h FD(Liouvil)t(le{)165 1795 y(von)f(Neumann)f(e)l(quation)35 b FE([305,)11 b(306])323 1932 y FA(@)5 b(\032)p 323 1969 92 4 v 329 2045 a(@)g(t)448 1988 y FE(=)22 b Fs(\000)622 1932 y FE(i)p 610 1969 48 4 v 610 2045 a(\026)-42 b FA(h)695 1988 y FE([)p FA(H)r(;)14 b(\032)p FE(])19 b(+)f Fs(L)1051 2000 y Fv(B)1108 1988 y FA(\032)c(;)1529 b FE(\(7.22\))165 2161 y(where)33 b(dissipation)f(e\013ects)h(are)f(tak)n(en)g(in)n(to)h (accoun)n(t)f(through)g(the)i(Liouville)e(bath)165 2260 y(op)r(erator)26 b Fs(L)557 2272 y Fv(B)614 2260 y FE(.)i(Without)g (the)g(dissipation)f(term,)g(\(7.22\))g(is)g(equiv)-5 b(alen)n(t)27 b(to)g(the)h(time-)165 2360 y(dep)r(enden)n(t)e(Sc)n (hr\177)-42 b(odinger)24 b(equation.)h(Ho)n(w)n(ev)n(er,)e(solving)h (\(7.22\))h(for)g(a)g(closed)f(system)165 2460 y(is)37 b(not)g(advisable,)f(since)h(a)f FA(N)d Fs(\002)25 b FA(N)45 b FE(matrix)37 b(has)f(to)h(b)r(e)g(determined)g(if)h(the)f(w)n (a)n(v)n(e)165 2559 y(functions)d(are)f(expanded)g(in)h(a)f(set)g(of)h FA(N)42 b FE(basis)33 b(functions)h(while)f(in)h(the)g(ordinary)165 2659 y(time-dep)r(enden)n(t)h(Sc)n(hr\177)-42 b(odinger)31 b(equation)i(the)h(w)n(a)n(v)n(e)e(function)i(is)f(just)h(represen)n (ted)165 2759 y(b)n(y)21 b(a)g FA(N)9 b FE(-dimensional)21 b(v)n(ector.)f(Still,)i(the)f(computational)g(e\013ort)g(asso)r(ciated) f(with)i(the)165 2858 y(densit)n(y-matrix)e(formalism)g(is)h(necessary) e(in)i(order)e(to)i(include)g(dissipation)f(e\013ects)h(in)165 2958 y(the)28 b(quan)n(tum)f(dynamics.)f(This)h(is)g(not)g(only)f (essen)n(tial)g(for)h(scattering)f(and)h(reactiv)n(e)165 3057 y(pro)r(cesses)i(at)g(surface,)g(but)h(also)f(for)g(reactions)g (induced)h(b)n(y)f(electronic)g(transitions)165 3157 y(\(see)39 b(Sect.)14 b(9.5\).)38 b(The)h(dissipativ)n(e)f(term)g(can)h 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Fv(B)1339 3854 y FE(is)h(not)h(fully)h(sp)r (eci\014ed.)f(There)g(is)f(a)h(phenomeno-)165 3954 y(logical)31 b(form)h(prop)r(osed)f(b)n(y)g(Lindblad)h([307])f(whic)n(h)h(guaran)n (tees)e(that)i(at)g(all)g(times)165 4054 y(the)39 b(diagonal)e(elemen)n (ts)h(of)g FA(\032)h FE(prop)r(erly)e(corresp)r(ond)g(to)h(state)g(p)r (opulations.)g(The)165 4153 y(Lindblad)28 b(semigroup)e(functional)i (is)g(giv)n(en)e(b)n(y)313 4315 y Fs(L)370 4327 y Fv(B)427 4315 y FA(\032)d FE(=)581 4236 y Fu(X)623 4415 y Fv(k)715 4247 y Fu(\000)753 4315 y FA(C)812 4327 y Fv(k)853 4315 y FA(\032C)961 4279 y Fx(+)955 4340 y Fv(k)1035 4315 y Fs(\000)1118 4247 y Fu(\010)1166 4315 y FA(C)1231 4279 y Fx(+)1225 4340 y Fv(k)1287 4315 y FA(C)1346 4327 y Fv(k)1387 4315 y FA(;)14 b(\032)1467 4247 y Fu(\011\001)1581 4315 y FA(;)1113 b FE(\(7.23\))165 4543 y(where)22 b Fs(f)p FA(A;)14 b(B)t Fs(g)22 b FE(=)h FA(AB)11 b FE(+)c FA(B)t(A)22 b FE(denotes)f(the)i(an)n(ticomm)n(utator.)d(The)i FA(C)2401 4555 y Fv(k)2464 4543 y 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cp eoclip n 3465 7875 m 3825 7875 l gs col0 s gr gr % arrowhead n 3673 7905 m 3793 7875 l 3673 7845 l 3673 7905 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 2685 7845 m 2685 7905 l 2852 7905 l 2732 7875 l 2852 7845 l cp eoclip n 3015 7875 m 2700 7875 l gs col0 s gr gr % arrowhead n 2852 7845 m 2732 7875 l 2852 7905 l 2852 7845 l cp gs 0.00 setgray ef gr col0 s % Polyline n 2610 2565 m 3060 2115 l gs col0 s gr % Polyline n 3510 3465 m 3960 3015 l gs col0 s gr % Polyline gs clippath 2890 2308 m 2848 2350 l 2966 2469 l 2903 2363 l 3009 2426 l cp eoclip n 3150 2610 m 2880 2340 l gs col0 s gr gr % arrowhead n 3009 2426 m 2903 2363 l 2966 2469 l 3009 2426 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 3769 3271 m 3811 3229 l 3693 3110 l 3757 3217 l 3650 3153 l cp eoclip n 3510 2970 m 3780 3240 l gs col0 s gr gr % arrowhead n 3650 3153 m 3757 3217 l 3693 3110 l 3650 3153 l cp gs 0.00 setgray ef gr col0 s % Polyline n 2025 2250 m 2025 2251 l 2025 2254 l 2026 2264 l 2026 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Polyline n 4957 7177 m 4957 7360 l gs col0 s gr % Polyline n 6082 6526 m 6082 6337 l gs col0 s gr % Polyline n 6082 7177 m 6082 7360 l gs col0 s gr % Polyline n 7207 6526 m 7207 6337 l gs col0 s gr % Polyline n 7207 7177 m 7207 7360 l gs col0 s gr % Polyline n 9457 6526 m 9457 6337 l gs col0 s gr % Polyline n 9457 7177 m 9457 7360 l gs col0 s gr % Polyline n 2707 6526 m 2707 6337 l gs col0 s gr % Polyline n 2707 7177 m 2707 7360 l gs col0 s gr % Polyline n 8332 6526 m 8332 6337 l gs col0 s gr % Polyline n 8332 7177 m 8332 7360 l gs col0 s gr % Polyline n 1793 6301 m 1604 6301 l gs col0 s gr % Polyline n 2444 6301 m 2627 6301 l gs col0 s gr % Polyline n 2946 6301 m 2757 6301 l gs col0 s gr % Polyline n 3597 6301 m 3780 6301 l gs col0 s gr % Polyline n 4043 6301 m 3854 6301 l gs col0 s gr % Polyline n 4694 6301 m 4877 6301 l gs col0 s gr % Polyline n 5196 6301 m 5007 6301 l gs col0 s gr % Polyline n 5847 6301 m 6030 6301 l gs col0 s gr % Polyline n 6293 6316 m 6104 6316 l gs col0 s gr % Polyline n 6944 6316 m 7127 6316 l gs col0 s gr % Polyline n 7446 6316 m 7257 6316 l gs col0 s gr % Polyline n 8097 6316 m 8280 6316 l gs col0 s gr % Polyline n 8543 6316 m 8354 6316 l gs col0 s gr % Polyline n 9194 6316 m 9377 6316 l gs col0 s gr % Polyline n 9696 6316 m 9507 6316 l gs col0 s gr % Polyline n 10347 6316 m 10530 6316 l gs col0 s gr % Polyline n 1778 7411 m 1589 7411 l gs col0 s gr % Polyline n 2429 7411 m 2612 7411 l gs col0 s gr % Polyline n 2931 7411 m 2742 7411 l gs col0 s gr % Polyline n 3582 7411 m 3765 7411 l gs col0 s gr % Polyline n 4028 7411 m 3839 7411 l gs col0 s gr % Polyline n 4679 7411 m 4862 7411 l gs col0 s gr % Polyline n 5181 7411 m 4992 7411 l gs col0 s gr % Polyline n 5832 7411 m 6015 7411 l gs col0 s gr % Polyline n 6278 7426 m 6089 7426 l gs col0 s gr % Polyline n 6929 7426 m 7112 7426 l gs col0 s gr % Polyline n 7431 7426 m 7242 7426 l gs col0 s gr % Polyline n 8082 7426 m 8265 7426 l gs col0 s gr % Polyline n 8528 7426 m 8339 7426 l gs col0 s gr 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10279 7335 l 10291 7348 l 10302 7364 l 10311 7381 l 10319 7397 l 10326 7411 l 10330 7421 l 10332 7425 l 10332 7426 l gs col-1 s gr $F2psEnd rs %%EndDocument @endspecial 2173 1572 a currentpoint grestore moveto 2173 1572 a 165 1697 a Fz(Fig.)39 b(7.2.)g FC(Summary)34 b(of)i(the)e(di\013eren)n(t)g(collision)j(pro)r (cesses)f(in)e(nonreactiv)n(e)h(scattering)165 1780 y(\(after)27 b([332]\).)313 2051 y Ft(K)399 2008 y Fw(k)399 2077 y Fv(f)465 2051 y FE(=)c Ft(K)640 2008 y Fw(k)640 2075 y Fv(i)696 2051 y FE(+)18 b Ft(G)853 2063 y Fv(mn)975 2051 y FE(+)1154 1973 y Fu(X)1058 2151 y Fx(exc)n(h)p Fv(:)p Fx(phon)p Fv(:)1384 2051 y Fs(\006)p Ft(Q)13 b FA(;)1160 b FE(\(7.27\))165 2287 y(where)27 b Ft(Q)h FE(is)f(a)g(t)n(w)n(o-dimensional)f(phonon-momen)n(tum)h(v)n(ector)f (parallel)g(to)h(the)h(sur-)165 2386 y(face.)e(The)h(plus-signs)e(in)i (the)f(sum)h(corresp)r(ond)e(to)h(the)g(excitation)g(or)g(emission)f (of)i(a)165 2486 y(phonon)32 b(while)g(the)g(min)n(us-signs)f(represen) 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y(\(HAS\))k(has)d(b)r(een)i(used)f (in)n(tensiv)n(ely)f(to)h(study)h(surface)e(crystallograph)n(y)e(and)j (the)165 2606 y(shap)r(e)25 b(of)f(ph)n(ysisorption)f(p)r(oten)n(tials) i(\(see,)f(e.g.,)g([335])g(and)g(references)f(therein\).)i(He-)165 2705 y(lium)j(atom)f(scattering)f(has)h(furthermore)f(b)r(een)h(emplo)n (y)n(ed)g(extensiv)n(ely)f(in)i(order)d(to)165 2805 y(determine)34 b(the)f(surface)g(phonon)g(sp)r(ectrum)g(in)h(one-phonon)e(collisions)g (via)h(\(7.27\))165 2904 y(and)28 b(\(7.28\))f([335].)290 3004 y(Hydrogen)k(molecules)g(ha)n(v)n(e)f(b)r(een)j(utilized)f(less)f (frequen)n(tly)h(in)g(order)e(to)i(study)165 3104 y(in)n(teraction)j(p) r(oten)n(tials)h([336].)e(The)i(coheren)n(t)f(elastic)g(scattering)g (of)h(molecules)f(is)165 3203 y(more)29 b(complex)h(than)g(atom)f (scattering)g(b)r(ecause)g(in)h(addition)g(to)g(parallel)f(momen-)165 3303 y(tum)j(transfer)f(the)h(in)n(ternal)e(degrees)h(of)g(freedom)g (of)g(the)h(molecule,)f(rotations)f(and)165 3403 y(vibrations,)24 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/Times-Roman-iso ff 450.00 scf sf 3150 8325 m gs 1 -1 sc (x) col0 sh gr /Times-Roman-iso ff 450.00 scf sf 5850 8325 m gs 1 -1 sc (x) col0 sh gr /Times-Roman-iso ff 450.00 scf sf 8775 8325 m gs 1 -1 sc (x) col0 sh gr /Times-Roman-iso ff 450.00 scf sf 11475 4725 m gs 1 -1 sc (E) col0 sh gr /Times-Roman-iso ff 450.00 scf sf 1575 900 m gs 1 -1 sc (V\(x\)) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 3420 8460 m gs 1 -1 sc (i) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 6120 8460 m gs 1 -1 sc (T) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 9000 8460 m gs 1 -1 sc (f) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 6570 4590 m gs 1 -1 sc (a) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 3330 4680 m gs 1 -1 sc (0) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 6210 3510 m gs 1 -1 sc (T) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 11790 4860 m gs 1 -1 sc (b) col0 sh gr /Times-Roman-iso ff 450.00 scf sf 6300 8325 m gs 1 -1 sc (= 0) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 9180 6300 m gs 1 -1 sc (f) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 4050 3600 m gs 1 -1 sc (+) col0 sh gr /Times-Roman-iso ff 300.00 scf sf 8730 2700 m gs 1 -1 sc (-) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 2055 1499 a currentpoint grestore moveto 2055 1499 a 165 1623 a Fz(Fig.)35 b(8.1.)h FC(Sc)n(hematic)c(represen)n(tation)g(of)g(escap)r(e)g(pro)r (cesses)h(b)r(et)n(w)n(een)f(to)f(lo)r(cally)i(stable)165 1706 y(states)27 b(with)f(forw)n(ard)h(rate)f Fk(k)1041 1675 y Fl(+)1117 1706 y FC(and)g(bac)n(kw)n(ard)f(rate)h Fk(k)1810 1675 y Fi(\000)290 1955 y FE(Consider)h(a)g(p)r(oten)n(tial)h FA(V)19 b FE(\()p FA(x)p FE(\))29 b(along)d(the)i(reaction)f(path)h(co) r(ordinate)e FA(x)j FE(connect-)165 2055 y(ing)34 b(t)n(w)n(o)e(lo)r (cally)h(stable)g(states)g(\(Fig.)14 b(8.1\).)33 b(A)n(t)h FA(x)f FE(=)g FA(x)1963 2067 y Fx(T)2047 2055 y FE(=)g(0)g(the)h (transition)e(state)165 2155 y(is)f(lo)r(cated.)g(The)g(barrier)e(for)h (the)i(forw)n(ard)d(escap)r(e)h(is)h(giv)n(en)f(b)n(y)h FA(E)2353 2167 y 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FA(k)356 3398 y Fx(TST)515 3386 y FE(=)612 3330 y FA(k)655 3342 y Fx(B)706 3330 y FA(T)p 612 3367 V 665 3443 a(h)840 3330 y FE(1)p 814 3367 94 4 v 814 3443 a FA(Z)871 3455 y Fx(0)959 3386 y FE(exp)1100 3269 y Fu(\022)1161 3386 y Fs(\000)1262 3330 y FA(E)1323 3342 y Fv(a)p 1236 3367 154 4 v 1236 3443 a FA(k)1279 3455 y Fx(B)1329 3443 y FA(T)1399 3269 y Fu(\023)1488 3386 y FA(:)1247 b FE(\(8.8\))165 3577 y(In)27 b(the)g(harmonic)f (appro)n(ximation,)f(the)i(partition)g(sum)g(in)g(the)g(initial)g(w)n (ell)f(is)h(giv)n(en)165 3676 y(b)n(y)h FA(Z)338 3688 y Fx(0)398 3676 y FE(=)22 b FA(k)528 3688 y Fx(B)579 3676 y FA(T)9 b(=)p FE(\026)-42 b FA(h)o(!)778 3688 y Fx(0)815 3676 y FE(,)28 b(i.e.,)g(w)n(e)f(obtain)g(the)h(follo)n(wing)f (rate)313 3871 y FA(k)356 3883 y Fx(TST)515 3871 y FE(=)614 3815 y FA(!)666 3827 y Fx(0)p 612 3852 92 4 v 612 3928 a FE(2)p FA(\031)756 3871 y FE(exp)896 3754 y Fu(\022)958 3871 y Fs(\000)1058 3815 y FA(E)1119 3827 y Fv(a)p 1032 3852 154 4 v 1032 3928 a FA(k)1075 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FE(nonlinear)34 b(co)r(ordinate)g(\()p FA(i)h FE(=)f(0\))h (coupled)g(to)f FA(N)44 b FE(vibrational)33 b(degrees)h(of)h(freedom.) 165 382 y(In)30 b(the)h(harmonic)d(appro)n(ximation,)g(whic)n(h)i(is)g (v)-5 b(alid)30 b(for)f(\026)-42 b FA(h!)29 b Fs(\034)e FA(k)2302 394 y Fx(B)2352 382 y FA(T)12 b FE(,)29 b(the)i(partition)165 482 y(sums)j FA(Z)437 494 y Fx(0)508 482 y FE(and)f FA(Z)732 494 y Fx(TS)854 482 y FE(in)h(the)g(initial)h(w)n(ell)e(and)h(at)f(the) i(transition)e(state)g(are)g(simply)165 581 y(giv)n(en)27 b(b)n(y)313 807 y FA(Z)370 819 y Fx(0)458 807 y FE(=)597 703 y Fv(N)574 728 y Fu(Y)573 905 y Fv(i)p Fx(=0)694 665 y Fu(\()790 751 y FA(k)833 763 y Fx(B)884 751 y FA(T)p 771 788 192 4 v 771 885 a FE(\026)-42 b FA(h!)874 842 y Fx(\(0\))871 908 y Fv(i)1000 665 y Fu(\))1095 807 y FA(;)97 b(Z)1272 819 y Fx(TS)1410 807 y FE(=)1550 703 y Fv(N)1527 728 y Fu(Y)1526 905 y Fv(i)p Fx(=1)1647 690 y Fu(\032)1738 751 y FA(k)1781 763 y Fx(B)1832 751 y FA(T)p 1719 788 191 4 v 1719 866 a FE(\026)-42 b FA(h!)1822 838 y Fx(TS)1819 890 y Fv(i)1948 690 y Fu(\033)2038 807 y FA(;)656 b FE(\(8.10\))165 1058 y(where)25 b FA(!)458 1015 y Fx(\(0\))455 1081 y Fv(i)572 1058 y FE(and)g FA(!)786 1028 y Fx(TS)783 1080 y Fv(i)899 1058 y FE(are)f(the)h(vibrational)f (frequencies)g(in)h(the)h(initial)f(w)n(ell)g(and)g(the)165 1158 y(transition)36 b(state,)h(resp)r(ectiv)n(ely)-7 b(.)36 b(W)-7 b(e)36 b(note)h(in)g(passing)e(that)i(often)g(the)g (transition)165 1258 y(state)i(is)h(denoted)f(b)n(y)g(\()p Fs(6)p FE(=\),)h(i.e.)f FA(Z)1322 1270 y Fx(TS)1452 1258 y Fs(\021)k FA(Z)1623 1227 y Fw(6)p Fx(=)1677 1258 y FE(.)d(The)f(transition)g(rate)f(can)h(no)n(w)g(b)r(e)165 1357 y(expressed)27 b(as)g([439])313 1562 y FA(k)356 1574 y Fx(TST)517 1562 y FE(=)644 1506 y FA(k)687 1518 y Fx(B)738 1506 y FA(T)p 644 1543 154 4 v 697 1619 a(h)845 1506 y(Z)908 1476 y Fx(TS)p 845 1543 151 4 v 874 1619 a FA(Z)931 1631 y Fx(0)1020 1562 y FE(exp)1161 1445 y Fu(\022)1222 1562 y Fs(\000)1322 1506 y FA(E)1383 1518 y Fv(a)p 1296 1543 154 4 v 1296 1619 a FA(k)1339 1631 y Fx(B)1390 1619 y FA(T)1460 1445 y Fu(\023)517 1915 y FE(=)669 1859 y(1)p 644 1896 92 4 v 644 1972 a(2)p FA(\031)808 1722 y Fv(N)798 1739 y Fu(Q)783 1874 y Fv(i)p Fx(=0)905 1801 y FA(!)960 1758 y Fx(\(0\))957 1824 y Fv(i)p 783 1896 266 4 v 808 1954 a(N)798 1970 y Fu(Q)783 2106 y Fv(i)p Fx(=1)905 2032 y FA(!)960 2004 y Fx(TS)957 2056 y Fv(i)1100 1915 y FE(exp)1241 1798 y Fu(\022)1302 1915 y Fs(\000)1402 1859 y FA(E)1463 1871 y Fv(a)p 1376 1896 154 4 v 1376 1972 a FA(k)1419 1984 y Fx(B)1470 1972 y FA(T)1540 1798 