Møller-Plesset perturbation theory: example "BH-cc-pVQZ-1.5Re"

Molecule X 1^Sigma+ State of BH. Basis CC-PVQZ. Structure ""

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ExamplesBH-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-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 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 O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZ

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -25.068 122 645 589 71  -25.068 122 645 589 71 
2 -0.081 938 525 443 876  -25.150 061 171 033 586 
3 -0.017 980 499 622 796  -25.168 041 670 656 382 
4 -0.008 291 734 763 881  -25.176 333 405 420 263 
5 -0.003 650 049 678 834  -25.179 983 455 099 097 
6 -0.001 778 840 004 301  -25.181 762 295 103 398 
7 -0.000 836 604 717 881  -25.182 598 899 821 279 
8 -0.000 389 169 610 53  -25.182 988 069 431 809 
9 -0.000 169 461 063 087  -25.183 157 530 494 896 
10 -0.000 066 771 188 01  -25.183 224 301 682 906 
11 -0.000 020 750 411 574  -25.183 245 052 094 48 
12 -0.000 002 116 491 81  -25.183 247 168 586 29 
13  0.000 004 091 799 208  -25.183 243 076 787 082 
14  0.000 005 081 298 193  -25.183 237 995 488 889 
15  0.000 004 228 667 559  -25.183 233 766 821 33 
16  0.000 002 986 196 633  -25.183 230 780 624 697 
17  0.000 001 898 907 242  -25.183 228 881 717 455 
18  0.000 001 106 315 091  -25.183 227 775 402 364 
19  0.000 000 588 654 639  -25.183 227 186 747 725 
20  0.000 000 278 735  -25.183 226 908 012 725 
21  0.000 000 108 417 856  -25.183 226 799 594 869 
22  0.000 000 023 995 551  -25.183 226 775 599 318 
23 -0.000 000 011 748 489  -25.183 226 787 347 807 
24 -0.000 000 022 363 869  -25.183 226 809 711 676 
25 -0.000 000 021 599 352  -25.183 226 831 311 028 
26 -0.000 000 016 819 464  -25.183 226 848 130 492 
27 -0.000 000 011 550 237  -25.183 226 859 680 729 
28 -0.000 000 007 189 955  -25.183 226 866 870 684 
29 -0.000 000 004 068 355  -25.183 226 870 939 039 
30 -0.000 000 002 053 22  -25.183 226 872 992 259 
31 -0.000 000 000 868 1  -25.183 226 873 860 359 
32 -0.000 000 000 239 318  -25.183 226 874 099 677 
33  0.000 000 000 049 913  -25.183 226 874 049 764 
34  0.000 000 000 150 843  -25.183 226 873 898 921 
35  0.000 000 000 159 229  -25.183 226 873 739 692 
36  0.000 000 000 130 372  -25.183 226 873 609 32 
37  0.000 000 000 092 981  -25.183 226 873 516 339 
38  0.000 000 000 059 811  -25.183 226 873 456 528 
39  0.000 000 000 034 93  -25.183 226 873 421 598 
40  0.000 000 000 018 25  -25.183 226 873 403 348 
41  0.000 000 000 008 094  -25.183 226 873 395 254 
42  0.000 000 000 002 508  -25.183 226 873 392 746 
43 -0.000 000 000 000 18  -25.183 226 873 392 926 
44 -0.000 000 000 001 199  -25.183 226 873 394 125 
45 -0.000 000 000 001 362  -25.183 226 873 395 487 
46 -0.000 000 000 001 156  -25.183 226 873 396 643 
47 -0.000 000 000 000 846  -25.183 226 873 397 489 
48 -0.000 000 000 000 556  -25.183 226 873 398 045 
49 -0.000 000 000 000 332  -25.183 226 873 398 377 
Exact energy -25.179 249 972 456 6 
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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 =  0.6937, b = -3.1204 and c =  3.6662
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.07 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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ExamplesBH-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-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 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 O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZ

Known inaccuracies


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Designed by A. Sergeev.