The HF/6-31G bonded energies (atomic units) are shown for fragmentation Levels 1 to 4, together with the corresponding energy (kJ/mol) relative to the average for all 20 structures at that Level of fragmentation. The 20 structures are also contained in this supplementary material. The relative energy data is illustrated in Figure 4.3 Geom Level 1 Level 2 Level 3 Level 4 Level 1 (rel) Level 2 (rel) Level 3 (rel) Level 4 (rel) 1 -50168.947278 -50169.996114 -50169.923912 -50170.004016 -232.37744629 -344.03066098 -155.14531085 -108.42139326 2 -50168.940428 -50169.974789 -50169.995380 -50170.101958 -214.39206504 -288.04192782 -342.78484443 -365.56820300 3 -50168.954241 -50169.961201 -50170.003553 -50170.107827 -250.65802618 -252.36694441 -364.24373541 -380.97964935 4 -50168.893753 -50169.971618 -50169.934614 -50170.051188 -91.846788472 -279.71522283 -183.24373478 -232.27158402 5 -50168.857232 -50169.887795 -50169.894942 -50169.974784 4.0370832680 -59.637739945 -79.086038510 -31.675134957 6 -50168.953874 -50169.948982 -50169.994677 -50170.099898 -249.69656756 -220.28411866 -340.93877136 -360.16101489 7 -50168.817424 -50169.856941 -50169.902404 -50169.970006 108.55369248 21.368477425 -98.675579277 -19.128492713 8 -50168.882049 -50169.892170 -50169.862030 -50169.990844 -61.119429592 -71.125813429 7.3253786838 -73.839323070 9 -50168.860679 -50169.811134 -50169.783567 -50169.915861 -5.0121566919 141.63425184 213.32966513 123.02779254 10 -50168.809533 -50169.848861 -50169.809626 -50169.892474 129.27195143 42.584111113 144.91107511 184.43092814 11 -50168.859797 -50169.861354 -50169.842881 -50169.925524 -2.6963759070 9.7836466717 57.601401120 97.657039934 12 -50168.818971 -50169.818776 -50169.873240 -50169.961526 104.49250081 121.57196408 -22.105628287 3.1361518810 13 -50168.788131 -50169.778711 -50169.776851 -50169.837307 185.46202264 226.76144457 230.96308998 329.27059254 14 -50168.844995 -50169.859650 -50169.883395 -50169.982983 36.165190513 14.256205612 -48.769302857 -53.199879000 15 -50168.846213 -50169.868074 -50169.888995 -50170.004360 32.968637421 -7.8598167839 -63.470976783 -109.32599327 16 -50168.864742 -50169.898169 -50169.903429 -50169.999750 -15.679780585 -86.874142666 -101.36843360 -97.223556745 17 -50168.862731 -50169.847116 -50169.828181 -50169.929730 -10.399011612 47.163759215 96.196450650 86.615974907 18 -50168.782873 -50169.738849 -50169.739273 -50169.834880 199.26870614 331.41922560 329.62253005 335.64438210 19 -50168.868869 -50169.840114 -50169.842367 -50169.969851 -26.514126870 65.547715262 58.950800473 -18.722645013 20 -50168.721674 -50169.641237 -50169.612993 -50169.699658 359.94463564 587.69883321 661.17131591 690.67043596 The HF/6-31G energies (atomic units) calculated in the presence of charges are shown for fragmentation Levels 1 to 4, together with the corresponding energy (kJ/mol) relative to the average for all 20 structures at that Level of fragmentation. The relative energy data is illustrated in Figure 4.4 Geom Level 1 Level 2 Level 3 Level 4 Level 1 (rel) Level 2 (rel) Level 3 (rel) Level 4 (rel) 1 -50186.785573 -50172.248597 -50172.395379 -50172.096503 89.074977177 455.37358788 153.43659275 296.51631612 2 -50186.997132 -50172.396490 -50172.485933 -50172.278383 -466.37361229 67.081435498 -84.311412909 -181.01054779 3 -50187.037581 -50172.760649 -50172.793625 -50172.528146 -572.57057693 -889.01874201 -892.15915770 -836.76280423 4 -50186.946028 -50172.697959 -50172.734892 -50172.430332 -332.19860730 -724.42536008 -737.95582975 -579.95214843 5 -50186.687838 -50172.432277 -50172.445875 -50172.212895 345.67854243 -26.875984158 20.860443930 -9.0706007543 6 -50186.685733 -50172.378880 -50172.443007 -50172.249263 351.20496909 113.31528050 28.389130644 -104.55446470 7 -50186.822261 -50172.450565 -50172.466067 -50172.208182 -7.2485583452 -74.893192639 -32.154877596 3.3027623862 8 -50187.302963 -50172.607372 -50172.609954 -50172.382038 -1269.3314532 -486.59017353 -409.92985911 -453.15561768 9 -50187.117833 -50172.549979 -50172.545548 -50172.261469 -783.27261983 -335.90399321 -240.83225227 -136.60329554 10 -50186.296982 -50172.192170 -50172.221989 -50172.056538 1371.8716984 603.52375271 608.67190073 401.44294744 11 -50186.214468 -50172.260324 -50172.287290 -50172.033390 1588.5114312 424.58458548 437.22479410 462.22037519 12 -50186.685533 -50172.521816 -50172.516534 -50172.295543 351.73151145 -261.96109420 -164.65582747 -226.06327804 13 a -50172.205459 -50172.211196 -50172.014735 a 568.63307942 637.01053786 511.19891220 14 a -50172.269168 -50172.340416 -50172.050302 a 401.36413260 297.74335640 417.81708496 15 -50187.440851 -50172.518053 -50172.472460 -50172.290214 -1631.3579958 -252.08108307 -48.939059173 -212.07307418 16 -50187.515920 -50172.555383 -50172.643409 -50172.327838 -1828.4512461 -350.09109038 -497.76488567 -310.85438094 17 a -50172.582647 -50172.588347 -50172.339258 a -421.67252765 -353.20116208 -340.83689659 18 -50186.514653 -50172.264310 -50172.345274 -50172.054699 800.37552091 414.11962153 284.98630754 406.27178546 19 -50186.801002 -50172.524882 -50172.503839 -50172.298938 48.567554914 -270.01298248 -131.32442042 -234.97679926 20 -50186.079191 -50172.023917 -50172.025349 -50171.780126 1943.6817612 1045.2718427 1124.9516367 1127.1642982 (a) The HF/6-31G energy calculation for some Level 1 fragments (in the presence of charges) did not converge, and are therefore excluded from the data presented in Figure 4.4 Computational Cost: Ab initio calculations were carried out on a single processor of a shared multiple-processor node, so that computational times vary depending on the usage of the node by other processes. Hence, the times shown below are only indicative. The time required to calculate Eb [see Eq (2.12)] for structure 1 at HF/6-31G, on a single processor, is shown versus the Level of fragmentation. Level Time (mins) Longest Fragment calculation time (secs) ______________________________________________________________ 1 13.7 13.2 2 27.2 16.7 3 113.5 52.6 4 175.5 92.1 The time required to calculate the bonding component of Etot [see Eq. (3.3)] for structure 1 at HF/6-31G, on a single processor, in the presence of charges. Level Time (mins) _____________________________ 1 95.0 2 85.3 3 180.3 4 272.9