y Fu(\023)1629 1915 y FA(:)1065 b FE(\(8.11\))194 2230 y(This)29 b(result)g(for)f(the)h(TST)g(rate)f(can)h(b)r(e)g (reform)n(ulated)f(emplo)n(ying)g(the)h(Helmholtz)165 2329 y(free)f(energy)e FA(F)40 b FE(via)27 b(the)h(substitution)313 2479 y FA(Z)h FE(=)22 b(exp[)p Fs(\000)p FE(\()p FA(E)i Fs(\000)18 b FA(T)12 b(S)5 b FE(\))p FA(=)p FE(\()p FA(k)1167 2491 y Fx(B)1216 2479 y FA(T)12 b FE(\)])23 b(=)f(exp[)p Fs(\000)p FA(F)7 b(=)p FE(\()p FA(k)1834 2491 y Fx(B)1885 2479 y FA(T)12 b FE(\)])716 b(\(8.12\))165 2628 y(Inserting)27 b(this)h(expression)e(in)n(to)i(\(8.11\),)f(w)n(e)g(arriv)n(e)e(at)313 2827 y FA(k)356 2839 y Fx(TST)515 2827 y FE(=)612 2771 y FA(k)655 2783 y Fx(B)706 2771 y FA(T)p 612 2808 V 665 2884 a(h)818 2827 y FE(exp)958 2710 y Fu(\022)1029 2771 y FA(\001S)p 1029 2808 125 4 v 1045 2884 a(k)1088 2896 y Fx(B)1164 2710 y Fu(\023)1267 2827 y FE(exp)1408 2710 y Fu(\022)1469 2827 y Fs(\000)1569 2771 y FA(E)1630 2783 y Fv(a)p 1543 2808 154 4 v 1543 2884 a FA(k)1586 2896 y Fx(B)1637 2884 y FA(T)1707 2710 y Fu(\023)1791 2827 y FE(=)e FA(k)1922 2839 y Fx(0)2001 2827 y FE(exp)2142 2710 y Fu(\022)2203 2827 y Fs(\000)2303 2771 y FA(E)2364 2783 y Fv(a)p 2277 2808 V 2277 2884 a FA(k)2320 2896 y Fx(B)2371 2884 y FA(T)2441 2710 y Fu(\023)2530 2827 y FA(;)164 b FE(\(8.13\))165 3022 y(where)35 b FA(\001S)41 b FE(=)36 b FA(S)726 3034 y Fx(TS)838 3022 y Fs(\000)23 b FA(S)977 3034 y Fx(0)1050 3022 y FE(is)35 b(the)h(en)n(trop)n(y)e(c)n (hange)g(and)i FA(S)2105 3034 y Fx(TS)2228 3022 y FE(and)f FA(S)2448 3034 y Fx(0)2521 3022 y FE(are)g(the)g(en-)165 3122 y(trop)n(y)40 b(of)h(the)g(2)p FA(N)9 b FE(-dimensional)40 b(phase)g(space)g(at)h(the)g(transition)f(state)h(and)g(the)165 3221 y(2\()p FA(N)28 b FE(+)18 b(1\)-dimensional)27 b(phase)h(space)f (in)i(the)f(initial)h(w)n(ell.)f(Hence)g(w)n(e)g(ha)n(v)n(e)f(deriv)n (ed)165 3321 y(the)37 b(Arrhenius)e(expression)g(\(8.1\))h(from)g (transition)f(state)h(theory)-7 b(.)35 b(Note)h(that)h(the)165 3421 y(prefactor)26 b FA(k)561 3433 y Fx(0)625 3421 y FE(whic)n(h)g(is)g(usually)g(assumed)g(to)h(b)r(e)f(temp)r (erature-indep)r(enden)n(t)h(has)f(in)165 3520 y(fact)34 b(a)e(linear)h(dep)r(endence)g(on)g(the)h(temp)r(erature)e(according)g (to)h(\(8.13\).)f(Ho)n(w)n(ev)n(er,)165 3620 y(since)e(the)h(temp)r (erature)e(dep)r(endence)i(is)f(dominated)g(b)n(y)g(the)g(exp)r(onen)n (tial)g(term,)g(it)165 3719 y(is)k(still)f(often)h(justi\014ed)g(to)f (neglect)g(the)h(temp)r(erature)f(dep)r(endence)h(of)f(the)h(prefac-) 165 3819 y(tor.)27 b(F)-7 b(urthermore,)26 b(as)g(\(8.11\))h(sho)n(ws,) f(in)h(the)g(harmonic)f(appro)n(ximation)g(the)h(linear)165 3919 y(temp)r(erature)36 b(dep)r(endence)g(of)f(the)h(\014rst)f(factor) g(is)g(canceled)g(b)n(y)h(the)g(temp)r(erature)165 4018 y(dep)r(endence)28 b(of)g(the)g(en)n(trop)n(y)e(c)n(hange.)290 4118 y(In)e(principle,)g(all)g(v)-5 b(ariables)22 b(in)i(\(8.11\))g (can)f(b)r(e)h(ev)-5 b(aluated)24 b(from)g(electronic)f(struc-)165 4218 y(ture)35 b(calculations)f(since)g(they)h(are)f(all)h(related)f (to)g(the)i(p)r(oten)n(tial)e(energy)g(surface.)165 4317 y(Ho)n(w)n(ev)n(er,)39 b(usually)h(the)h(determination)f(of)h(eigenmo)r (de-frequencies)e(is)i(computa-)165 4417 y(tionally)28 b(v)n(ery)f(demanding)h(since)g(it)g(in)n(v)n(olv)n(es)e(the)j(ev)-5 b(aluation)27 b(and)h(diagonalization)165 4516 y(of)i(a)f(Hesse)h (matrix.)f(Hence)h(often)g(the)g(prefactor)f(in)h(\(8.11\))f(is)g(just) i(estimated)e(and)165 4616 y(only)f(barrier)d(heigh)n(ts)i(are)g (computed)h(from)f(\014rst)h(principles.)p eop end %%Page: 241 71 TeXDict begin 241 252 bop 2223 100 a FC(8.2)42 b(Di\013usion)152 b(241)290 282 y FE(F)-7 b(urthermore,)32 b(it)i(is)g(not)f(trivial)g (to)g(lo)r(cate)g(the)h(transition)f(state.)g(There)g(is)g(no)165 382 y(uniquely)g(de\014ned)f(w)n(a)n(y)f(of)h(\014nding)g(the)g(minim)n (um)h(energy)e(path)h(b)r(et)n(w)n(een)g(a)g(giv)n(en)165 482 y(initial)d(and)f(\014nal)g(state.)g(One)g(w)n(a)n(y)f(to)h (determine)g(this)g(path)h(is)f(to)g(simply)g(map)g(out)165 581 y(the)22 b(relev)-5 b(an)n(t)21 b(p)r(oten)n(tial)h(energy)e (surface)h(in)h(great)e(detail,)i(but)g(this)g(can)f(b)r(e)h(computa-) 165 681 y(tionally)e(v)n(ery)g(demanding.)g(Ho)n(w)n(ev)n(er,)f(there)h (are)g(robust)g(metho)r(ds)g(that)h(can)f(b)r(e)h(used)165 780 y(to)j(\014nd)g(a)g(minim)n(um)g(energy)f(path.)h(In)g(the)g FD(nudge)l(d)i(elastic)i(b)l(and)e(metho)l(d)33 b FE([440,)7 b(441],)165 880 y(\014rst)19 b(the)h(energy)e(and)h(the)g(forces)f(of)h (the)h(system)f(are)f(determined)h(along)f(a)h(string)f(usu-)165 980 y(ally)26 b(in)n(terp)r(olating)g(linearly)g(b)r(et)n(w)n(een)g (initial)h(and)f(\014nal)h(state.)f(Neigh)n(b)r(oring)f(p)r(oin)n(ts) 165 1079 y(along)h(the)g(string)g(are)g(connected)g(b)n(y)g(springs)f (in)i(order)e(to)i(guaran)n(tee)d(a)i(con)n(tin)n(uous)165 1179 y(path.)f(Then)h(an)e(optimization)h(algorithm)f(is)h(p)r (erformed)f(whic)n(h)h(in)n(v)n(olv)n(es)e(force)h(pro-)165 1279 y(jections)d(of)f(b)r(oth)i(the)e(true)h(forces)f(and)g(the)h (spring)f(forces.)f(Th)n(us)i(the)g(string)f(of)g(p)r(oin)n(ts)165 1378 y(is)26 b(dragged)e(closer)g(and)i(closer)e(to)i(the)g(minim)n(um) g(energy)f(path)h(un)n(til)g(the)g(transition)165 1478 y(state)38 b(is)g(lo)r(cated.)f(In)h(that)g(w)n(a)n(y)-7 b(,)37 b(also)f(nonin)n(tuitiv)n(e)i(transition)f(state)h(geometries) 165 1577 y(migh)n(t)28 b(b)r(e)g(detected.)165 1901 y Fy(8.2)42 b(Di\013usion)165 2105 y FE(A)30 b(single)f(particle)f(on)h (a)g(surface)g(can)f(jump)j(laterally)d(along)g(the)h(surface)g(from)g (one)165 2204 y(stable)34 b(adsorption)e(site)h(to)g(the)h(next.)g (This)g(pro)r(cess)e(is)h(a)g(t)n(ypical)g(pro)r(cess)g(that)g(is)165 2304 y(driv)n(en)28 b(b)n(y)g(thermal)g(\015uctuations.)g(Eac)n(h)f (adsorbate)g(p)r(erforms)g(thermal)h(vibrations)165 2403 y(around)g(the)g(equilibrium)g(site)h(in)f(the)h(adsorption)d(w)n(ell.) i(The)h(rate)e(for)h(a)g(jump)h(to)f(a)165 2503 y(next)g(nearest)f (neigh)n(b)r(or)f(site)i(is)g(then)g(giv)n(en)e(b)n(y)i(an)f(Arrhenius) g(expression)313 2698 y FA(k)356 2710 y Fx(j)404 2698 y FE(=)c FA(k)535 2710 y Fx(0)614 2698 y FE(exp)754 2581 y Fu(\022)815 2698 y Fs(\000)928 2642 y FA(E)989 2654 y Fv(a)p 890 2679 178 4 v 890 2755 a FA(k)933 2767 y Fx(B)984 2755 y FA(T)1033 2767 y Fv(s)1078 2581 y Fu(\023)1166 2698 y FA(;)1528 b FE(\(8.14\))165 2892 y(where)35 b FA(E)474 2904 y Fv(a)549 2892 y FE(is)g(the)g(energetic)f(barrier)f(to) i(the)g(next-nearest)f(neigh)n(b)r(or)g(site)g(and)h FA(T)2894 2904 y Fv(s)165 2992 y FE(is)c(the)g(surface)f(temp)r (erature.)h(T)-7 b(o)30 b(obtain)h(a)f(more)g(detailed)h(understanding) f(of)h(the)165 3092 y(so-called)25 b(self-di\013usion)g(pro)r(cess,)g (w)n(e)g(in)n(tro)r(duce)g(the)h(probabilit)n(y)f FA(P)12 b FE(\()p Ft(R)q FA(;)i(t)p FE(\))26 b(that)g(the)165 3191 y(lattice)32 b(site)h Ft(R)g FE(on)e(the)i(surface)e(is)h(o)r (ccupied)g(a)g(time)g FA(t)p FE(.)g(The)g(probabilit)n(y)f(that)i(the) 165 3291 y(atom)28 b(is)f(still)h(at)f(site)h Ft(R)g FE(at)g(time)g FA(t)18 b FE(+)h FA(\001t)27 b FE(can)h(b)r(e)g (expressed)e(as)313 3452 y FA(P)12 b FE(\()p Ft(R)q FA(;)i(t)k FE(+)g FA(\001t)p FE(\))24 b(=)893 3373 y Fu(X)914 3552 y Fr(R)970 3535 y Fp(0)1055 3452 y FA(W)12 b FE(\()p Ft(R)q FA(;)i Ft(R)1359 3418 y Fw(0)1383 3452 y FA(;)g(\001t)p FE(\))28 b FA(P)12 b FE(\()p Ft(R)1749 3418 y Fw(0)1772 3452 y FA(;)i(t)p FE(\))g FA(:)809 b FE(\(8.15\))165 3681 y(Here)28 b FA(W)12 b FE(\()p Ft(R)q FA(;)i Ft(R)666 3650 y Fw(0)690 3681 y FA(;)g(\001t)p FE(\))28 b(describ)r(es)f(the)h (conditional)f(probabilit)n(y)g(that)g(the)i(atom)e(is)g(at)165 3780 y(site)h Ft(R)h FE(at)e(time)i FA(t)18 b FE(+)g FA(\001t)28 b FE(giv)n(en)f(that)h(it)g(w)n(as)f(at)h(site)g Ft(R)1935 3750 y Fw(0)1987 3780 y FE(at)f(time)h FA(t)p FE(.)g(No)n(w)g(w)n(e)f(assume)165 3880 y(that)e(only)g(nearest-neigh)n (b)r(or)d(\(n.n.\))j(jumps)h(can)e(o)r(ccur)g(and)g(that)h(the)g(time)g FA(\001t)g FE(is)g(so)165 3979 y(short)f(that)h(at)g(most)g(one)f(jump) i(happ)r(ens)e(during)h(this)g(time.)g(Since)g FA(k)2421 3991 y Fx(j)2471 3979 y FE(is)f(the)h(o)n(v)n(erall)165 4079 y(rate)k(that)h(a)f(jump)h(to)g(an)n(y)e(of)i(the)g(nearest)e (neigh)n(b)r(ors)h(o)r(ccurs,)f(the)i(rate)f(of)g(a)g(jump)165 4179 y(to)g(a)g(particular)e(nearest)h(neigh)n(b)r(or)g(is)h(giv)n(en)f (b)n(y)h FA(k)1817 4191 y Fx(j)1842 4179 y FA(=)-5 b(N)37 b FE(where)29 b FA(N)37 b FE(is)29 b(the)h(n)n(um)n(b)r(er)e(of)165 4278 y(nearest)k(neigh)n(b)r(ors.)f(Then)i(the)g(probabilit)n(y)e(of)h (a)g(jump)i(to)e(this)h(nearest)e(neigh)n(b)r(or)165 4378 y(site)23 b(within)h(the)f(time)g FA(\001t)g FE(is)g(simply)f FA(\001t)9 b Fs(\001)g FA(k)1533 4390 y Fx(j)1558 4378 y FA(=)-5 b(N)9 b FE(.)22 b(Th)n(us)h(w)n(e)f(can)h(write)f(the)h (probabilit)n(y)165 4478 y FA(W)40 b FE(as)p eop end %%Page: 242 72 TeXDict begin 242 253 bop 165 100 a FC(242)153 b(8.)42 b(Kinetic)26 b(Mo)r(deling)h(of)f(Pro)r(cesses)i(on)e(Surfaces)313 444 y FA(W)12 b FE(\()p Ft(R)q FA(;)i Ft(R)618 410 y Fw(0)641 444 y FA(;)g(\001t)p FE(\))51 b(=)975 199 y Fu(8)975 274 y(>)975 299 y(>)975 324 y(>)975 349 y(<)975 498 y(>)975 523 y(>)975 548 y(>)975 573 y(:)1062 273 y FA(k)1105 285 y Fx(j)1130 273 y FA(\001t=)-5 b(N)36 b(;)457 b FE(if)35 b Ft(R)q FA(;)14 b Ft(R)2114 243 y Fw(0)2165 273 y FE(n)p FA(:)p FE(n)p FA(:)28 b(;)1062 443 y FE(1)45 b Fs(\000)1277 381 y Fu(P)1260 514 y Fv(n:n:)1423 443 y FA(k)1466 455 y Fx(j)1491 443 y FA(\001t=)-5 b(N)36 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292.5 ClipEllips 98.8731 49.4366 61.004 409 251 ClipBox 9.45254 89.9681 -0.0105251 -179.397 361.5 250.5 ClipEllips 98.8731 49.4366 -179.397 409 251 ClipBox 9.42605 89.968 -0.010524 120.343 385 292 ClipEllips 48.4366 131.549 109.138 409 251 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore newpath 0 0 moveto 0 432 rlineto 540 0 rlineto 0 -432 rlineto closepath 0 setgray 1 setlinewidth stroke end grestore showpage %%Trailer %%EOF %%EndDocument @endspecial 1096 1005 a currentpoint grestore moveto 1096 1005 a 1179 1005 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1179 1005 a @beginspecial 30 @llx 211 @lly 565 @urx 639 @ury 992 @rwi @setspecial %%BeginDocument: diff_100_hop2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: RasMol Version 2.7.1 %%Title: diff_100_hop2.eps %%BoundingBox: 30 211 565 639 %%Pages: 1 %%EndComments %%EndProlog %%BeginSetup 1 setlinecap 1 setlinejoin [] 0 setdash 1 setlinewidth 0 setgray %%EndSetup %%Page: 1 1 gsave 14 dict 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grestore gsave %% 3 3 11.3952 90 -0 -59.3493 197 288.5 ClipEllips 98.8731 49.4366 -59.3493 173 329 ClipBox 10.6113 89.9714 -0.0105798 -119.82 149.5 288 ClipEllips 98.8731 49.4366 -119.82 173 329 ClipBox 9.41278 89.8718 -0.0210468 -179.397 125.5 328.5 ClipEllips 48.4366 -168.255 -190.538 173 329 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 1 1 13.5407 89.9773 -0.0107514 -179.384 267.5 248.5 ClipEllips 48.4366 -163.162 -195.606 314 249 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 3 3 12.3936 90 -0 -59.8757 290.5 289.5 ClipEllips 98.8731 49.4366 -59.8757 267 330 ClipBox 11.6876 89.9739 -0.0106371 -179.39 220 329.5 ClipEllips 98.8731 49.4366 -179.39 267 330 ClipBox 11.6555 89.9739 -0.0106353 -119.291 244 289 ClipEllips 48.4366 -105.38 -133.202 267 330 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 2 2 11.6876 89.9739 -0.0106371 -179.39 314 330.5 ClipEllips 98.8731 49.4366 -179.39 361 331 ClipBox 10.6113 89.9714 -0.0105798 -119.82 337.5 290 ClipEllips 48.4366 -107.18 -132.461 361 331 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 2 2 11.3842 89.9733 -0.0106203 120.651 385 290.5 ClipEllips 98.8731 49.4366 120.651 409 250 ClipBox 9.41278 89.8718 -0.0210468 -179.397 361.5 249.5 ClipEllips 48.4366 -168.255 -190.538 409 250 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 2 2 11.6555 89.9739 -0.0106353 -119.291 432 291 ClipEllips 98.8731 49.4366 -119.291 455 332 ClipBox 11.6555 89.8954 -0.0212706 -179.39 408 331.5 ClipEllips 48.4366 -165.519 -193.262 455 332 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore newpath 0 0 moveto 0 432 rlineto 540 0 rlineto 0 -432 rlineto closepath 0 setgray 1 setlinewidth stroke end grestore showpage %%Trailer %%EOF %%EndDocument @endspecial 2915 1005 a currentpoint grestore moveto 2915 1005 a 165 1507 a Fz(b)p FC(\))269 1767 y gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 269 1767 a @beginspecial 30 @llx 211 @lly 565 @urx 639 @ury 992 @rwi @setspecial %%BeginDocument: diff_100_exc1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: RasMol Version 2.7.1 %%Title: diff_100_exc1.eps %%BoundingBox: 30 211 565 639 %%Pages: 1 %%EndComments %%EndProlog %%BeginSetup 1 setlinecap 1 setlinejoin [] 0 setdash 1 setlinewidth 0 setgray %%EndSetup %%Page: 1 1 gsave 14 dict begin /handleerror { showpage } def /Inten { dup 4 index mul exch dup 4 index mul exch 3 index mul setrgbcolor } def /Dot { moveto 0 0 rlineto stroke } def /Wire { moveto lineto stroke } def /Label { moveto 1 -1 scale show mtrx setmatrix } def /Stick { closepath setrgbcolor fill } def /StickEnd { matrix currentmatrix 6 1 roll translate rotate 1 scale 0 0 3 2 roll 90 -90 arc setmatrix } def /Shade { closepath clip 45 rotate dup -0.81649658092 mul scale 0.2 Inten fill 0 0 0.999512 0 360 arc 0.2 Inten fill 0 0.03125 0.998045 0 360 arc 0.225806 Inten fill 0 0.0625 0.995596 0 360 arc 0.251613 Inten fill 0 0.09375 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0.411765 0.411765 48.4366 Shade grestore 0.411765 0.411765 0.411765 48.4366 126 346 Sphere gsave %% 1 1 9.46575 89.9681 -0.0105257 180 173.5 346 ClipEllips 48.4366 191.254 168.746 221 346 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 1 1 13.513 89.9088 -0.0214992 -179.384 267.5 346.5 ClipEllips 48.4366 -163.23 -195.538 314 347 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 1 1 9.45254 89.9681 -0.0105251 -179.397 361.5 347.5 ClipEllips 48.4366 -168.159 -190.635 409 348 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore 0.803922 0.803922 0.803922 45.1638 174 149 Sphere 0.411765 0.411765 0.411765 48.4366 126 229 Sphere gsave %% 1 1 9.41278 89.8718 -0.0210468 -179.397 173.5 229.5 ClipEllips 48.4366 -168.255 -190.538 221 230 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 1 1 13.5499 89.9773 -0.0107521 180 267.5 230 ClipEllips 48.4366 196.234 163.766 314 230 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 1 1 9.41278 89.8718 -0.0210468 -179.397 361.5 230.5 ClipEllips 48.4366 -168.255 -190.538 409 231 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore 0.411765 0.411765 0.411765 48.4366 78 310 Sphere gsave %% 1 1 9.46575 89.9681 -0.0105257 180 125.5 310 ClipEllips 48.4366 191.254 168.746 173 310 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 1 1 11.6876 89.9739 -0.0106371 -179.39 220 310.5 ClipEllips 48.4366 -165.44 -193.341 267 311 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 1 1 11.6555 89.8954 -0.0212706 -179.39 314 311.5 ClipEllips 48.4366 -165.519 -193.262 361 312 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore gsave %% 1 1 11.6876 89.9739 -0.0106371 -179.39 408 312.5 ClipEllips 48.4366 -165.44 -193.341 455 313 ClipSphere 0.411765 0.411765 0.411765 48.4366 Shade grestore newpath 0 0 moveto 0 432 rlineto 540 0 rlineto 0 -432 rlineto closepath 0 setgray 1 setlinewidth stroke end grestore showpage %%Trailer %%EOF %%EndDocument @endspecial 1096 1767 a currentpoint grestore moveto 1096 1767 a 1179 1767 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1179 1767 a @beginspecial 30 @llx 211 @lly 565 @urx 639 @ury 992 @rwi @setspecial %%BeginDocument: diff_100_exc2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: RasMol Version 2.7.1 %%Title: diff_100_exc2.eps %%BoundingBox: 30 211 565 639 %%Pages: 1 %%EndComments %%EndProlog %%BeginSetup 1 setlinecap 1 setlinejoin [] 0 setdash 1 setlinewidth 0 setgray %%EndSetup %%Page: 1 1 gsave 14 dict begin /handleerror { showpage } def /Inten { dup 4 index mul exch dup 4 index mul exch 3 index mul setrgbcolor } def /Dot { moveto 0 0 rlineto stroke } def /Wire { moveto lineto stroke } def /Label { moveto 1 -1 scale show mtrx setmatrix } def /Stick { closepath setrgbcolor fill } def /StickEnd { matrix currentmatrix 6 1 roll translate rotate 1 scale 0 0 3 2 roll 90 -90 arc setmatrix } def /Shade { closepath clip 45 rotate 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rlineto 540 0 rlineto 0 -432 rlineto closepath clip 0.827451 0.827451 0.827451 setrgbcolor fill 0.411765 0.411765 0.411765 48.5232 85 128 Sphere gsave %% 1 1 12.0104 89.8985 -0.0212706 -179.39 132 128.5 ClipEllips 48.5232 -165.111 -193.67 179 129 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0416 89.9747 -0.0106371 -179.39 226 129.5 ClipEllips 48.5232 -165.034 -193.747 273 130 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0104 89.8985 -0.0212706 -179.39 320 130.5 ClipEllips 48.5232 -165.111 -193.67 367 131 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 9.89948 89.9695 -0.0105257 180 414.5 131 ClipEllips 48.5232 191.757 168.243 462 131 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 131 209 Sphere gsave %% 1 1 9.84885 89.8775 -0.0210468 -179.397 178.5 209.5 ClipEllips 48.5232 -167.748 -191.046 226 210 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 13.8474 89.9778 -0.0107514 -179.384 272.5 210.5 ClipEllips 48.5232 -162.814 -195.954 319 211 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 9.89948 89.9695 -0.0105257 180 366.5 211 ClipEllips 48.5232 191.757 168.243 414 211 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 131 92 Sphere gsave %% 1 1 9.84885 89.8775 -0.0210468 -179.397 178.5 92.5 ClipEllips 48.5232 -167.748 -191.046 226 93 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 13.8474 89.9778 -0.0107514 -179.384 272.5 93.5 ClipEllips 48.5232 -162.814 -195.954 319 94 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 9.89948 89.9695 -0.0105257 180 366.5 94 ClipEllips 48.5232 191.757 168.243 414 94 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 83 173 Sphere gsave %% 1 1 9.88685 89.9695 -0.0105251 -179.397 130.5 173.5 ClipEllips 48.5232 -167.656 -191.138 178 174 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 13.8474 89.9778 -0.0107514 -179.384 224.5 174.5 ClipEllips 48.5232 -162.814 -195.954 271 175 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 9.86153 89.8777 -0.021048 180 318.5 175 ClipEllips 48.5232 191.665 168.335 366 175 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0416 89.9747 -0.0106371 -179.39 413 175.5 ClipEllips 48.5232 -165.034 -193.747 460 176 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 129 254 Sphere gsave %% 1 1 9.86153 89.8777 -0.021048 180 176.5 254 ClipEllips 48.5232 191.665 168.335 224 254 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0416 89.9747 -0.0106371 -179.39 271 254.5 ClipEllips 48.5232 -165.034 -193.747 318 255 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0104 89.8985 -0.0212706 -179.39 365 255.5 ClipEllips 48.5232 -165.111 -193.67 412 256 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 129 137 Sphere gsave %% 1 1 9.89948 89.9695 -0.0105257 180 176.5 137 ClipEllips 48.5232 191.757 168.243 224 137 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0416 89.9747 -0.0106371 -179.39 271 137.5 ClipEllips 48.5232 -165.034 -193.747 318 138 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0104 89.8985 -0.0212706 -179.39 365 138.5 ClipEllips 48.5232 -165.111 -193.67 412 139 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 81 217 Sphere gsave %% 1 1 9.89948 89.9695 -0.0105257 180 128.5 217 ClipEllips 48.5232 191.757 168.243 176 217 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0104 89.8985 -0.0212706 -179.39 223 217.5 ClipEllips 48.5232 -165.111 -193.67 270 218 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0416 89.9747 -0.0106371 -179.39 317 218.5 ClipEllips 48.5232 -165.034 -193.747 364 219 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 9.84885 89.8775 -0.0210468 -179.397 411.5 219.5 ClipEllips 48.5232 -167.748 -191.046 459 220 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 128 298 Sphere gsave %% 1 1 12.0416 89.9747 -0.0106371 -179.39 175 298.5 ClipEllips 48.5232 -165.034 -193.747 222 299 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0104 89.8985 -0.0212706 -179.39 269 299.5 ClipEllips 48.5232 -165.111 -193.67 316 300 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 9.88685 89.9695 -0.0105251 -179.397 363.5 300.5 ClipEllips 48.5232 -167.656 -191.138 411 301 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 128 181 Sphere 0.215686 0.215686 0.215686 45.2446 251 122 Sphere gsave %% 1 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0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 126 343 Sphere gsave %% 1 1 9.84885 89.8775 -0.0210468 -179.397 173.5 343.5 ClipEllips 48.5232 -167.748 -191.046 221 344 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 13.8564 89.9778 -0.0107521 180 267.5 344 ClipEllips 48.5232 196.581 163.419 314 344 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 9.84885 89.8775 -0.0210468 -179.397 361.5 344.5 ClipEllips 48.5232 -167.748 -191.046 409 345 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.803922 0.803922 0.803922 45.2446 194 148 Sphere 0.411765 0.411765 0.411765 48.5232 126 225 Sphere gsave %% 1 1 9.84885 89.8775 -0.0210468 -179.397 173.5 225.5 ClipEllips 48.5232 -167.748 -191.046 221 226 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 13.8564 89.9778 -0.0107521 180 267.5 226 ClipEllips 48.5232 196.581 163.419 314 226 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 9.84885 89.8775 -0.0210468 -179.397 361.5 226.5 ClipEllips 48.5232 -167.748 -191.046 409 227 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore 0.411765 0.411765 0.411765 48.5232 78 306 Sphere gsave %% 1 1 9.89948 89.9695 -0.0105257 180 125.5 306 ClipEllips 48.5232 191.757 168.243 173 306 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0104 89.8985 -0.0212706 -179.39 220 306.5 ClipEllips 48.5232 -165.111 -193.67 267 307 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0416 89.9747 -0.0106371 -179.39 314 307.5 ClipEllips 48.5232 -165.034 -193.747 361 308 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore gsave %% 1 1 12.0104 89.8985 -0.0212706 -179.39 408 308.5 ClipEllips 48.5232 -165.111 -193.67 455 309 ClipSphere 0.411765 0.411765 0.411765 48.5232 Shade grestore newpath 0 0 moveto 0 432 rlineto 540 0 rlineto 0 -432 rlineto closepath 0 setgray 1 setlinewidth stroke end grestore showpage %%Trailer %%EOF %%EndDocument @endspecial 2006 1767 a currentpoint grestore moveto 2006 1767 a 2088 1767 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 2088 1767 a @beginspecial 30 @llx 211 @lly 565 @urx 639 @ury 992 @rwi @setspecial %%BeginDocument: diff_100_exc3.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: RasMol Version 2.7.1 %%Title: diff_100_exc3.eps %%BoundingBox: 30 211 565 639 %%Pages: 1 %%EndComments %%EndProlog %%BeginSetup 1 setlinecap 1 setlinejoin [] 0 setdash 1 setlinewidth 0 setgray %%EndSetup %%Page: 1 1 gsave 14 dict begin /handleerror { showpage } def /Inten { dup 4 index mul exch dup 4 index mul exch 3 index mul setrgbcolor } def /Dot { moveto 0 0 rlineto stroke } def /Wire { moveto lineto stroke } def /Label { moveto 1 -1 scale show mtrx setmatrix } def /Stick { closepath setrgbcolor fill } def /StickEnd { matrix currentmatrix 6 1 roll translate rotate 1 scale 0 0 3 2 roll 90 -90 arc setmatrix } def /Shade { closepath clip 45 rotate dup 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0.754544 0 360 arc 0.716129 Inten fill 0 0.65625 0.726184 0 360 arc 0.741935 Inten fill 0 0.6875 0.695269 0 360 arc 0.767742 Inten fill 0 0.71875 0.661438 0 360 arc 0.793548 Inten fill 0 0.75 0.624218 0 360 arc 0.819355 Inten fill 0 0.78125 0.582961 0 360 arc 0.845161 Inten fill 0 0.8125 0.536736 0 360 arc 0.870968 Inten fill 0 0.84375 0.484123 0 360 arc 0.896774 Inten fill 0 0.875 0.422742 0 360 arc 0.922581 Inten fill 0 0.90625 0.347985 0 360 arc 0.948387 Inten fill 0 0.9375 0.248039 0 360 arc 0.974194 Inten fill pop pop pop } def /ClipSphere { newpath translate 0 0 5 2 roll arc } def /ClipBox { translate rotate dup lineto dup neg dup 0 rlineto 0 exch rlineto 0 rlineto closepath clip newpath mtrx setmatrix } def /ClipEllips { translate rotate 1 scale 0 0 4 2 roll dup neg arc reversepath mtrx setmatrix } def /Sphere { gsave translate 0 0 2 index 0 360 arc Shade grestore } def 30 639 translate 0.990741 -0.990741 scale /mtrx matrix currentmatrix def newpath 0 0 moveto 0 432 rlineto 540 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0.7472 l 0.5120 0.7568 l 0.5226 0.7684 l 0.5333 0.7813 l 0.5440 0.7950 l 0.5546 0.8090 l 0.5653 0.8229 l 0.5760 0.8366 l 0.5866 0.8499 l 0.5868 0.8501 l s n 0.4338 0.8501 m 0.4373 0.8337 l 0.4480 0.8003 l 0.4586 0.7797 l 0.4693 0.7691 l 0.4800 0.7660 l 0.4906 0.7685 l 0.5013 0.7752 l 0.5120 0.7848 l 0.5226 0.7964 l 0.5333 0.8093 l 0.5440 0.8230 l 0.5546 0.8370 l 0.5647 0.8501 l s n 0.4410 0.8501 m 0.4480 0.8283 l 0.4586 0.8077 l 0.4693 0.7971 l 0.4800 0.7940 l 0.4906 0.7965 l 0.5013 0.8032 l 0.5120 0.8128 l 0.5226 0.8244 l 0.5333 0.8373 l 0.5433 0.8501 l s n 0.4512 0.8501 m 0.4586 0.8357 l 0.4693 0.8251 l 0.4800 0.8220 l 0.4906 0.8245 l 0.5013 0.8312 l 0.5120 0.8408 l 0.5205 0.8501 l s [] 0 SD 0.0060 SLW n 0.4444 0.8501 m 0.4444 0.8500 l 0.4563 0.8234 l 0.4681 0.7992 l 0.4800 0.7774 l 0.4918 0.7577 l 0.5037 0.7398 l 0.5155 0.7237 l 0.5274 0.7090 l 0.5392 0.6958 l 0.5511 0.6838 l 0.5629 0.6730 l 0.5748 0.6632 l 0.5866 0.6543 l 0.5985 0.6463 l 0.6103 0.6390 l 0.6222 0.6325 l 0.6340 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Ft(r)s FA(;)g Ft(R)p FE(\))p Fs(j)p FA( )s FE(\()p Ft(r)s FA(;)g Ft(R)q FE(\))1994 1011 y Fu(\013)2047 1078 y FA(;)647 b FE(\(9.15\))165 1251 y(whic)n(h,)28 b(using)f(the)h(Hellmann{F)-7 b(eynman)28 b(theorem,)f(can)g(b)r(e)h (transformed)e(to)313 1449 y FA(M)394 1461 y Fv(I)457 1393 y FA(d)500 1362 y Fx(2)p 442 1430 V 442 1506 a FA(dt)515 1482 y Fx(2)562 1449 y Ft(R)635 1461 y Fv(I)696 1449 y FE(=)c Fs(\000)848 1382 y Fu(\012)887 1449 y FA( )s FE(\()p Ft(r)s FA(;)14 b Ft(R)q FE(\))p Fs(jr)1257 1461 y Fr(R)1314 1470 y Fe(I)1351 1449 y FA(H)1420 1461 y Fx(el)1473 1449 y FE(\()p Ft(r)s FA(;)g Ft(R)p FE(\))p Fs(j)p FA( )s FE(\()p Ft(r)s FA(;)g Ft(R)q FE(\))1994 1382 y Fu(\013)2047 1449 y FA(:)647 b FE(\(9.16\))165 1621 y(The)28 b(mean-\014eld)f(approac)n(h)e(prop)r(erly)i(conserv)n (es)e(the)j(total)f(energy)-7 b(,)26 b(furthermore)h(it)165 1721 y(do)r(es)f(not)g(dep)r(end)h(on)f(the)h(c)n(hoice)e(of)h(the)h (quan)n(tum)f(represen)n(tation)e(since)i(the)h(w)n(a)n(v)n(e)165 1821 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b(de\014ned)g(as)313 3560 y Ft(d)364 3572 y Fv(ij)445 3560 y FE(=)533 3493 y Fu(\012)572 3560 y FA(\036)621 3572 y Fv(i)649 3560 y FE(\()p Ft(r)s FA(;)14 b Ft(R)q FE(\))p Fs(jr)962 3572 y Fr(R)1023 3560 y Fs(j)p FA(\036)1095 3572 y Fv(j)1130 3560 y FE(\()p Ft(r)s FA(;)g Ft(R)q FE(\))1351 3493 y Fu(\013)1404 3560 y FA(;)1290 b FE(\(9.19\))165 3710 y(where)19 b(the)g(gradien)n(t)f(is) h(tak)n(en)g(with)g(resp)r(ect)g(to)g(all)g(atomic)f(co)r(ordinates)g Ft(R)q FE(.)h(Inserting)165 3810 y(the)28 b(w)n(a)n(v)n(e)e(function)i (\(9.17\))f(in)n(to)h(\(9.14\),)f(one)g(obtains)g([497])f(\(see)i (Exercise)e(9.2\))313 3976 y FA(i)p FE(\026)-42 b FA(h)10 b FE(_)-34 b FA(c)425 3988 y Fv(k)489 3976 y FE(=)577 3897 y Fu(X)621 4074 y Fv(j)711 3976 y FA(c)747 3988 y Fv(j)782 3976 y FE(\()p FA(V)862 3988 y Fv(k)q(j)952 3976 y Fs(\000)18 b FA(i)p FE(\026)-42 b FA(h)1137 3954 y FE(_)1112 3976 y Ft(R)19 b Fs(\001)g Ft(d)1295 3988 y Fv(k)q(j)1367 3976 y FE(\))14 b FA(:)1281 b FE(\(9.20\))165 