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

Molecule X 1^Sigma+ State of BH. Basis CC-PVDZ. 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 -25.064 066 278 620 671  -25.064 066 278 620 671 
2 -0.065 575 569 246 811  -25.129 641 847 867 482 
3 -0.020 569 142 083 552  -25.150 210 989 951 034 
4 -0.008 592 363 825 304  -25.158 803 353 776 338 
5 -0.003 933 687 267 132  -25.162 737 041 043 47 
6 -0.001 847 912 819 771  -25.164 584 953 863 241 
7 -0.000 854 411 799 79  -25.165 439 365 663 031 
8 -0.000 376 511 099 43  -25.165 815 876 762 461 
9 -0.000 151 016 359 036  -25.165 966 893 121 497 
10 -0.000 049 645 001 924  -25.166 016 538 123 421 
11 -0.000 007 939 978 036  -25.166 024 478 101 457 
12  0.000 006 385 799 262  -25.166 018 092 302 195 
13  0.000 009 148 610 662  -25.166 008 943 691 533 
14  0.000 007 754 344 67  -25.166 001 189 346 863 
15  0.000 005 417 020 8  -25.165 995 772 326 063 
16  0.000 003 345 984 442  -25.165 992 426 341 621 
17  0.000 001 856 519 244  -25.165 990 569 822 377 
18  0.000 000 911 987 296  -25.165 989 657 835 081 
19  0.000 000 372 479 568  -25.165 989 285 355 513 
20  0.000 000 097 036 474  -25.165 989 188 319 039 
21 -0.000 000 023 159 021  -25.165 989 211 478 06 
22 -0.000 000 061 187 495  -25.165 989 272 665 555 
23 -0.000 000 061 281 468  -25.165 989 333 947 023 
24 -0.000 000 047 665 044  -25.165 989 381 612 067 
25 -0.000 000 032 086 965  -25.165 989 413 699 032 
26 -0.000 000 019 235 253  -25.165 989 432 934 285 
27 -0.000 000 010 218 994  -25.165 989 443 153 279 
28 -0.000 000 004 603 433  -25.165 989 447 756 712 
29 -0.000 000 001 483 997  -25.165 989 449 240 709 
30  0.000 000 000 019 728  -25.165 989 449 220 981 
31  0.000 000 000 587 89  -25.165 989 448 633 091 
32  0.000 000 000 678 661  -25.165 989 447 954 43 
33  0.000 000 000 568 102  -25.165 989 447 386 328 
34  0.000 000 000 404 26  -25.165 989 446 982 068 
35  0.000 000 000 254 974  -25.165 989 446 727 094 
36  0.000 000 000 143 085  -25.165 989 446 584 009 
37  0.000 000 000 069 399  -25.165 989 446 514 61 
38  0.000 000 000 026 109  -25.165 989 446 488 501 
39  0.000 000 000 003 76  -25.165 989 446 484 741 
40 -0.000 000 000 005 735  -25.165 989 446 490 476 
41 -0.000 000 000 008 227  -25.165 989 446 498 703 
42 -0.000 000 000 007 466  -25.165 989 446 506 169 
43 -0.000 000 000 005 595  -25.165 989 446 511 764 
44 -0.000 000 000 003 685  -25.165 989 446 515 449 
45 -0.000 000 000 002 16  -25.165 989 446 517 609 
46 -0.000 000 000 001 107  -25.165 989 446 518 716 
47 -0.000 000 000 000 46  -25.165 989 446 519 176 
48 -0.000 000 000 000 109  -25.165 989 446 519 285 
49  0.000 000 000 000 053  -25.165 989 446 519 232 
Exact energy -25.165 989 446 518 8 
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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 = -3.0371 and c =  2.8570
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.06 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.