Implementation of the Incremental Scheme for Molecular Dipole and Quadrupole Moments

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Molecular Dipole and Quadrupole Moments

Joachim Friedrich

^a

, Sonia Coriani

^b,c

, Trygve Helgaker

^c

, Michael Dolg

^a

April 24, 2009

Affiliation: ^aInstitute for Theoretical Chemistry, University of Cologne, Gre- instr. 4, 50939 Cologne, Germany

b Dipartmento di Scienze Chimiche, Universit`a degli Studi di Trieste via Licio Giogieri 1, I-34127 Trieste, Italy

c Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Norway

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1 -0.0527 -0.2157 0.0116 0.1713 -0.2157 0.0116 0.3259 -0.2160 0.0117 -0.2157 -0.5356 0.0011 -0.2157 -0.1554 0.0011 -0.2160 4.2043 0.0012 0.0116 0.0011 0.5883 0.0116 0.0011 -0.0159 0.0117 0.0012 -4.5302

2 -0.1767 0.0216 0.0181 0.0473 0.0216 0.0181 0.2019 0.0213 0.0181 0.0216 -0.3866 0.0114 0.0216 -0.0064 0.0114 0.0213 4.3533 0.0114 0.0181 0.0114 0.5634 0.0181 0.0114 -0.0409 0.0181 0.0114 -4.5551

3 -0.2259 -0.0240 -0.0073 -0.0019 -0.0240 -0.0074 0.1527 -0.0243 -0.0073 -0.0240 -0.3863 0.0082 -0.0240 -0.0061 0.0082 -0.0243 4.3536 0.0082 -0.0073 0.0082 0.6123 -0.0074 0.0082 0.0080 -0.0073 0.0082 -4.5062

4 -0.2247 0.0011 -0.0005 -0.0007 0.0011 -0.0005 0.1539 0.0008 -0.0004 0.0011 -0.3794 -0.0020 0.0011 0.0008 -0.0020 0.0008 4.3605 -0.0020 -0.0005 -0.0020 0.6041 -0.0005 -0.0020 -0.0002 -0.0004 -0.0020 -4.5145

exact -0.2240 0.0000 0.0000 0.1546 -0.0003 0.0000

0.0000 -0.3802 -0.0000 -0.0003 4.3597 0.0000

0.0000 -0.0000 0.6042 0.0000 0.0000 -4.5143

Table 1: QPM of furan, aug-cc-pVDZ basis.

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1 -0.1103 -0.0294 -0.0132 -0.0818 -0.0294 -0.0132 -0.0703 -0.0297 -0.0132 -0.0294 -0.4472 -0.0029 -0.0294 0.1820 -0.0029 -0.0297 4.3935 -0.0029 -0.0132 -0.0029 0.5575 -0.0132 -0.0029 -0.1002 -0.0132 -0.0029 -4.3232

2 0.1262 -0.0600 -0.0175 0.1547 -0.0600 -0.0175 0.1662 -0.0603 -0.0175 -0.0600 -0.7248 -0.0129 -0.0600 -0.0957 -0.0129 -0.0603 4.1158 -0.0129 -0.0175 -0.0129 0.5987 -0.0175 -0.0129 -0.0590 -0.0175 -0.0129 -4.2820

3 -0.0425 0.0022 0.0062 -0.0140 0.0021 0.0062 -0.0025 0.0019 0.0062 0.0022 -0.6220 -0.0083 0.0021 0.0072 -0.0083 0.0019 4.2187 -0.0083 0.0062 -0.0083 0.6645 0.0062 -0.0083 0.0069 0.0062 -0.0083 -4.2162

4 -0.0291 -0.0025 0.0006 -0.0006 -0.0026 0.0006 0.0109 -0.0028 0.0006 -0.0025 -0.6289 0.0015 -0.0026 0.0003 0.0015 -0.0028 4.2118 0.0016 0.0006 0.0015 0.6580 0.0006 0.0015 0.0003 0.0006 0.0016 -4.2227

exact -0.0285 0.0000 0.0000 0.0115 -0.0003 0.0000

0.0000 -0.6292 -0.0000 -0.0003 4.2115 0.0000

0.0000 -0.0000 0.6576 0.0000 0.0000 -4.2230

Table 2: QPM of furan, cc-pVDZ basis.

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1 -0.3171 0.0405 0.1096 -0.1406 0.0405 -0.0712 5.4173 0.0374 -3.1787 0.0405 -0.5255 0.0122 0.0405 0.2931 0.0121 0.0374 2.7264 0.0109 0.1096 0.0122 0.8426 -0.0712 0.0121 -0.1525 -3.1787 0.0109 -8.1437

2 0.0528 -0.0727 0.2158 0.2294 -0.0728 0.0350 5.7873 -0.0759 -3.0725 -0.0727 -0.9058 0.0167 -0.0728 -0.0872 0.0166 -0.0759 2.3461 0.0154 0.2158 0.0167 0.8530 0.0350 0.0166 -0.1421 -3.0725 0.0154 -8.1333