4209 y(In)30 b(the)g(adiabatic)e(represen)n(tation,)g(the)i(matrix)f (elemen)n(ts)g FA(V)2151 4221 y Fv(k)q(j)2253 4209 y FE(are)f(zero)g(while)i(in)g(a)165 4309 y(diabatic)e(represen)n(tation) d(the)j(nonadiabatic)f(coupling)g(v)n(ector)f(v)-5 b(anishes.)290 4408 y(In)23 b(an)n(y)f(surface-hopping)g(metho)r(d,)i(the)f(classical) f(particles)g(mo)n(v)n(e)g(on)h(the)g(p)r(oten-)165 4508 y(tial)28 b(energy)f(of)h(one)f(particular)g(quan)n(tum)h(state)f(sub)5 b(ject)28 b(to)g(the)g(classical)f(equation)165 4607 y(of)h(motion)p eop end %%Page: 279 80 TeXDict begin 279 290 bop 1647 100 a FC(9.4)42 b(Electronic)27 b(F)-6 b(riction)26 b(E\013ects)152 b(279)313 323 y FA(M)394 335 y Fv(I)457 267 y FA(d)500 237 y Fx(2)p 442 304 111 4 v 442 380 a FA(dt)515 356 y Fx(2)562 323 y Ft(R)635 335 y Fv(I)696 323 y FE(=)22 b Fs(\000r)917 335 y Fr(R)974 344 y Fe(I)1011 256 y Fu(\012)1050 323 y FA(\036)1099 335 y Fv(i)1127 323 y FE(\()p Ft(r)s FA(;)14 b Ft(R)q FE(\))p Fs(j)p FA(H)1440 335 y Fx(el)1493 323 y FE(\()p 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b(hopping)i(algorithm)f(that)i (guaran)n(tees)d(the)j(correct)e(p)r(opula-)165 1198 y(tion)27 b Fs(j)p FA(c)394 1210 y Fv(j)429 1198 y FE(\()p FA(t)p FE(\))p Fs(j)h FE(of)f(eac)n(h)f(state)h(in)g(an)g(ensem)n(ble)g (of)g(man)n(y)f(calculated)h(tra)5 b(jectories)25 b(with)165 1297 y(the)j(minim)n(um)h(n)n(um)n(b)r(er)e(of)h(hops)f(\(see)g (Exercise)f(9.3\).)290 1397 y(There)h(are)f(also)h(ca)n(v)n(eats)e(of)i (surface)g(hopping)g(algorithms.)f(They)h(are)g(not)g(inde-)165 1497 y(p)r(enden)n(t)20 b(of)f(the)h(quan)n(tum)f(represen)n(tation)e ([497,)s(499],)g(and)i(there)g(is)g(some)f(am)n(biguit)n(y)165 1596 y(in)31 b(the)h(v)n(elo)r(cit)n(y)d(adjustmen)n(t)j(if)f FA(V)1286 1608 y Fv(k)q(k)1364 1596 y FE(\()p Ft(R)q FE(\))e Fs(6)p FE(=)f FA(V)1671 1608 y Fv(ll)1718 1596 y FE(\()p Ft(R)q FE(\))j(at)g(the)g(p)r(osition)f(of)h(the)g(switc)n(h) 165 1696 y(b)r(et)n(w)n(een)21 b(state)g FA(k)j FE(and)d FA(l)r FE(.)g(In)g(addition,)g(they)g(are)f(computationally)g(more)g (demanding)165 1795 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0.607843 12.6822 131 462 Sphere 0.803922 0.803922 0.803922 7.92638 227 238 Sphere 1 1 1 6.3411 196 214 Sphere 1 1 1 6.3411 203 349 Sphere 1 1 1 6.3411 189 349 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 268 454.5 ClipEllips 12.6822 163.541 110.155 276 447 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 308 447 Sphere 0.803922 0.803922 0.803922 7.92638 260 340 Sphere gsave %% 2 2 6.04883 86.4856 -0.179425 136.848 204 454.5 ClipEllips 27.3644 13.6822 136.848 212 447 ClipBox 6.48755 84.6455 -0.229416 45 219.5 454.5 ClipEllips 12.6822 73.0179 16.9821 212 447 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 244 447 Sphere 0.803922 0.803922 0.803922 7.92638 196 340 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 220 285.5 ClipEllips 12.6822 163.541 110.155 228 278 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 139.5 454.5 ClipEllips 12.6822 161.407 115.746 148 447 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 260 278 Sphere 0.607843 0.607843 0.607843 12.6822 180 447 Sphere 0.607843 0.607843 0.607843 12.6822 164 278 Sphere 0.607843 0.607843 0.607843 12.6822 196 278 Sphere 0.607843 0.607843 0.607843 12.6822 115 447 Sphere 0.607843 0.607843 0.607843 12.6822 212 110 Sphere 0.607843 0.607843 0.607843 12.6822 325 482 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 251.27 440.639 ClipEllips 30.535 15.2675 138.814 260 433 ClipBox 7.87357 85.2055 -0.228934 41.1859 268.717 440.627 ClipEllips 14.2675 72.2387 10.1332 260 433 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 260 482 Sphere 0.607843 0.607843 0.607843 12.6822 292 482 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 187.27 440.639 ClipEllips 30.535 15.2675 138.814 196 433 ClipBox 7.87357 85.2055 -0.228934 41.1859 204.717 440.627 ClipEllips 14.2675 72.2387 10.1332 196 433 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 276 313 Sphere 0.607843 0.607843 0.607843 12.6822 196 482 Sphere 0.607843 0.607843 0.607843 12.6822 228 482 Sphere gsave %% 2 2 7.48591 86.9317 -0.178707 140.528 122.775 440.597 ClipEllips 30.535 15.2675 140.528 132 433 ClipBox 7.87357 85.2055 -0.228934 41.1859 140.717 440.627 ClipEllips 14.2675 72.2387 10.1332 132 433 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 212 313 Sphere 0.607843 0.607843 0.607843 12.6822 132 482 Sphere 0.607843 0.607843 0.607843 12.6822 244 313 Sphere 0.607843 0.607843 0.607843 12.6822 164 482 Sphere 0.803922 0.803922 0.803922 7.92638 196 207 Sphere 1 1 1 6.3411 299 420 Sphere 1 1 1 6.3411 285 420 Sphere 0.607843 0.607843 0.607843 12.6822 228 146 Sphere 0.607843 0.607843 0.607843 12.6822 148 313 Sphere 0.607843 0.607843 0.607843 12.6822 180 313 Sphere 0.607843 0.607843 0.607843 12.6822 99 482 Sphere 1 1 1 6.3411 235 420 Sphere 1 1 1 6.3411 220 420 Sphere 0.607843 0.607843 0.607843 12.6822 196 146 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 300 474.5 ClipEllips 12.6822 163.541 110.155 308 467 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 1 1 1 6.3411 171 420 Sphere 1 1 1 6.3411 157 420 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 236 474.5 ClipEllips 12.6822 163.541 110.155 244 467 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 276 467 Sphere 0.803922 0.803922 0.803922 7.92638 292 411 Sphere 1 1 1 6.3411 260 387 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 252 305.5 ClipEllips 12.6822 163.541 110.155 260 298 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 172 474.5 ClipEllips 12.6822 163.541 110.155 180 467 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 212 467 Sphere 0.803922 0.803922 0.803922 7.92638 228 411 Sphere 1 1 1 6.3411 196 219 Sphere 1 1 1 6.3411 196 387 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 188 305.5 ClipEllips 12.6822 163.541 110.155 196 298 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 107 474.5 ClipEllips 12.6822 163.541 110.155 115 467 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 228 298 Sphere 0.607843 0.607843 0.607843 12.6822 148 467 Sphere 0.803922 0.803922 0.803922 7.92638 164 411 Sphere 1 1 1 6.3411 132 387 Sphere 0.607843 0.607843 0.607843 12.6822 213 130 Sphere 0.607843 0.607843 0.607843 12.6822 164 298 Sphere 1 1 1 6.3411 235 186 Sphere 1 1 1 6.3411 221 186 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 284 459 ClipEllips 12.6822 158.078 111.922 292 451 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 325 451 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 220 459 ClipEllips 12.6822 158.078 111.922 228 451 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 260 451 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 236 290 ClipEllips 12.6822 158.078 111.922 244 282 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.37013 86.1665 -0.174078 135 156 459 ClipEllips 12.6822 158.078 111.922 164 451 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 276 282 Sphere 0.607843 0.607843 0.607843 12.6822 196 451 Sphere 0.803922 0.803922 0.803922 7.92638 228 177 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 172 290 ClipEllips 12.6822 158.078 111.922 180 282 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 99 451 Sphere 0.607843 0.607843 0.607843 12.6822 213 282 Sphere 0.607843 0.607843 0.607843 12.6822 132 451 Sphere 0.607843 0.607843 0.607843 12.6822 196 115 Sphere gsave %% 1 1 6.48755 84.6455 -0.229416 135 220.5 122.5 ClipEllips 12.6822 163.018 106.982 228 115 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 148 282 Sphere 0.607843 0.607843 0.607843 12.6822 309 487 Sphere 0.803922 0.803922 0.803922 7.92638 260 380 Sphere 0.607843 0.607843 0.607843 12.6822 244 487 Sphere 0.607843 0.607843 0.607843 12.6822 276 487 Sphere 0.803922 0.803922 0.803922 7.92638 196 380 Sphere gsave %% 2 2 8.86492 87.0646 -0.197546 139.086 219.718 276.177 ClipEllips 30.535 15.2675 139.086 228 269 ClipBox 8.28768 85.2718 -0.235702 39.0939 236.76 276.117 ClipEllips 14.2675 72.2075 5.98022 228 269 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 260 318 Sphere 0.607843 0.607843 0.607843 12.6822 180 487 Sphere 0.607843 0.607843 0.607843 12.6822 293 318 Sphere 0.607843 0.607843 0.607843 12.6822 213 487 Sphere 0.803922 0.803922 0.803922 7.92638 132 380 Sphere gsave %% 2 2 8.4211 87.0486 -0.190476 140.906 155.225 276.13 ClipEllips 30.535 15.2675 140.906 164 269 ClipBox 8.28768 85.2718 -0.235702 39.0939 172.76 276.117 ClipEllips 14.2675 72.2075 5.98022 164 269 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 197 318 Sphere 0.607843 0.607843 0.607843 12.6822 116 487 Sphere 0.607843 0.607843 0.607843 12.6822 228 318 Sphere 0.607843 0.607843 0.607843 12.6822 148 487 Sphere 0.607843 0.607843 0.607843 12.6822 213 150 Sphere 0.607843 0.607843 0.607843 12.6822 132 318 Sphere 0.607843 0.607843 0.607843 12.6822 244 150 Sphere 0.607843 0.607843 0.607843 12.6822 164 318 Sphere 1 1 1 6.3411 267 257 Sphere 1 1 1 6.3411 253 257 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 260 386.408 ClipEllips 6.3411 -55.0766 -124.923 260 391 ClipSphere 1 1 1 6.3411 Shade grestore 0.607843 0.607843 0.607843 12.6822 180 150 Sphere 0.607843 0.607843 0.607843 12.6822 293 471 Sphere 1 1 1 6.3411 204 257 Sphere 1 1 1 6.3411 189 257 Sphere gsave %% 1 1 4.01145 80.7608 -0.340503 -95.1944 196.582 386.401 ClipEllips 6.3411 -60.6503 -129.739 197 391 ClipSphere 1 1 1 6.3411 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 133.152 220.5 479 ClipEllips 12.6822 159.845 106.459 228 471 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 260 471 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 132 386.408 ClipEllips 6.3411 -55.0766 -124.923 132 391 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 300 358 Sphere 1 1 1 6.3411 285 358 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 236 310.5 ClipEllips 12.6822 163.541 110.155 244 303 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.37013 86.1665 -0.174078 135 156 479 ClipEllips 12.6822 158.078 111.922 164 471 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 276 303 Sphere 0.607843 0.607843 0.607843 12.6822 197 471 Sphere 0.803922 0.803922 0.803922 7.92638 260 248 Sphere 1 1 1 6.3411 228 224 Sphere 1 1 1 6.3411 235 358 Sphere 1 1 1 6.3411 221 358 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 172 310.5 ClipEllips 12.6822 163.541 110.155 180 303 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.48755 84.6455 -0.229416 45 220.5 310.5 ClipEllips 12.6822 73.0179 16.9821 213 303 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 132 471 Sphere 0.803922 0.803922 0.803922 7.92638 197 248 Sphere 1 1 1 6.3411 171 358 Sphere 1 1 1 6.3411 157 358 Sphere gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 188.5 142.5 ClipEllips 12.6822 161.407 115.746 197 135 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.48755 84.6455 -0.229416 135 220.5 142.5 ClipEllips 12.6822 163.018 106.982 228 135 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 148 303 Sphere 0.803922 0.803922 0.803922 7.92638 293 349 Sphere 1 1 1 6.3411 164 224 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 268 463.5 ClipEllips 12.6822 163.541 110.155 276 456 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 309 456 Sphere 0.803922 0.803922 0.803922 7.92638 228 349 Sphere 0.607843 0.607843 0.607843 12.6822 293 287 Sphere gsave %% 2 2 6.04883 86.4856 -0.179425 136.848 205 463.5 ClipEllips 27.3644 13.6822 136.848 213 456 ClipBox 6.48755 84.6455 -0.229416 45 220.5 463.5 ClipEllips 12.6822 73.0179 16.9821 213 456 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 244 456 Sphere 0.803922 0.803922 0.803922 7.92638 164 349 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 133.152 220.5 295 ClipEllips 12.6822 159.845 106.459 228 287 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 140 463.5 ClipEllips 12.6822 163.541 110.155 148 456 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 260 287 Sphere 0.607843 0.607843 0.607843 12.6822 180 456 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 236 127 ClipEllips 12.6822 158.078 111.922 244 119 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.37013 86.1665 -0.174078 135 156 295 ClipEllips 12.6822 158.078 111.922 164 287 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 197 287 Sphere 0.607843 0.607843 0.607843 12.6822 116 456 Sphere 0.607843 0.607843 0.607843 12.6822 181 119 Sphere 0.607843 0.607843 0.607843 12.6822 213 119 Sphere 0.607843 0.607843 0.607843 12.6822 132 287 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 301.73 449.639 ClipEllips 30.535 15.2675 41.1859 293 442 ClipBox 7.48591 86.9317 -0.178707 140.528 283.775 449.597 ClipEllips 14.2675 170.619 110.436 293 442 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 236.73 449.639 ClipEllips 30.535 15.2675 41.1859 228 442 ClipBox 8.47971 87.0522 -0.191346 136.975 219.767 449.684 ClipEllips 14.2675 171.955 101.995 228 442 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 260 492 Sphere 0.607843 0.607843 0.607843 12.6822 293 492 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 172.73 449.639 ClipEllips 30.535 15.2675 41.1859 164 442 ClipBox 8.01403 87.0113 -0.1849 138.814 155.27 449.639 ClipEllips 14.2675 171.477 106.151 164 442 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 277 323 Sphere 0.607843 0.607843 0.607843 12.6822 197 492 Sphere 0.607843 0.607843 0.607843 12.6822 309 323 Sphere 0.607843 0.607843 0.607843 12.6822 228 492 Sphere 0.803922 0.803922 0.803922 7.92638 228 217 Sphere 0.607843 0.607843 0.607843 12.6822 213 323 Sphere 0.607843 0.607843 0.607843 12.6822 132 492 Sphere 0.607843 0.607843 0.607843 12.6822 244 323 Sphere 0.607843 0.607843 0.607843 12.6822 164 492 Sphere 0.803922 0.803922 0.803922 7.92638 164 217 Sphere 1 1 1 6.3411 268 430 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 205.73 