Table S1. The dependence of the quality of the CHELMO charges on the restraint weight factor x.
The absolute mean deviation of the electrostatic potential obtained from the CHELMO charges and from the wavefunction was calculated for different values of x in equation (9). For comparison, the corresponding absolute mean deviation from charges estimated directly from the electrostatic potential are also included (ESP fit). The electrostatic potential points used are those of the merged sets of points used in the CHELP, CHELPG, and Merz-Kollman methods, except for the two copper complexes where the electrostatic potential points were selected as described in the legend to Table VII. Unit: 10**(-6) a.u.
x (Angstrom) H2O CH3OH CH3O- (CH3)2O Pentane H2NCHO CH3CN 0 3083 1635 1297 1349 2202 1700 994 1 2259 1487 902 1282 1692 1517 930 2 1929 1451 925 1243 1769 1490 895 3 1857 1398 1013 1217 2014 1487 873 4 1843 1376 1070 1202 2229 1488 860 5 1843 1416 1105 1196 2397 1489 852 6 1845 1519 1127 1202 2528 1491 846 7 1848 1220
8 1851
ESP fit 1848 1405 86 1305 1314 1372 963 # points 4501 6776 6229 8730 13117 6886 7105
x (Angstrom) Imidazole CH3S- DMSO Cu(I) Cu(II) complex complex 0 2990 3701 2424 289 181 1 2420 3994 2393 244 150 2 2269 4307 2499 220 143 3 2220 4431 2599 206 143 4 2202 4455 2658 199 147 5 2195 4446 2675 197 153 6 2193 4430 198 160 7 202 169 8 208 179 ESP fit 2370 3665 2326 199 153 # points 8844 6169 9593 38923 38997
directly from the wavefunction are compared. The electrostatic potential points used are the merged sets of points used in the CHELP, CHELPG, Merz-Kollman, and CHELP-BOW methods. Moments and potentials are given in atomic units.
complex quadrupole 1.806 1.356 1.765 0.601 0.311 0.328 0.203 0.475 octupole 17.158 16.840 19.686 16.032 15.743 15.588 15.496 15.901 hexadecapole 29.894 23.328 25.110 23.989 20.821 20.926 19.645 16.170 potential 0.00216 0.00244 0.00189 0.00127 0.00124 0.00123 0.00123 0.00137 weighted pot 0.01642 0.01960 0.01470 0.00815 0.00754 0.00740 0.00733 0.00802 Cu(II) dipole 1.085 3.056 0.229 0.129 0.103 0.094 0.000 0.000 complex quadrupole 1.788 5.326 1.322 0.581 0.518 0.360 0.147 0.349 octupole 13.630 15.655 14.813 13.953 13.212 13.344 12.876 12.299 hexadecapole 27.885 27.530 26.658 24.414 25.186 22.564 21.110 19.709 potential 0.00301 0.00858 0.00128 0.00096 0.00096 0.00089 0.00089 0.00107 weighted pot 0.02564 0.07645 0.00960 0.00616 0.00575 0.00519 0.00485 0.00582 Sum dipole 8.372 19.103 33.786* 3.105 1.125 1.076 1.118 0.142 0.084 quadrupole 16.002 23.861 27.074* 12.991 9.693 12.262 8.806 7.135 8.950 octupole 63.971 68.819 36.897* 74.336 67.629 68.272 63.612 62.059 60.923 hexadecapole 95.490 109.756 47.768* 91.836 78.170 81.049 68.993 71.415 68.055 potential 0.03953 0.07420 0.12862* 0.02402 0.01793 0.01933 0.01754 0.01787 0.01863 weighted pot 0.08441 0.17562 0.15370* 0.04430 0.02723 0.02695 0.02470 0.02365 0.02557 *The sums for the AIM method are not comparable with those of the other