3 -0.1560 0.0177 0.1805 0.0206 0.0177 -0.0003 5.5785 0.0146 -3.1078 0.0177 -0.8362 -0.0060 0.0177 -0.0176 -0.0061 0.0146 2.4157 -0.0073 0.1805 -0.0060 0.9922 -0.0003 -0.0061 -0.0029 -3.1078 -0.0073 -7.9942

4 -0.1884 0.0050 0.1769 -0.0119 0.0049 -0.0038 5.5460 0.0018 -3.1114 0.0050 -0.8224 -0.0017 0.0049 -0.0038 -0.0017 0.0018 2.4295 -0.0030 0.1769 -0.0017 1.0108 -0.0038 -0.0017 0.0157 -3.1114 -0.0030 -7.9755

exact -0.1766 0.0000 0.1808 5.5579 -0.0031 -3.1075

0.0000 -0.8186 0.0001 -0.0031 2.4333 -0.0012

0.1808 0.0001 0.9951 -3.1075 -0.0012 -7.9912

Table 3: QPM of aniline, cc-pVDZ basis.

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1 -0.2514 -0.0360 -0.0140 0.2860 -0.0360 -0.0140 3.0895 -0.0362 -0.0142 -0.0360 -0.5594 0.0070 -0.0360 -0.0221 0.0071 -0.0362 2.7802 0.0074 -0.0140 0.0070 0.8108 -0.0140 0.0071 -0.2639 -0.0142 0.0074 -5.8697

2 -0.7082 0.0269 0.0074 -0.1708 0.0269 0.0073 2.6327 0.0267 0.0071 0.0269 -0.3165 0.0059 0.0269 0.2208 0.0059 0.0267 3.0231 0.0062 0.0074 0.0059 1.0247 0.0073 0.0059 -0.0500 0.0071 0.0062 -5.6558

3 -0.4631 -0.0335 -0.0008 0.0743 -0.0336 -0.0009 2.8778 -0.0338 -0.0011 -0.0335 -0.6087 0.0007 -0.0336 -0.0715 0.0007 -0.0338 2.7308 0.0010 -0.0008 0.0007 1.0719 -0.0009 0.0007 -0.0028 -0.0011 0.0010 -5.6086

4 -0.5410 0.0033 -0.0005 -0.0036 0.0032 -0.0005 2.7999 0.0030 -0.0007 0.0033 -0.5376 -0.0013 0.0032 -0.0004 -0.0012 0.0030 2.8020 -0.0009 -0.0005 -0.0013 1.0786 -0.0005 -0.0012 0.0039 -0.0007 -0.0009 -5.6019

exact -0.5375 0.0000 0.0000 2.8035 -0.0002 -0.0002

0.0000 -0.5372 -0.0000 -0.0002 2.8023 0.0003

0.0000 -0.0000 1.0747 -0.0002 0.0003 -5.6058

Table 4: QPM of benzene, cc-pVDZ basis.

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1 -0.2616 -0.1249 0.0163 0.5893 0.2021 0.0163 29.9459 9.1712 0.0174 -0.1249 0.0920 -0.0044 0.2021 -0.2923 -0.0044 9.1712 -14.4146 -0.0042 0.0163 -0.0044 0.1697 0.0163 -0.0044 -0.2970 0.0174 -0.0042 -15.5313

2 -0.7347 -0.3413 -0.0041 0.1162 -0.0143 -0.0041 29.4728 8.9547 -0.0030 -0.3413 0.3205 0.0005 -0.0143 -0.0638 0.0005 8.9547 -14.1861 0.0008 -0.0041 0.0005 0.4142 -0.0041 0.0005 -0.0524 -0.0030 0.0008 -15.2867

3 -0.8468 -0.3140 0.0016 0.0042 0.0130 0.0016 29.3608 8.9820 0.0027 -0.3140 0.3836 -0.0010 0.0130 -0.0007 -0.0010 8.9820 -14.1229 -0.0008 0.0016 -0.0010 0.4631 0.0016 -0.0010 -0.0035 0.0027 -0.0008 -15.2378

4 -0.8515 -0.3265 -0.0003 -0.0006 0.0006 -0.0003 29.3560 8.9696 0.0008 -0.3265 0.3849 0.0001 0.0006 0.0006 0.0001 8.9696 -14.1217 0.0003 -0.0003 0.0001 0.4666 -0.0003 0.0001 0.0000 0.0008 0.0003 -15.2343

exact -0.8510 -0.3270 -0.0000 29.3565 8.9690 0.0011

-0.3270 0.3843 -0.0000 8.9690 -14.1222 0.0002

-0.0000 -0.0000 0.4666 0.0011 0.0002 -15.2343

Table 5: QPM of LiC5H7, 6-31G** basis.