112.639 ClipEllips 30.535 15.2675 41.1859 197 105 ClipBox 8.01403 87.0113 -0.1849 138.814 188.27 112.639 ClipEllips 14.2675 171.477 106.151 197 105 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 228 155 Sphere 0.607843 0.607843 0.607843 12.6822 148 323 Sphere 0.607843 0.607843 0.607843 12.6822 260 155 Sphere 0.607843 0.607843 0.607843 12.6822 181 323 Sphere 1 1 1 6.3411 204 430 Sphere 1 1 1 6.3411 253 430 Sphere 0.607843 0.607843 0.607843 12.6822 164 155 Sphere 0.607843 0.607843 0.607843 12.6822 197 155 Sphere 0.607843 0.607843 0.607843 12.6822 116 323 Sphere 1 1 1 6.3411 139 430 Sphere 1 1 1 6.3411 190 430 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 236 484 ClipEllips 12.6822 158.078 111.922 244 476 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 277 476 Sphere gsave %% 1 1 3.52599 86.9017 -0.16169 124.992 255.983 425.739 ClipEllips 7.92638 149.823 100.161 260 420 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 235 93 Sphere 1 1 1 6.3411 125 430 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 228 223.408 ClipEllips 6.3411 -55.0766 -124.923 228 228 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 293 397 Sphere 0.607843 0.607843 0.607843 12.6822 261 307 Sphere 0.607843 0.607843 0.607843 12.6822 181 476 Sphere 0.607843 0.607843 0.607843 12.6822 293 307 Sphere 0.607843 0.607843 0.607843 12.6822 213 476 Sphere gsave %% 1 1 3.52599 86.9017 -0.16169 124.992 192.983 425.739 ClipEllips 7.92638 149.823 100.161 197 420 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 221 93 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 164 223.408 ClipEllips 6.3411 -55.0766 -124.923 164 228 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 228 397 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 189 315 ClipEllips 12.6822 158.078 111.922 197 307 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 228 307 Sphere 0.607843 0.607843 0.607843 12.6822 148 476 Sphere gsave %% 1 1 3.52599 86.9017 -0.16169 124.992 127.983 425.739 ClipEllips 7.92638 149.823 100.161 132 420 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 164 397 Sphere 1 1 1 6.3411 268 195 Sphere 1 1 1 6.3411 253 195 Sphere gsave %% 2 2 6.04883 86.4856 -0.179425 136.848 205 147.5 ClipEllips 27.3644 13.6822 136.848 213 140 ClipBox 6.48755 84.6455 -0.229416 45 220.5 147.5 ClipEllips 12.6822 73.0179 16.9821 213 140 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.37013 86.1665 -0.174078 135 124 315 ClipEllips 12.6822 158.078 111.922 132 307 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 244 140 Sphere 0.607843 0.607843 0.607843 12.6822 165 307 Sphere gsave %% 1 1 4.13087 87.1117 -0.172774 127.875 223.909 89.2596 ClipEllips 7.92638 157.821 97.9286 228 84 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 204 195 Sphere 1 1 1 6.3411 190 195 Sphere 0.607843 0.607843 0.607843 12.6822 181 140 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 285 468.5 ClipEllips 12.6822 163.541 110.155 293 461 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 1 1 1 6.3411 197 60 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 301 299.5 ClipEllips 12.6822 163.541 110.155 309 292 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.6587 86.696 -0.185296 135 220.5 468.5 ClipEllips 12.6822 164.994 105.006 228 461 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 261 461 Sphere 0.803922 0.803922 0.803922 7.92638 261 186 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 236 299.5 ClipEllips 12.6822 163.541 110.155 244 292 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 156.5 468.5 ClipEllips 12.6822 161.407 115.746 165 461 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 277 292 Sphere 0.607843 0.607843 0.607843 12.6822 197 461 Sphere 0.803922 0.803922 0.803922 7.92638 197 186 Sphere 0.607843 0.607843 0.607843 12.6822 261 124 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 173 299.5 ClipEllips 12.6822 163.541 110.155 181 292 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.48755 84.6455 -0.229416 45 220.5 299.5 ClipEllips 12.6822 73.0179 16.9821 213 292 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 132 461 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 189 132 ClipEllips 12.6822 158.078 111.922 197 124 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 116 292 Sphere 0.607843 0.607843 0.607843 12.6822 228 124 Sphere 0.607843 0.607843 0.607843 12.6822 148 292 Sphere 0.607843 0.607843 0.607843 12.6822 165 124 Sphere 0.803922 0.803922 0.803922 7.92638 293 390 Sphere 0.607843 0.607843 0.607843 12.6822 277 496 Sphere 0.803922 0.803922 0.803922 7.92638 228 390 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 269.73 285.639 ClipEllips 30.535 15.2675 41.1859 261 278 ClipBox 7.48591 86.9317 -0.178707 140.528 251.775 285.597 ClipEllips 14.2675 170.619 110.436 261 278 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 293 328 Sphere 0.607843 0.607843 0.607843 12.6822 213 496 Sphere 0.607843 0.607843 0.607843 12.6822 325 328 Sphere 0.607843 0.607843 0.607843 12.6822 244 496 Sphere 0.803922 0.803922 0.803922 7.92638 165 390 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 205.73 285.639 ClipEllips 30.535 15.2675 41.1859 197 278 ClipBox 8.01403 87.0113 -0.1849 138.814 188.27 285.639 ClipEllips 14.2675 171.477 106.151 197 278 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 228 328 Sphere 0.607843 0.607843 0.607843 12.6822 261 328 Sphere 0.607843 0.607843 0.607843 12.6822 181 496 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 140.73 285.639 ClipEllips 30.535 15.2675 41.1859 132 278 ClipBox 8.01403 87.0113 -0.1849 138.814 123.27 285.639 ClipEllips 14.2675 171.477 106.151 132 278 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 245 160 Sphere 0.607843 0.607843 0.607843 12.6822 277 160 Sphere 0.607843 0.607843 0.607843 12.6822 197 328 Sphere 0.607843 0.607843 0.607843 12.6822 148 496 Sphere 0.803922 0.803922 0.803922 7.92638 197 53 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 293 396.408 ClipEllips 6.3411 -55.0766 -124.923 293 401 ClipSphere 1 1 1 6.3411 Shade grestore 0.607843 0.607843 0.607843 12.6822 213 160 Sphere 0.607843 0.607843 0.607843 12.6822 132 328 Sphere 0.607843 0.607843 0.607843 12.6822 165 328 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 228 396.408 ClipEllips 6.3411 -55.0766 -124.923 228 401 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 300 266 Sphere 1 1 1 6.3411 286 266 Sphere 0.607843 0.607843 0.607843 12.6822 149 160 Sphere 0.607843 0.607843 0.607843 12.6822 181 160 Sphere 0.607843 0.607843 0.607843 12.6822 100 328 Sphere gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 252.5 488.5 ClipEllips 12.6822 161.407 115.746 261 481 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 4.04166 80.8012 -0.341743 -90 165 396.408 ClipEllips 6.3411 -55.0766 -124.923 165 401 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 236 266 Sphere 1 1 1 6.3411 221 266 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 269 320 ClipEllips 12.6822 158.078 111.922 277 312 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 309 312 Sphere gsave %% 1 1 6.48755 84.6455 -0.229416 135 220.5 488.5 ClipEllips 12.6822 163.018 106.982 228 481 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 4.13087 87.1117 -0.172774 127.875 288.909 262.26 ClipEllips 17.8528 8.92638 127.875 293 257 ClipBox 4.13087 87.1117 -0.172774 52.125 297.091 262.26 ClipEllips 7.92638 82.0714 22.1786 293 257 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 172 266 Sphere 1 1 1 6.3411 158 266 Sphere 1 1 1 6.3411 268 368 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 205 320 ClipEllips 12.6822 158.078 111.922 213 312 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 245 312 Sphere gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 156.5 488.5 ClipEllips 12.6822 161.407 115.746 165 481 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 197 481 Sphere gsave %% 2 2 4.13087 87.1117 -0.172774 127.875 223.909 262.26 ClipEllips 17.8528 8.92638 127.875 228 257 ClipBox 3.66199 86.9644 -0.163846 48.3665 232.607 262.183 ClipEllips 7.92638 74.3357 22.3972 228 257 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore gsave %% 1 1 4.04166 80.8012 -0.341743 -90 197 59.408 ClipEllips 6.3411 -55.0766 -124.923 197 64 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 204 368 Sphere 1 1 1 6.3411 261 234 Sphere 1 1 1 6.3411 254 368 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 133.152 220.5 152 ClipEllips 12.6822 159.845 106.459 228 144 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 261 144 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 173 320 ClipEllips 12.6822 158.078 111.922 181 312 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 1 1 1 6.3411 140 368 Sphere 1 1 1 6.3411 197 234 Sphere 1 1 1 6.3411 190 368 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 189 152 ClipEllips 12.6822 158.078 111.922 197 144 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.37013 86.1665 -0.174078 135 108 320 ClipEllips 12.6822 158.078 111.922 116 312 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 149 312 Sphere 0.803922 0.803922 0.803922 7.92638 165 257 Sphere gsave %% 1 1 4.13087 87.1117 -0.172774 127.875 256.909 364.26 ClipEllips 7.92638 157.821 97.9286 261 359 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 236 31 Sphere 1 1 1 6.3411 132 234 Sphere 1 1 1 6.3411 125 368 Sphere 0.607843 0.607843 0.607843 12.6822 165 144 Sphere gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 317.5 304.5 ClipEllips 12.6822 161.407 115.746 326 297 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 236.5 473.5 ClipEllips 12.6822 161.407 115.746 245 466 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 277 466 Sphere gsave %% 1 1 4.13087 87.1117 -0.172774 127.875 192.909 364.26 ClipEllips 7.92638 157.821 97.9286 197 359 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 221 31 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 253 304.5 ClipEllips 12.6822 163.541 110.155 261 297 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 293 297 Sphere gsave %% 2 2 6.04883 86.4856 -0.179425 136.848 205 473.5 ClipEllips 27.3644 13.6822 136.848 213 466 ClipBox 6.48755 84.6455 -0.229416 45 220.5 473.5 ClipEllips 12.6822 73.0179 16.9821 213 466 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 4.13087 87.1117 -0.172774 127.875 127.909 364.26 ClipEllips 7.92638 157.821 97.9286 132 359 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 269 136.5 ClipEllips 12.6822 163.541 110.155 277 129 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 229 297 Sphere 0.607843 0.607843 0.607843 12.6822 149 466 Sphere 0.607843 0.607843 0.607843 12.6822 181 466 Sphere gsave %% 1 1 3.66199 86.9644 -0.163846 131.634 224.393 27.1831 ClipEllips 7.92638 157.603 105.664 229 22 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 0.607843 0.607843 0.607843 12.6822 245 129 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 157 304.5 ClipEllips 12.6822 163.541 110.155 165 297 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 197 297 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 173 136.5 ClipEllips 12.6822 163.541 110.155 181 129 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 100 297 Sphere 0.607843 0.607843 0.607843 12.6822 213 129 Sphere 0.607843 0.607843 0.607843 12.6822 132 297 Sphere 0.607843 0.607843 0.607843 12.6822 149 129 Sphere gsave %% 2 2 7.87357 85.2055 -0.228934 41.1859 269.717 459.627 ClipEllips 30.535 15.2675 41.1859 261 452 ClipBox 7.87357 85.2055 -0.228934 138.814 252.283 459.627 ClipEllips 14.2675 169.867 107.761 261 452 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 261 501 Sphere 0.803922 0.803922 0.803922 7.92638 261 227 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 188.27 459.639 ClipEllips 30.535 15.2675 138.814 197 452 ClipBox 7.87357 85.2055 -0.228934 41.1859 205.717 459.627 ClipEllips 14.2675 72.2387 10.1332 197 452 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 277 332 Sphere 0.607843 0.607843 0.607843 12.6822 197 501 Sphere 0.607843 0.607843 0.607843 12.6822 309 332 Sphere 0.607843 0.607843 0.607843 12.6822 229 501 Sphere 0.607843 0.607843 0.607843 12.6822 293 165 Sphere 0.607843 0.607843 0.607843 12.6822 213 332 Sphere 0.607843 0.607843 0.607843 12.6822 245 332 Sphere 0.607843 0.607843 0.607843 12.6822 165 501 Sphere 0.803922 0.803922 0.803922 7.92638 197 227 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 220.27 122.639 ClipEllips 30.535 15.2675 138.814 229 115 ClipBox 7.87357 85.2055 -0.228934 41.1859 237.717 122.627 ClipEllips 14.2675 72.2387 10.1332 229 115 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 229 165 Sphere 0.607843 0.607843 0.607843 12.6822 149 332 Sphere 0.607843 0.607843 0.607843 12.6822 261 165 Sphere 0.607843 0.607843 0.607843 12.6822 181 332 Sphere 0.803922 0.803922 0.803922 7.92638 133 227 Sphere 1 1 1 6.3411 236 439 Sphere 1 1 1 6.3411 221 439 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 156.27 122.639 ClipEllips 30.535 15.2675 138.814 165 115 ClipBox 7.87357 85.2055 -0.228934 41.1859 173.717 122.627 ClipEllips 14.2675 72.2387 10.1332 165 115 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 165 165 Sphere 0.607843 0.607843 0.607843 12.6822 197 165 Sphere 0.607843 0.607843 0.607843 12.6822 116 332 Sphere 1 1 1 6.3411 172 439 Sphere 1 1 1 6.3411 158 439 Sphere 0.607843 0.607843 0.607843 12.6822 133 165 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 237 493.5 ClipEllips 12.6822 163.541 110.155 245 486 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 1 1 1 6.3411 268 102 Sphere 1 1 1 6.3411 254 102 Sphere 1 1 1 6.3411 261 238 Sphere 1 1 1 6.3411 261 406 Sphere gsave %% 2 2 5.53067 87.9213 -0.131432 135 269 157 ClipEllips 27.3644 13.6822 135 277 149 ClipBox 5.37013 86.1665 -0.174078 45 285 157 ClipEllips 12.6822 68.0781 21.9219 277 149 