Møller-Plesset perturbation theory: example "HF aug-cc-pVDZ 1.5r_e"

Molecule X 1^Sigma+ State of HF. Basis AUG-CC-PVDZ. Structure ""

Content


ExamplesAr cc-pVDZBH aug-cc-pVQZ 0.9r_eBH aug-cc-pVQZ 1.0r_eBH aug-cc-pVQZ 1.1r_eBH aug-cc-pVQZ 1.2r_eBH aug-cc-pVQZ 1.3r_eBH aug-cc-pVQZ 1.4r_eBH aug-cc-pVQZ 1.5r_eBH aug-cc-pVQZ 1.6r_eBH aug-cc-pVQZ 1.7r_eBH aug-cc-pVQZ 1.8r_eBH aug-cc-pVQZ 1.9r_eBH aug-cc-pVQZ 2.0r_eBH aug-cc-pVQZ 2.1r_eBH aug-cc-pVQZ 2.2r_eBH cc-pVDZ 1.5ReBH cc-pVDZ 2ReBH cc-pVDZ ReBH cc-pVQZ 1.5ReBH cc-pVQZ 2ReBH cc-pVQZ ReBH cc-pVTZ 1.5ReBH cc-pVTZ 2ReBH cc-pVTZ ReH- cc-pV5ZH- cc-pVQZHF aug-cc-pVDZ 1.5r_eHF aug-cc-pVDZ 2.0r_eHF aug-cc-pVDZ r_eHF cc-pVDZ 1.5ReHF cc-pVDZ 2ReHF cc-pVDZ Rena-pl aug-cc-pvdzNe cc-pVDZO2- aug-cc-pVDZ
MoleculeArX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHH- ionH- ionX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -99.922 340 166 018 316  -99.922 340 166 018 316 
2 -0.246 751 433 767 074  -100.169 091 599 785 39 
3  0.004 532 557 284 56  -100.164 559 042 500 83 
4 -0.016 545 880 142 576  -100.181 104 922 643 406 
5  0.006 656 741 043 538  -100.174 448 181 599 868 
6 -0.008 208 786 673 166  -100.182 656 968 273 034 
7  0.007 130 043 024 466  -100.175 526 925 248 568 
8 -0.007 568 620 959 112  -100.183 095 546 207 68 
9  0.007 854 109 606 042  -100.175 241 436 601 638 
10 -0.008 636 011 338 253  -100.183 877 447 939 891 
11  0.009 716 556 113 794  -100.174 160 891 826 097 
12 -0.011 253 873 042 223  -100.185 414 764 868 32 
13  0.013 327 687 161 377  -100.172 087 077 706 943 
14 -0.016 106 422 262 344  -100.188 193 499 969 287 
15  0.019 811 437 795 032  -100.168 382 062 174 255 
16 -0.024 754 024 796 304  -100.193 136 086 970 559 
17  0.031 367 086 364 965  -100.161 769 000 605 594 
18 -0.040 251 595 586 375  -100.202 020 596 191 969 
19  0.052 246 949 097 557  -100.149 773 647 094 412 
20 -0.068 527 769 698 917  -100.218 301 416 793 329 
21  0.090 745 873 292 145  -100.127 555 543 501 184 
22 -0.121 232 991 102 874  -100.248 788 534 604 058 
23  0.163 295 024 502 573  -100.085 493 510 101 485 
24 -0.221 638 419 305 176  -100.307 131 929 406 661 
25  0.302 991 336 500 424  -100.004 140 592 906 237 
26 -0.417 011 058 185 917  -100.421 151 651 092 154 
27  0.577 614 268 597 183  -99.843 537 382 494 971 
28 -0.804 933 510 191 62  -100.648 470 892 686 591 
29  1.128 203 815 746 432  -99.520 267 076 940 159 
30 -1.590 035 022 361 154  -101.110 302 099 301 313 
31  2.252 754 199 022 829  -98.857 547 900 278 484 
32 -3.207 849 206 516 753  -102.065 397 106 795 237 
33  4.590 070 410 375 12  -97.475 326 696 420 117 
34 -6.598 547 697 779 179  -104.073 874 394 199 296 
35  9.528 499 796 672 051  -94.545 374 597 527 245 
36 -13.818 976 724 594 087  -108.364 351 322 121 332 
37  20.124 930 079 642 635  -88.239 421 242 478 697 
38 -29.426 284 904 654 111  -117.665 706 147 132 808 
39  43.193 419 803 815 857  -74.472 286 343 316 951 
40 -63.638 834 921 915 226  -138.111 121 265 232 177 
41  94.100 799 380 950 562  -44.010 321 884 281 615 
42 -139.629 533 528 436 866  -183.639 855 412 718 481 