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1 0.6077 -0.0176 0.0868 -0.0571 0.0269 -0.0032 -14.6335 0.0730 -1.9341 -0.0176 -0.6555 0.0229 0.0269 0.0417 0.0008 0.0730 15.3917 0.5461 0.0868 0.0229 0.0478 -0.0032 0.0008 0.0153 -1.9341 0.5461 -0.7582

2 0.6736 -0.0474 0.0897 0.0088 -0.0028 -0.0003 -14.5677 0.0432 -1.9312 -0.0474 -0.7032 0.0221 -0.0028 -0.0060 0.0000 0.0432 15.3440 0.5453 0.0897 0.0221 0.0297 -0.0003 0.0000 -0.0028 -1.9312 0.5453 -0.7763

3 0.6644 -0.0438 0.0900 -0.0004 0.0008 0.0000 -14.5769 0.0468 -1.9309 -0.0438 -0.6974 0.0221 0.0008 -0.0001 0.0000 0.0468 15.3498 0.5453 0.0900 0.0221 0.0330 0.0000 0.0000 0.0006 -1.9309 0.5453 -0.7729

4 0.6648 -0.0446 0.0900 -0.0000 0.0000 0.0000 -14.5765 0.0460 -1.9309 -0.0446 -0.6972 0.0221 0.0000 0.0000 0.0000 0.0460 15.3500 0.5453 0.0900 0.0221 0.0324 0.0000 0.0000 -0.0000 -1.9309 0.5453 -0.7735

exact 0.6648 -0.0446 0.0900 -14.5764 0.0460 -1.9309

-0.0446 -0.6972 0.0221 0.0460 15.3499 0.5453

0.0900 0.0221 0.0324 -1.9309 0.5453 -0.7735

Table 6: QPM of (H²O)⁶, aug-cc-pVDZ basis.

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1 0.0928 -0.0574 -0.0295 -0.1195 -0.0574 -0.0064 -1.2293 -0.0575 0.5640 -0.0574 -0.1338 0.0071 -0.0574 0.0189 0.0071 -0.0575 1.4827 0.0070 -0.0295 0.0071 0.0410 -0.0064 0.0071 0.1007 0.5640 0.0070 -0.2534

2 0.3716 0.0086 -0.0195 0.1593 0.0086 0.0036 -0.9505 0.0085 0.5740 0.0086 -0.2411 0.0149 0.0086 -0.0884 0.0149 0.0085 1.3755 0.0148 -0.0195 0.0149 -0.1305 0.0036 0.0149 -0.0709 0.5740 0.0148 -0.4250

3 0.2284 0.0015 -0.0291 0.0161 0.0015 -0.0059 -1.0937 0.0014 0.5645 0.0015 -0.1624 0.0005 0.0015 -0.0097 0.0005 0.0014 1.4541 0.0005 -0.0291 0.0005 -0.0660 -0.0059 0.0005 -0.0064 0.5645 0.0005 -0.3604

4 0.2133 0.0009 -0.0237 0.0009 0.0009 -0.0006 -1.1089 0.0008 0.5698 0.0009 -0.1530 -0.0001 0.0009 -0.0004 -0.0001 0.0008 1.4635 -0.0001 -0.0237 -0.0001 -0.0602 -0.0006 -0.0001 -0.0006 0.5698 -0.0001 -0.3547

exact 0.2123 0.0000 -0.0231 -1.1098 -0.0001 0.5704

0.0000 -0.1527 -0.0000 -0.0001 1.4639 -0.0001

-0.0231 -0.0000 -0.0596 0.5704 -0.0001 -0.3541

Table 7: QPM of octane, cc-pVDZ basis.

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1 1.7383 -0.1026 -0.0618 -0.3457 -0.1014 0.0928 2.0379 -0.1005 2.6338 -0.1026 -1.2574 -0.0341 -0.1014 0.5967 -0.0286 -0.1005 3.1329 -0.0056 -0.0618 -0.0341 -0.4809 0.0928 -0.0286 -0.2510 2.6338 -0.0056 -5.1709

2 2.8115 0.0892 -0.1383 0.7275 0.0903 0.0162 3.1111 0.0912 2.5573 0.0892 -1.9362 -0.0077 0.0903 -0.0821 -0.0022 0.0912 2.4541 0.0208 -0.1383 -0.0077 -0.8753 0.0162 -0.0022 -0.6454 2.5573 0.0208 -5.5653

3 2.2236 0.0302 -0.1949 0.1396 0.0313 -0.0404 2.5233 0.0322 2.5007 0.0302 -2.0284 0.0016 0.0313 -0.1743 0.0070 0.0322 2.3619 0.0300 -0.1949 0.0016 -0.1952 -0.0404 0.0070 0.0347 2.5007 0.0300 -4.8852

4 2.0116 0.0081 -0.1513 -0.0724 0.0092 0.0032 2.3113 0.0101 2.5443 0.0081 -1.8212 -0.0114 0.0092 0.0329 -0.0060 0.0101 2.5691 0.0171 -0.1513 -0.0114 -0.1904 0.0032 -0.0060 0.0394 2.5443 0.0171 -4.8804

exact 2.0840 -0.0011 -0.1545 2.3836 0.0009 2.5411

-0.0011 -1.8541 -0.0054 0.0009 2.5362 0.0231

-0.1545 -0.0054 -0.2299 2.5411 0.0231 -4.9198

Table 8: QPM of p-nitroanilin, cc-pVDZ basis.