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 6.19179 88.0833 -0.135526 136.848 189 324.5 ClipEllips 27.3644 13.6822 136.848 197 317 ClipBox 6.04883 86.4856 -0.179425 43.1524 205 324.5 ClipEllips 12.6822 69.8453 16.4595 197 317 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 6.04883 86.4856 -0.179425 43.1524 237 324.5 ClipEllips 27.3644 13.6822 43.1524 229 317 ClipBox 6.04883 86.4856 -0.179425 136.848 221 324.5 ClipEllips 12.6822 163.541 110.155 229 317 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 253 324.5 ClipEllips 12.6822 163.541 110.155 261 317 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 173 493.5 ClipEllips 12.6822 163.541 110.155 181 486 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 293 317 Sphere 0.607843 0.607843 0.607843 12.6822 213 486 Sphere gsave %% 2 2 4.13087 87.1117 -0.172774 127.875 160.909 435.26 ClipEllips 17.8528 8.92638 127.875 165 430 ClipBox 4.13087 87.1117 -0.172774 52.125 169.091 435.26 ClipEllips 7.92638 82.0714 22.1786 165 430 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 0.803922 0.803922 0.803922 7.92638 229 430 Sphere 1 1 1 6.3411 204 102 Sphere 1 1 1 6.3411 190 102 Sphere gsave %% 1 1 4.24673 85.269 -0.263117 -90 133 233.457 ClipEllips 6.3411 -50.3306 -129.669 133 238 ClipSphere 1 1 1 6.3411 Shade grestore gsave %% 1 1 4.04166 80.8012 -0.341743 -90 197 233.408 ClipEllips 6.3411 -55.0766 -124.923 197 238 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 197 406 Sphere 1 1 1 6.3411 300 205 Sphere 1 1 1 6.3411 286 205 Sphere gsave %% 2 2 5.53067 87.9213 -0.131432 135 205 157 ClipEllips 27.3644 13.6822 135 213 149 ClipBox 5.37013 86.1665 -0.174078 45 221 157 ClipEllips 12.6822 68.0781 21.9219 213 149 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 5.48528 87.9082 -0.131181 138.576 124.5 324.5 ClipEllips 27.3644 13.6822 138.576 133 317 ClipBox 6.04883 86.4856 -0.179425 43.1524 141 324.5 ClipEllips 12.6822 69.8453 16.4595 133 317 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 5.37013 86.1665 -0.174078 45 253 157 ClipEllips 27.3644 13.6822 45 245 149 ClipBox 5.37013 86.1665 -0.174078 135 237 157 ClipEllips 12.6822 158.078 111.922 245 149 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 6.04883 86.4856 -0.179425 43.1524 173 324.5 ClipEllips 27.3644 13.6822 43.1524 165 317 ClipBox 6.04883 86.4856 -0.179425 136.848 157 324.5 ClipEllips 12.6822 163.541 110.155 165 317 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 4.13087 87.1117 -0.172774 127.875 256.909 98.2596 ClipEllips 17.8528 8.92638 127.875 261 93 ClipBox 4.13087 87.1117 -0.172774 52.125 265.091 98.2596 ClipEllips 7.92638 82.0714 22.1786 261 93 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 229 69 Sphere 1 1 1 6.3411 236 205 Sphere 1 1 1 6.3411 222 205 Sphere gsave %% 2 2 5.53067 87.9213 -0.131432 135 141 157 ClipEllips 27.3644 13.6822 135 149 149 ClipBox 5.37013 86.1665 -0.174078 45 157 157 ClipEllips 12.6822 68.0781 21.9219 149 149 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 5.37013 86.1665 -0.174078 45 189 157 ClipEllips 27.3644 13.6822 45 181 149 ClipBox 5.37013 86.1665 -0.174078 135 173 157 ClipEllips 12.6822 158.078 111.922 181 149 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 4.13087 87.1117 -0.172774 127.875 192.909 98.2596 ClipEllips 17.8528 8.92638 127.875 197 93 ClipBox 4.13087 87.1117 -0.172774 52.125 201.091 98.2596 ClipEllips 7.92638 82.0714 22.1786 197 93 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore gsave %% 2 2 4.13087 87.1117 -0.172774 127.875 288.909 201.26 ClipEllips 17.8528 8.92638 127.875 293 196 ClipBox 4.13087 87.1117 -0.172774 52.125 297.091 201.26 ClipEllips 7.92638 82.0714 22.1786 293 196 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 165 69 Sphere 1 1 1 6.3411 172 205 Sphere 1 1 1 6.3411 158 205 Sphere gsave %% 1 1 5.48528 87.9082 -0.131181 138.576 301.5 309.5 ClipEllips 12.6822 163.142 114.011 310 302 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 5.53067 87.9213 -0.131432 135 221 478 ClipEllips 27.3644 13.6822 135 229 470 ClipBox 5.37013 86.1665 -0.174078 45 237 478 ClipEllips 12.6822 68.0781 21.9219 229 470 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.37013 86.1665 -0.174078 135 253 478 ClipEllips 12.6822 158.078 111.922 261 470 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 6.04883 86.4856 -0.179425 43.1524 253 309.5 ClipEllips 27.3644 13.6822 43.1524 245 302 ClipBox 6.04883 86.4856 -0.179425 136.848 237 309.5 ClipEllips 12.6822 163.541 110.155 245 302 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.37013 86.1665 -0.174078 45 173 478 ClipEllips 12.6822 68.0781 21.9219 165 470 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 6.04883 86.4856 -0.179425 43.1524 285 309.5 ClipEllips 27.3644 13.6822 43.1524 277 302 ClipBox 6.04883 86.4856 -0.179425 136.848 269 309.5 ClipEllips 12.6822 163.541 110.155 277 302 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 5.37013 86.1665 -0.174078 45 205 478 ClipEllips 27.3644 13.6822 45 197 470 ClipBox 5.37013 86.1665 -0.174078 135 189 478 ClipEllips 12.6822 158.078 111.922 197 470 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.803922 0.803922 0.803922 7.92638 229 196 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 253 141.5 ClipEllips 12.6822 163.541 110.155 261 134 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 173 309.5 ClipEllips 12.6822 163.541 110.155 181 302 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 293 134 Sphere 0.607843 0.607843 0.607843 12.6822 213 302 Sphere 0.803922 0.803922 0.803922 7.92638 165 196 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 189 141.5 ClipEllips 12.6822 163.541 110.155 197 134 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 117 302 Sphere 0.607843 0.607843 0.607843 12.6822 229 134 Sphere 0.607843 0.607843 0.607843 12.6822 149 302 Sphere 0.607843 0.607843 0.607843 12.6822 133 134 Sphere 0.607843 0.607843 0.607843 12.6822 165 134 Sphere 0.803922 0.803922 0.803922 7.92638 261 399 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 284.27 295.639 ClipEllips 30.535 15.2675 138.814 293 288 ClipBox 7.33519 85.0667 -0.221404 39.4725 302.212 295.586 ClipEllips 14.2675 67.8847 11.0602 293 288 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 294 337 Sphere 0.607843 0.607843 0.607843 12.6822 213 506 Sphere 0.607843 0.607843 0.607843 12.6822 245 506 Sphere 0.803922 0.803922 0.803922 7.92638 197 399 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 220.27 295.639 ClipEllips 30.535 15.2675 138.814 229 288 ClipBox 7.87357 85.2055 -0.228934 41.1859 237.717 295.627 ClipEllips 14.2675 72.2387 10.1332 229 288 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 310 169 Sphere 0.607843 0.607843 0.607843 12.6822 229 337 Sphere 0.607843 0.607843 0.607843 12.6822 261 337 Sphere 0.607843 0.607843 0.607843 12.6822 181 506 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 156.27 295.639 ClipEllips 30.535 15.2675 138.814 165 288 ClipBox 7.87357 85.2055 -0.228934 41.1859 173.717 295.627 ClipEllips 14.2675 72.2387 10.1332 165 288 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 245 169 Sphere 0.607843 0.607843 0.607843 12.6822 165 337 Sphere 0.607843 0.607843 0.607843 12.6822 277 169 Sphere 0.607843 0.607843 0.607843 12.6822 198 337 Sphere 0.803922 0.803922 0.803922 7.92638 229 62 Sphere 0.607843 0.607843 0.607843 12.6822 181 169 Sphere 0.607843 0.607843 0.607843 12.6822 213 169 Sphere 0.607843 0.607843 0.607843 12.6822 133 337 Sphere 0.803922 0.803922 0.803922 7.92638 165 62 Sphere 1 1 1 6.3411 268 275 Sphere 1 1 1 6.3411 254 275 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 261 405.408 ClipEllips 6.3411 -55.0766 -124.923 261 410 ClipSphere 1 1 1 6.3411 Shade grestore 0.607843 0.607843 0.607843 12.6822 117 169 Sphere 0.607843 0.607843 0.607843 12.6822 149 169 Sphere 1 1 1 6.3411 205 275 Sphere 1 1 1 6.3411 190 275 Sphere gsave %% 1 1 4.01145 80.7608 -0.340503 -95.1944 197.582 405.401 ClipEllips 6.3411 -60.6503 -129.739 198 410 ClipSphere 1 1 1 6.3411 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 269 329.5 ClipEllips 12.6822 163.541 110.155 277 322 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 5.32338 86.1405 -0.173749 138.576 189.5 498.5 ClipEllips 27.3644 13.6822 138.576 198 491 ClipBox 6.48755 84.6455 -0.229416 45 205.5 498.5 ClipEllips 12.6822 73.0179 16.9821 198 491 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 229 491 Sphere 1 1 1 6.3411 140 275 Sphere 1 1 1 6.3411 126 275 Sphere 1 1 1 6.3411 294 243 Sphere gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 285.5 161.5 ClipEllips 12.6822 161.407 115.746 294 154 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.6587 86.696 -0.185296 135 205.5 329.5 ClipEllips 12.6822 164.994 105.006 213 322 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 245 322 Sphere 0.803922 0.803922 0.803922 7.92638 261 266 Sphere 1 1 1 6.3411 229 74 Sphere 1 1 1 6.3411 229 243 Sphere 1 1 1 6.3411 236 377 Sphere 1 1 1 6.3411 222 377 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 221 161.5 ClipEllips 12.6822 163.541 110.155 229 154 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 141 329.5 ClipEllips 12.6822 163.541 110.155 149 322 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 261 154 Sphere 0.607843 0.607843 0.607843 12.6822 181 322 Sphere 0.803922 0.803922 0.803922 7.92638 198 266 Sphere 1 1 1 6.3411 165 74 Sphere 1 1 1 6.3411 165 243 Sphere 1 1 1 6.3411 172 377 Sphere 1 1 1 6.3411 158 377 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 157 161.5 ClipEllips 12.6822 163.541 110.155 165 154 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.48755 84.6455 -0.229416 45 205.5 161.5 ClipEllips 12.6822 73.0179 16.9821 198 154 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.803922 0.803922 0.803922 7.92638 133 266 Sphere 1 1 1 6.3411 268 41 Sphere 1 1 1 6.3411 254 41 Sphere 0.607843 0.607843 0.607843 12.6822 133 154 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 237 483 ClipEllips 12.6822 158.078 111.922 245 475 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.803922 0.803922 0.803922 7.92638 229 368 Sphere 1 1 1 6.3411 205 41 Sphere 1 1 1 6.3411 190 41 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 253 314 ClipEllips 12.6822 158.078 111.922 261 306 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 181 475 Sphere 0.607843 0.607843 0.607843 12.6822 294 306 Sphere 0.607843 0.607843 0.607843 12.6822 213 475 Sphere 0.803922 0.803922 0.803922 7.92638 165 368 Sphere 0.607843 0.607843 0.607843 12.6822 278 138 Sphere 0.607843 0.607843 0.607843 12.6822 198 306 Sphere 0.607843 0.607843 0.607843 12.6822 310 138 Sphere 0.607843 0.607843 0.607843 12.6822 229 306 Sphere 0.803922 0.803922 0.803922 7.92638 261 32 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 133.152 205.5 146 ClipEllips 12.6822 159.845 106.459 213 138 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 133 306 Sphere 0.607843 0.607843 0.607843 12.6822 245 138 Sphere 0.607843 0.607843 0.607843 12.6822 165 306 Sphere 0.803922 0.803922 0.803922 7.92638 198 32 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 141 146 ClipEllips 12.6822 158.078 111.922 149 138 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 182 138 Sphere 0.607843 0.607843 0.607843 12.6822 117 138 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 220.27 468.639 ClipEllips 30.535 15.2675 138.814 229 461 ClipBox 7.87357 85.2055 -0.228934 41.1859 237.717 468.627 ClipEllips 14.2675 72.2387 10.1332 229 461 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.803922 0.803922 0.803922 7.92638 294 236 Sphere 0.607843 0.607843 0.607843 12.6822 278 342 Sphere 0.607843 0.607843 0.607843 12.6822 198 511 Sphere 0.607843 0.607843 0.607843 12.6822 229 511 Sphere 0.803922 0.803922 0.803922 7.92638 229 236 Sphere gsave %% 2 2 8.4211 87.0486 -0.190476 140.906 252.225 132.13 ClipEllips 30.535 15.2675 140.906 261 125 ClipBox 7.77849 85.1853 -0.227508 37.4054 270.252 132.075 ClipEllips 14.2675 67.9889 6.8218 261 125 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 294 174 Sphere 0.607843 0.607843 0.607843 12.6822 213 342 Sphere 0.607843 0.607843 0.607843 12.6822 326 174 Sphere 0.607843 0.607843 0.607843 12.6822 245 342 Sphere 0.803922 0.803922 0.803922 7.92638 165 236 Sphere gsave %% 2 2 8.4211 87.0486 -0.190476 140.906 189.225 132.13 ClipEllips 30.535 15.2675 140.906 198 125 ClipBox 8.73846 85.3025 -0.244266 40.9144 206.265 132.163 ClipEllips 14.2675 76.3088 5.51997 198 125 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 229 174 Sphere 0.607843 0.607843 0.607843 12.6822 149 342 Sphere 0.607843 0.607843 0.607843 12.6822 261 174 Sphere 0.607843 0.607843 0.607843 12.6822 182 342 Sphere 1 1 1 6.3411 205 449 Sphere 1 1 1 6.3411 191 449 Sphere gsave %% 2 2 8.4211 87.0486 -0.190476 140.906 124.225 132.13 ClipEllips 30.535 15.2675 140.906 133 125 ClipBox 8.28768 85.2718 -0.235702 39.0939 141.76 132.117 ClipEllips 14.2675 72.2075 5.98022 133 125 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 165 174 Sphere 0.607843 0.607843 0.607843 12.6822 198 174 Sphere 1 1 1 6.3411 301 112 Sphere 1 1 1 6.3411 287 112 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 294 242.408 ClipEllips 6.3411 -55.0766 -124.923 294 247 ClipSphere 1 1 1 6.3411 Shade grestore 0.607843 0.607843 0.607843 12.6822 101 174 Sphere 0.607843 0.607843 0.607843 12.6822 133 174 Sphere 1 1 1 6.3411 236 112 Sphere 1 1 1 6.3411 222 112 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 229 242.408 ClipEllips 6.3411 -55.0766 -124.923 229 247 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 229 416 Sphere 0.607843 0.607843 0.607843 12.6822 262 326 Sphere 0.607843 0.607843 0.607843 12.6822 213 495 Sphere 0.803922 0.803922 0.803922 7.92638 198 440 Sphere 1 1 1 6.3411 173 112 Sphere 1 1 1 6.3411 158 112 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 165 242.408 