Møller-Plesset perturbation theory: example "H--cc-pV5Z"

Molecule H- ion. Basis AUG-CC-PV5Z. Structure ""

Content


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 -0.487 888 810 147 051  -0.487 888 810 147 051 
2 -0.029 742 982 034 774  -0.517 631 792 181 825 
3 -0.005 845 919 913 486  -0.523 477 712 095 311 
4 -0.002 338 158 231 772  -0.525 815 870 327 083 
5 -0.000 859 410 711 534  -0.526 675 281 038 617 
6 -0.000 363 776 254 63  -0.527 039 057 293 247 
7 -0.000 171 719 522 055  -0.527 210 776 815 302 
8 -0.000 090 748 270 551  -0.527 301 525 085 853 
9 -0.000 052 052 739 163  -0.527 353 577 825 016 
10 -0.000 031 107 086 804  -0.527 384 684 911 82 
11 -0.000 018 762 017 039  -0.527 403 446 928 859 
12 -0.000 011 212 769 76  -0.527 414 659 698 619 
13 -0.000 006 574 626 881  -0.527 421 234 325 5 
14 -0.000 003 758 052 571  -0.527 424 992 378 071 
15 -0.000 002 080 406 493  -0.527 427 072 784 564 
16 -0.000 001 104 651 345  -0.527 428 177 435 909 
17 -0.000 000 552 961 514  -0.527 428 730 397 423 
18 -0.000 000 251 781 301  -0.527 428 982 178 724 
19 -0.000 000 094 882 037  -0.527 429 077 060 761 
20 -0.000 000 018 621 745  -0.527 429 095 682 506 
21  0.000 000 014 263 243  -0.527 429 081 419 263 
22  0.000 000 025 028 394  -0.527 429 056 390 869 
23  0.000 000 025 415 088  -0.527 429 030 975 781 
24  0.000 000 021 639 002  -0.527 429 009 336 779 
25  0.000 000 016 793 258  -0.527 428 992 543 521 
26  0.000 000 012 267 069  -0.527 428 980 276 452 
27  0.000 000 008 563 519  -0.527 428 971 712 933 
28  0.000 000 005 757 304  -0.527 428 965 955 629 
29  0.000 000 003 741 209  -0.527 428 962 214 42 
30  0.000 000 002 351 694  -0.527 428 959 862 726 
31  0.000 000 001 427 517  -0.527 428 958 435 209 
32  0.000 000 000 832 837  -0.527 428 957 602 372 
33  0.000 000 000 462 635  -0.527 428 957 139 737 
34  0.000 000 000 240 245  -0.527 428 956 899 492 
35  0.000 000 000 112 077  -0.527 428 956 787 415 
36  0.000 000 000 042 006  -0.527 428 956 745 409 
37  0.000 000 000 006 468  -0.527 428 956 738 941 
38 -0.000 000 000 009 419  -0.527 428 956 748 36 
39 -0.000 000 000 014 747  -0.527 428 956 763 107 
40 -0.000 000 000 014 861  -0.527 428 956 777 968 
41 -0.000 000 000 012 763  -0.527 428 956 790 731 
42 -0.000 000 000 010 034  -0.527 428 956 800 765 
43 -0.000 000 000 007 432  -0.527 428 956 808 197 
44 -0.000 000 000 005 259  -0.527 428 956 813 456 
45 -0.000 000 000 003 58  -0.527 428 956 817 036 
46 -0.000 000 000 002 352  -0.527 428 956 819 388 
47 -0.000 000 000 001 492  -0.527 428 956 820 88 
48 -0.000 000 000 000 912  -0.527 428 956 821 792 
49 -0.000 000 000 000 534  -0.527 428 956 822 326 
50 -0.000 000 000 000 296  -0.527 428 956 822 622 
51 -0.000 000 000 000 152  -0.527 428 956 822 774 
52 -0.000 000 000 000 068  -0.527 428 956 822 842 
53 -0.000 000 000 000 023  -0.527 428 956 822 865 
Exact energy -0.527 428 956 822 795 
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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 = -2.1211 and c =  0.1257
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -0.49 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.