43  207.884 851 761 420 89   24.244 996 348 702 409 
44 -310.513 753 228 826 715  -286.268 756 880 124 306 
45  465.269 068 104 360 485   179.000 311 224 236 179 
46 -699.274 545 280 395 046  -520.274 234 056 158 867 
47  1 054.066 895 780 831 828   533.792 661 724 672 961 
48 -1 593.397 173 497 219 001  -1 059.604 511 772 546 04 
49  2 415.324 720 095 069 551   1 355.720 208 322 523 511 
Exact energy  1 355.720 208 322 523 511 
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Coefficients of Moller-Plesset perturbation theory, semilogarithmic plot.
Red/blue dots correspond to positive/negative coefficients
Plot of MP coefficients
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Scaled coefficients of Møller-Plesset perturbation theory.
Parameters a =  1.6366, b = -4.2630 and c =  1.1691
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -99.92 is not shown because it is too small and out of scale
Plot of MP coefficients
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Convergence of summation approximants for the Møller - Plesset series
measured in growth of number of accurate decimal digits of summation results
with increase of n, number of used coefficients.
The summation methods are partial sums (red connected disks),
Pade approximants (blue circles),
quadratic approximants (green boxes),
cubic, quartic, fifth and sixth degree approximants
(triangles, diamonds, pentagonal and hexagonal stars respectively).
Plot of number of accurate digits
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Location of singularities in the complex plane of the parameter z.
Left panel refers to quadratic approximants,
right panel to differential approximants.
To view an individual approximant, click on the right bar.
To view all singularities with their weights, see this table.
Location of singularities in the  complex plane
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The function E(z) found by summation of its power series.
Dashed line indicates that the approximant is complex valued.
Red dot marks exact physical energy at z = 1.
To view results of summation of a specific number of terms of the series, click on the right bar.
Partial sums, Pade and quadratic approximants
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ExamplesAr cc-pVDZBH aug-cc-pVQZ 0.9r_eBH aug-cc-pVQZ 1.0r_eBH aug-cc-pVQZ 1.1r_eBH aug-cc-pVQZ 1.2r_eBH aug-cc-pVQZ 1.3r_eBH aug-cc-pVQZ 1.4r_eBH aug-cc-pVQZ 1.5r_eBH aug-cc-pVQZ 1.6r_eBH aug-cc-pVQZ 1.7r_eBH aug-cc-pVQZ 1.8r_eBH aug-cc-pVQZ 1.9r_eBH aug-cc-pVQZ 2.0r_eBH aug-cc-pVQZ 2.1r_eBH aug-cc-pVQZ 2.2r_eBH cc-pVDZ 1.5ReBH cc-pVDZ 2ReBH cc-pVDZ ReBH cc-pVQZ 1.5ReBH cc-pVQZ 2ReBH cc-pVQZ ReBH cc-pVTZ 1.5ReBH cc-pVTZ 2ReBH cc-pVTZ ReH- cc-pV5ZH- cc-pVQZHF aug-cc-pVDZ 1.5r_eHF aug-cc-pVDZ 2.0r_eHF aug-cc-pVDZ r_eHF cc-pVDZ 1.5ReHF cc-pVDZ 2ReHF cc-pVDZ Rena-pl aug-cc-pvdzNe cc-pVDZO2- aug-cc-pVDZ
MoleculeArX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHH- ionH- ionX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

Known inaccuracies


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Designed by A. Sergeev.