ClipEllips 6.3411 -55.0766 -124.923 165 247 ClipSphere 1 1 1 6.3411 Shade grestore gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 269.5 166.5 ClipEllips 12.6822 161.407 115.746 278 159 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 5.37013 86.1665 -0.174078 135 190 334 ClipEllips 12.6822 158.078 111.922 198 326 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 310 159 Sphere 0.607843 0.607843 0.607843 12.6822 229 326 Sphere 0.803922 0.803922 0.803922 7.92638 294 103 Sphere 1 1 1 6.3411 262 79 Sphere 1 1 1 6.3411 269 214 Sphere 1 1 1 6.3411 254 214 Sphere gsave %% 1 1 6.6587 86.696 -0.185296 135 205.5 166.5 ClipEllips 12.6822 164.994 105.006 213 159 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 245 159 Sphere 0.607843 0.607843 0.607843 12.6822 166 326 Sphere 0.803922 0.803922 0.803922 7.92638 229 103 Sphere 1 1 1 6.3411 205 214 Sphere 1 1 1 6.3411 191 214 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 141 166.5 ClipEllips 12.6822 163.541 110.155 149 159 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 182 159 Sphere 0.803922 0.803922 0.803922 7.92638 166 103 Sphere 1 1 1 6.3411 198 79 Sphere 1 1 1 6.3411 140 214 Sphere 1 1 1 6.3411 126 214 Sphere 0.607843 0.607843 0.607843 12.6822 117 159 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 221 487.5 ClipEllips 12.6822 163.541 110.155 229 480 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.803922 0.803922 0.803922 7.92638 262 205 Sphere 1 1 1 6.3411 133 79 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 318 151 ClipEllips 12.6822 158.078 111.922 326 143 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 237 318.5 ClipEllips 12.6822 163.541 110.155 245 311 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 278 311 Sphere gsave %% 1 1 6.48755 84.6455 -0.229416 45 205.5 487.5 ClipEllips 12.6822 73.0179 16.9821 198 480 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.803922 0.803922 0.803922 7.92638 198 205 Sphere 0.607843 0.607843 0.607843 12.6822 262 143 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 174 318.5 ClipEllips 12.6822 163.541 110.155 182 311 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 294 143 Sphere gsave %% 1 1 6.48755 84.6455 -0.229416 135 205.5 318.5 ClipEllips 12.6822 163.018 106.982 213 311 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.803922 0.803922 0.803922 7.92638 133 205 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 190 151 ClipEllips 12.6822 158.078 111.922 198 143 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 229 143 Sphere 0.607843 0.607843 0.607843 12.6822 149 311 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 125 151 ClipEllips 12.6822 158.078 111.922 133 143 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 166 143 Sphere 0.607843 0.607843 0.607843 12.6822 101 143 Sphere 0.803922 0.803922 0.803922 7.92638 229 409 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 270.73 304.639 ClipEllips 30.535 15.2675 41.1859 262 297 ClipBox 7.48591 86.9317 -0.178707 140.528 252.775 304.597 ClipEllips 14.2675 170.619 110.436 262 297 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 213 516 Sphere gsave %% 2 2 8.47971 87.0522 -0.191346 43.0251 206.233 304.684 ClipEllips 30.535 15.2675 43.0251 198 297 ClipBox 8.01403 87.0113 -0.1849 138.814 189.27 304.639 ClipEllips 14.2675 171.477 106.151 198 297 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 310 179 Sphere 0.607843 0.607843 0.607843 12.6822 229 347 Sphere 0.607843 0.607843 0.607843 12.6822 262 347 Sphere 0.803922 0.803922 0.803922 7.92638 262 72 Sphere 0.607843 0.607843 0.607843 12.6822 246 179 Sphere 0.607843 0.607843 0.607843 12.6822 166 347 Sphere 0.607843 0.607843 0.607843 12.6822 278 179 Sphere 0.607843 0.607843 0.607843 12.6822 198 347 Sphere 0.803922 0.803922 0.803922 7.92638 198 72 Sphere 0.607843 0.607843 0.607843 12.6822 182 179 Sphere 0.607843 0.607843 0.607843 12.6822 213 179 Sphere 0.803922 0.803922 0.803922 7.92638 133 72 Sphere 1 1 1 6.3411 237 285 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 229 415.408 ClipEllips 6.3411 -55.0766 -124.923 229 420 ClipSphere 1 1 1 6.3411 Shade grestore 0.607843 0.607843 0.607843 12.6822 117 179 Sphere 0.607843 0.607843 0.607843 12.6822 150 179 Sphere 1 1 1 6.3411 173 285 Sphere 1 1 1 6.3411 222 285 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 262 78.408 ClipEllips 6.3411 -55.0766 -124.923 262 83 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 159 285 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 286 171 ClipEllips 12.6822 158.078 111.922 294 163 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 133.152 205.5 339 ClipEllips 12.6822 159.845 106.459 213 331 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 246 331 Sphere gsave %% 1 1 3.52599 86.9017 -0.16169 124.992 224.983 280.739 ClipEllips 7.92638 149.823 100.161 229 275 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore gsave %% 1 1 4.04166 80.8012 -0.341743 -90 198 78.408 ClipEllips 6.3411 -55.0766 -124.923 198 83 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 205 387 Sphere 1 1 1 6.3411 191 387 Sphere 1 1 1 6.3411 262 253 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 221 171 ClipEllips 12.6822 158.078 111.922 229 163 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 262 163 Sphere 0.607843 0.607843 0.607843 12.6822 182 331 Sphere gsave %% 1 1 3.52599 86.9017 -0.16169 124.992 161.983 280.739 ClipEllips 7.92638 149.823 100.161 166 275 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore gsave %% 1 1 4.04166 80.8012 -0.341743 -90 133 78.408 ClipEllips 6.3411 -55.0766 -124.923 133 83 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 301 50 Sphere 1 1 1 6.3411 287 50 Sphere 1 1 1 6.3411 198 253 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 158 171 ClipEllips 12.6822 158.078 111.922 166 163 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 198 163 Sphere 1 1 1 6.3411 237 50 Sphere 1 1 1 6.3411 222 50 Sphere 0.607843 0.607843 0.607843 12.6822 133 163 Sphere 0.803922 0.803922 0.803922 7.92638 198 378 Sphere 1 1 1 6.3411 173 50 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 254 323.5 ClipEllips 12.6822 163.541 110.155 262 316 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 213 485 Sphere 0.803922 0.803922 0.803922 7.92638 294 41 Sphere 1 1 1 6.3411 159 50 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 270 155.5 ClipEllips 12.6822 163.541 110.155 278 148 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 6.04883 86.4856 -0.179425 136.848 190 323.5 ClipEllips 27.3644 13.6822 136.848 198 316 ClipBox 6.48755 84.6455 -0.229416 45 205.5 323.5 ClipEllips 12.6822 73.0179 16.9821 198 316 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 310 148 Sphere 0.607843 0.607843 0.607843 12.6822 230 316 Sphere 0.803922 0.803922 0.803922 7.92638 230 41 Sphere gsave %% 1 1 6.6587 86.696 -0.185296 135 205.5 155.5 ClipEllips 12.6822 164.994 105.006 213 148 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 246 148 Sphere 0.607843 0.607843 0.607843 12.6822 166 316 Sphere gsave %% 1 1 4.13087 87.1117 -0.172774 127.875 161.909 46.2596 ClipEllips 7.92638 157.821 97.9286 166 41 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 141.5 155.5 ClipEllips 12.6822 161.407 115.746 150 148 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 182 148 Sphere 0.607843 0.607843 0.607843 12.6822 117 148 Sphere 0.803922 0.803922 0.803922 7.92638 262 246 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 302.73 141.639 ClipEllips 30.535 15.2675 41.1859 294 134 ClipBox 8.01403 87.0113 -0.1849 138.814 285.27 141.639 ClipEllips 14.2675 171.477 106.151 294 134 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 246 351 Sphere 0.803922 0.803922 0.803922 7.92638 198 246 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 238.73 141.639 ClipEllips 30.535 15.2675 41.1859 230 134 ClipBox 7.48591 86.9317 -0.178707 140.528 220.775 141.597 ClipEllips 14.2675 170.619 110.436 230 134 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 262 184 Sphere 0.607843 0.607843 0.607843 12.6822 294 184 Sphere 0.607843 0.607843 0.607843 12.6822 213 351 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 41.1859 174.73 141.639 ClipEllips 30.535 15.2675 41.1859 166 134 ClipBox 8.01403 87.0113 -0.1849 138.814 157.27 141.639 ClipEllips 14.2675 171.477 106.151 166 134 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 230 184 Sphere 0.607843 0.607843 0.607843 12.6822 182 351 Sphere 0.607843 0.607843 0.607843 12.6822 166 184 Sphere 0.607843 0.607843 0.607843 12.6822 198 184 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 262 252.408 ClipEllips 6.3411 -55.0766 -124.923 262 257 ClipSphere 1 1 1 6.3411 Shade grestore 0.607843 0.607843 0.607843 12.6822 134 184 Sphere 1 1 1 6.3411 269 122 Sphere 1 1 1 6.3411 255 122 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 198 252.408 ClipEllips 6.3411 -55.0766 -124.923 198 257 ClipSphere 1 1 1 6.3411 Shade grestore gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 221.5 343.5 ClipEllips 12.6822 161.407 115.746 230 336 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 1 1 1 6.3411 205 122 Sphere 1 1 1 6.3411 191 122 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 238 176 ClipEllips 12.6822 158.078 111.922 246 168 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 278 168 Sphere gsave %% 2 2 6.04883 86.4856 -0.179425 136.848 190 343.5 ClipEllips 27.3644 13.6822 136.848 198 336 ClipBox 6.48755 84.6455 -0.229416 45 205.5 343.5 ClipEllips 12.6822 73.0179 16.9821 198 336 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 2 2 3.52599 86.9017 -0.16169 124.992 257.983 117.739 ClipEllips 17.8528 8.92638 124.992 262 112 ClipBox 3.52599 86.9017 -0.16169 55.008 266.017 117.739 ClipEllips 7.92638 79.839 30.177 262 112 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 1 1 1 6.3411 141 122 Sphere 1 1 1 6.3411 127 122 Sphere 1 1 1 6.3411 294 89 Sphere 1 1 1 6.3411 237 224 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 206 176 ClipEllips 12.6822 158.078 111.922 214 168 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 1 1 1 6.3411 230 89 Sphere 1 1 1 6.3411 173 224 Sphere 1 1 1 6.3411 223 224 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 142 176 ClipEllips 12.6822 158.078 111.922 150 168 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 182 168 Sphere 0.803922 0.803922 0.803922 7.92638 198 112 Sphere 1 1 1 6.3411 166 89 Sphere 1 1 1 6.3411 159 224 Sphere 0.803922 0.803922 0.803922 7.92638 134 112 Sphere gsave %% 1 1 4.13087 87.1117 -0.172774 127.875 225.909 220.26 ClipEllips 7.92638 157.821 97.9286 230 215 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 286 160.5 ClipEllips 12.6822 163.541 110.155 294 153 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 246 321 Sphere gsave %% 1 1 4.13087 87.1117 -0.172774 127.875 161.909 220.26 ClipEllips 7.92638 157.821 97.9286 166 215 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 0.607843 0.607843 0.607843 12.6822 262 153 Sphere 0.607843 0.607843 0.607843 12.6822 182 321 Sphere 0.607843 0.607843 0.607843 12.6822 214 321 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 190 160.5 ClipEllips 12.6822 163.541 110.155 198 153 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 230 153 Sphere 0.607843 0.607843 0.607843 12.6822 134 153 Sphere 0.607843 0.607843 0.607843 12.6822 166 153 Sphere 0.803922 0.803922 0.803922 7.92638 295 82 Sphere gsave %% 2 2 8.01403 87.0113 -0.1849 138.814 221.27 314.639 ClipEllips 30.535 15.2675 138.814 230 307 ClipBox 7.87357 85.2055 -0.228934 41.1859 238.717 314.627 ClipEllips 14.2675 72.2387 10.1332 230 307 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 230 356 Sphere 0.607843 0.607843 0.607843 12.6822 246 188 Sphere 0.607843 0.607843 0.607843 12.6822 278 188 Sphere 0.607843 0.607843 0.607843 12.6822 199 356 Sphere 0.803922 0.803922 0.803922 7.92638 230 82 Sphere 0.607843 0.607843 0.607843 12.6822 182 188 Sphere 0.607843 0.607843 0.607843 12.6822 214 188 Sphere 0.803922 0.803922 0.803922 7.92638 166 82 Sphere 0.607843 0.607843 0.607843 12.6822 150 188 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 295 88.408 ClipEllips 6.3411 -55.0766 -124.923 295 93 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 206 294 Sphere 1 1 1 6.3411 191 294 Sphere gsave %% 1 1 6.6587 86.696 -0.185296 135 206.5 348.5 ClipEllips 12.6822 164.994 105.006 214 341 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 4.04166 80.8012 -0.341743 -90 230 88.408 ClipEllips 6.3411 -55.0766 -124.923 230 93 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 230 262 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 222 180.5 ClipEllips 12.6822 163.541 110.155 230 173 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 262 173 Sphere 0.803922 0.803922 0.803922 7.92638 199 285 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 166 88.408 ClipEllips 6.3411 -55.0766 -124.923 166 93 ClipSphere 1 1 1 6.3411 Shade grestore gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 158 180.5 ClipEllips 12.6822 163.541 110.155 166 173 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.48755 84.6455 -0.229416 45 206.5 180.5 ClipEllips 12.6822 73.0179 16.9821 199 173 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 1 1 1 6.3411 269 60 Sphere 1 1 1 6.3411 255 60 Sphere 1 1 1 6.3411 206 60 Sphere 1 1 1 6.3411 191 60 Sphere 1 1 1 6.3411 141 60 Sphere 1 1 1 6.3411 127 60 Sphere 0.607843 0.607843 0.607843 12.6822 279 157 Sphere 0.607843 0.607843 0.607843 12.6822 199 325 Sphere 0.607843 0.607843 0.607843 12.6822 230 325 Sphere 0.803922 0.803922 0.803922 7.92638 262 51 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 133.152 206.5 165 ClipEllips 12.6822 159.845 106.459 214 157 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 246 157 Sphere 0.803922 0.803922 0.803922 7.92638 199 51 Sphere 0.607843 0.607843 0.607843 12.6822 150 157 Sphere 0.607843 0.607843 0.607843 12.6822 183 157 Sphere 0.803922 0.803922 0.803922 7.92638 134 51 Sphere 0.803922 0.803922 0.803922 7.92638 230 255 Sphere gsave %% 2 2 8.4211 87.0486 -0.190476 140.906 253.225 151.13 ClipEllips 30.535 15.2675 140.906 262 144 ClipBox 7.77849 85.1853 -0.227508 37.4054 271.252 151.075 ClipEllips 14.2675 67.9889 6.8218 262 144 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 262 193 Sphere 0.607843 0.607843 0.607843 12.6822 214 361 Sphere gsave %% 2 2 8.4211 87.0486 -0.190476 140.906 190.225 151.13 ClipEllips 30.535 15.2675 140.906 199 144 ClipBox 8.73846 85.3025 -0.244266 40.9144 207.265 151.163 ClipEllips 14.2675 76.3088 5.51997 199 144 ClipSphere 0.411765 0.411765 0.411765 14.2675 Shade grestore 0.607843 0.607843 0.607843 12.6822 199 193 Sphere 0.607843 0.607843 0.607843 12.6822 230 193 Sphere 0.607843 0.607843 0.607843 12.6822 166 193 Sphere 1 1 1 6.3411 237 131 Sphere 1 1 1 6.3411 223 131 Sphere gsave %% 1 1 4.62774 81.3798 -0.371391 -90 230 260.975 ClipEllips 6.3411 -47.4192 -132.581 230 265 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 174 131 Sphere 1 1 1 6.3411 159 131 Sphere gsave %% 1 1 6.04883 86.4856 -0.179425 136.848 238 185.5 ClipEllips 12.6822 163.541 110.155 246 178 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 1 1 1 6.3411 263 98 Sphere gsave %% 1 1 5.32338 86.1405 -0.173749 138.576 174.5 185.5 ClipEllips 12.6822 161.407 115.746 183 178 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore gsave %% 1 1 6.48755 84.6455 -0.229416 135 206.5 185.5 ClipEllips 12.6822 163.018 106.982 214 178 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.803922 0.803922 0.803922 7.92638 230 122 Sphere 1 1 1 6.3411 199 98 Sphere 1 1 1 6.3411 206 233 Sphere 1 1 1 6.3411 192 233 Sphere 0.803922 0.803922 0.803922 7.92638 167 122 Sphere 0.607843 0.607843 0.607843 12.6822 214 330 Sphere 0.803922 0.803922 0.803922 7.92638 199 224 Sphere gsave %% 1 1 5.37013 86.1665 -0.174078 135 222 170 ClipEllips 12.6822 158.078 111.922 230 162 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 263 162 Sphere 0.607843 0.607843 0.607843 12.6822 167 162 Sphere 0.607843 0.607843 0.607843 12.6822 199 162 Sphere 0.803922 0.803922 0.803922 7.92638 263 91 Sphere 0.607843 0.607843 0.607843 12.6822 247 198 Sphere 0.803922 0.803922 0.803922 7.92638 199 91 Sphere 0.607843 0.607843 0.607843 12.6822 183 198 Sphere 0.607843 0.607843 0.607843 12.6822 214 198 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 263 97.408 ClipEllips 6.3411 -55.0766 -124.923 263 102 ClipSphere 1 1 1 6.3411 Shade grestore gsave %% 1 1 4.04166 80.8012 -0.341743 -90 199 97.408 ClipEllips 6.3411 -55.0766 -124.923 199 102 ClipSphere 1 1 1 6.3411 Shade grestore gsave %% 1 1 5.37013 86.1665 -0.174078 135 222 190 ClipEllips 12.6822 158.078 111.922 230 182 ClipSphere 0.607843 0.607843 0.607843 12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 199 182 Sphere 1 1 1 6.3411 238 69 Sphere 1 1 1 6.3411 223 69 Sphere 1 1 1 6.3411 174 69 Sphere 1 1 1 6.3411 160 69 Sphere 0.803922 0.803922 0.803922 7.92638 231 60 Sphere gsave %% 1 1 6.6587 86.696 -0.185296 135 206.5 174.5 ClipEllips 12.6822 164.994 105.006 214 167 ClipSphere 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12.6822 Shade grestore 0.607843 0.607843 0.607843 12.6822 199 172 Sphere 0.803922 0.803922 0.803922 7.92638 231 101 Sphere 0.607843 0.607843 0.607843 12.6822 215 207 Sphere gsave %% 1 1 4.04166 80.8012 -0.341743 -90 231 107.408 ClipEllips 6.3411 -55.0766 -124.923 231 112 ClipSphere 1 1 1 6.3411 Shade grestore 1 1 1 6.3411 207 79 Sphere 1 1 1 6.3411 192 79 Sphere gsave %% 1 1 3.66199 86.9644 -0.163846 131.634 195.393 75.1831 ClipEllips 7.92638 157.603 105.664 200 70 ClipSphere 0.803922 0.803922 0.803922 7.92638 Shade grestore 0.607843 0.607843 0.607843 12.6822 215 177 Sphere newpath 0 0 moveto 0 542 rlineto 436 0 rlineto 0 -542 rlineto closepath 0 setgray 1 setlinewidth stroke end grestore showpage %%Trailer %%EOF %%EndDocument @endspecial 1937 2401 a currentpoint grestore moveto 1937 2401 a 165 2526 a Fz(Fig.)c(10.1.)g FC(Illustration)d(of)f(the)f(description)h(of)h(the)e(solid-liquid)h (in)n(terface)h(within)e(the)165 2609 y(sup)r(ercell)22 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translate 1 -1 scale % This junk string is used by the show operators /PATsstr 1 string def /PATawidthshow { % cx cy cchar rx ry string % Loop over each character in the string { % cx cy cchar rx ry char % Show the character dup % cx cy cchar rx ry char char PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char) false charpath % cx cy cchar rx ry char /clip load PATdraw % Move past the character (charpath modified the % current point) currentpoint % cx cy cchar rx ry char x y newpath moveto % cx cy cchar rx ry char % Reposition by cx,cy if the character in the string is cchar 3 index eq { % cx cy cchar rx ry 4 index 4 index rmoveto } if % Reposition all characters by rx ry 2 copy rmoveto % cx cy cchar rx ry } forall pop pop pop pop pop % - currentpoint newpath moveto } bind def /PATcg { 7 dict dup begin /lw currentlinewidth def /lc currentlinecap def /lj currentlinejoin def /ml currentmiterlimit def /ds [ currentdash ] def /cc [ currentrgbcolor ] def /cm matrix currentmatrix def end } bind def % PATdraw - calculates the boundaries of the object and % fills it with the current pattern /PATdraw { % proc save exch PATpcalc % proc nw nh px py 5 -1 roll exec % nw nh px py newpath PATfill % - restore } bind def % PATfill - performs the tiling for the shape /PATfill { % nw nh px py PATfill - PATDict /CurrentPattern get dup begin setfont % Set the coordinate system to Pattern Space PatternGState PATsg % Set the color for uncolored pattezns PaintType 2 eq { PATDict /PColor get PATsc } if % Create the string for showing 3 index string % nw nh px py str % Loop for each of the pattern sources 0 1 Multi 1 sub { % nw nh px py str source % Move to the starting location 3 index 3 index % nw nh px py str source px py moveto % nw nh px py str source % For multiple sources, set the appropriate color Multi 1 ne { dup PC exch get PATsc } if % Set the appropriate string for the source 0 1 7 index 1 sub { 2 index exch 2 index put } for pop % Loop over the number of vertical cells 3 index % nw nh px py str nh { % nw nh px py str currentpoint % nw nh px py str cx cy 2 index oldshow % nw nh px py str cx cy YStep add moveto % nw nh px py str } repeat % nw nh px py str } for 5 { pop } repeat end } bind def % PATkshow - kshow with the current pattezn /PATkshow { % proc string exch bind % string proc 1 index 0 get % string proc char % Loop over all but the last character in the string 0 1 4 index length 2 sub { % string proc char idx % Find the n+1th character in the string 3 index exch 1 add get % string proc char char+1 exch 2 copy % strinq proc char+1 char char+1 char % Now show the nth character PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr) false charpath % string proc char+1 char char+1 /clip load PATdraw % Move past the character (charpath modified the current point) currentpoint newpath moveto % Execute the user proc (should consume char and char+1) mark 3 1 roll % string proc char+1 mark char char+1 4 index exec % string proc char+1 mark... cleartomark % string proc char+1 } for % Now display the last character PATsstr dup 0 4 -1 roll put % string proc (char+1) false charpath % string proc /clip load PATdraw neewath pop pop % - } bind def % PATmp - the makepattern equivalent /PATmp { % patdict patmtx PATmp patinstance exch dup length 7 add % We will add 6 new entries plus 1 FID dict copy % Create a new dictionary begin % Matrix to install when painting the pattern TilingType PATtcalc /PatternGState PATcg def PatternGState /cm 3 -1 roll put % Check for multi pattern sources (Level 1 fast color patterns) currentdict /Multi known not { /Multi 1 def } if % Font dictionary definitions /FontType 3 def % Create a dummy encoding vector /Encoding 256 array def 3 string 0 1 255 { Encoding exch dup 3 index cvs cvn put } for pop /FontMatrix matrix def /FontBBox BBox def /BuildChar { mark 3 1 roll % mark dict char exch begin Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata] PaintType 2 eq Multi 1 ne or { XStep 0 FontBBox aload pop setcachedevice } { XStep 0 setcharwidth } ifelse currentdict % mark [paintdata] dict /PaintProc load % mark [paintdata] dict paintproc end gsave false PATredef exec true PATredef grestore cleartomark % - } bind def currentdict end % newdict /foo exch % /foo newlict definefont % newfont } bind def % PATpcalc - calculates the starting point and width/height % of the tile fill for the shape /PATpcalc { % - PATpcalc nw nh px py PATDict /CurrentPattern get begin gsave % Set up the coordinate system to Pattern Space % and lock down pattern PatternGState /cm get setmatrix BBox aload pop pop pop translate % Determine the bounding box of the shape pathbbox % llx lly urx ury grestore % Determine (nw, nh) the # of cells to paint width and height PatHeight div ceiling % llx lly urx qh 4 1 roll % qh llx lly urx PatWidth div ceiling % qh llx lly qw 4 1 roll % qw qh llx lly PatHeight div floor % qw qh llx ph 4 1 roll % ph qw qh llx PatWidth div floor % ph qw qh pw 4 1 roll % pw ph qw qh 2 index sub cvi abs % pw ph qs qh-ph exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph % Determine the starting point of the pattern fill %(px, py) 4 2 roll % nw nh pw ph PatHeight mul % nw nh pw py exch % nw nh py pw PatWidth mul exch % nw nh px py end } bind def % Save the original routines so that we can use them later on /oldfill /fill load def /oldeofill /eofill load def /oldstroke /stroke load def /oldshow /show load def /oldashow /ashow load def /oldwidthshow /widthshow load def /oldawidthshow /awidthshow load def /oldkshow /kshow load def % These defs are necessary so that subsequent procs don't bind in % the originals /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def /PATredef { MyAppDict begin { /fill { /clip load PATdraw newpath } bind def /eofill { /eoclip load PATdraw newpath } bind def /stroke { PATstroke } bind def /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def /ashow { 0 0 null 6 3 roll PATawidthshow } bind def /widthshow { 0 0 3 -1 roll PATawidthshow } bind def /awidthshow { PATawidthshow } bind def /kshow { PATkshow } bind def } { /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def } ifelse end } bind def false PATredef % Conditionally define setcmykcolor if not available /setcmykcolor where { pop } { /setcmykcolor { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor - pop } bind def } ifelse /PATsc { % colorarray aload length % c1 ... cn length dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /PATsg { % dict begin lw setlinewidth lc setlinecap lj setlinejoin ml setmiterlimit ds aload pop setdash cc aload pop setrgbcolor cm setmatrix end } bind def /PATDict 3 dict def /PATsp { true PATredef PATDict begin /CurrentPattern exch def % If it's an uncolored pattern, save the color CurrentPattern /PaintType get 2 eq { /PColor exch def } if /CColor [ currentrgbcolor ] def end } bind def % PATstroke - stroke with the current pattern /PATstroke { countdictstack save mark { currentpoint strokepath moveto PATpcalc % proc nw nh px py clip newpath PATfill } stopped { (*** PATstroke Warning: Path is too complex, stroking with gray) = cleartomark restore countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse gsave 0.5 setgray oldstroke grestore } { pop restore pop } ifelse newpath } bind def /PATtcalc { % modmtx tilingtype PATtcalc tilematrix % Note: tiling types 2 and 3 are not supported gsave exch concat % tilingtype matrix currentmatrix exch % cmtx tilingtype % Tiling type 1 and 3: constant spacing 2 ne { % Distort the pattern so that it occupies % an integral number of device pixels dup 4 get exch dup 5 get exch % tx ty cmtx XStep 0 dtransform round exch round exch % tx ty cmtx dx.x dx.y XStep div exch XStep div exch % tx ty cmtx a b 0 YStep dtransform round exch round exch % tx ty cmtx a b dy.x dy.y YStep div exch YStep div exch % tx ty cmtx a b c d 7 -3 roll astore % { a b c d tx ty } } if grestore } bind def /PATusp { false PATredef PATDict begin CColor PATsc end } bind def % right30 11 dict begin /PaintType 1 def /PatternType 1 def /TilingType 1 def /BBox [0 0 1 1] def /XStep 1 def /YStep 1 def /PatWidth 1 def /PatHeight 1 def /Multi 2 def /PaintData [ { clippath } bind { 32 16 true [ 32 0 0 -16 0 16 ] {<00030003000c000c0030003000c000c0030003000c000c00 30003000c000c00000030003000c000c0030003000c000c0 030003000c000c0030003000c000c000>} imagemask } bind ] def /PaintProc { pop exec fill } def currentdict end /P2 exch def /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa 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s gr % Ellipse n 8685 3735 162 162 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 5760 5040 162 162 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 5580 5355 162 162 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 5580 4140 162 162 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse 0.000 slw n 9360 6660 90 90 0 360 DrawEllipse gs col7 1.00 shd ef gr % Ellipse n 5040 6705 90 90 0 360 DrawEllipse gs col7 1.00 shd ef gr % Ellipse n 4995 4455 90 90 0 360 DrawEllipse gs col7 1.00 shd ef gr % Ellipse n 9360 4455 90 90 0 360 DrawEllipse gs col7 1.00 shd ef gr % Ellipse n 5670 4410 90 90 0 360 DrawEllipse gs col7 0.75 shd ef gr % Ellipse n 5985 4815 90 90 0 360 DrawEllipse gs col7 0.75 shd ef gr % Ellipse n 6480 4635 90 90 0 360 DrawEllipse gs col7 0.75 shd ef gr % Ellipse n 5670 6525 90 90 0 360 DrawEllipse gs col7 0.75 shd ef gr % Ellipse n 5985 7020 90 90 0 360 DrawEllipse gs col7 0.75 shd ef gr % Ellipse n 8640 4545 90 90 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