Møller-Plesset perturbation theory: example "BH-cc-pVDZ-2Re"

Molecule X 1^Sigma+ State of BH. Basis CC-PVDZ. 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 -24.993 152 771 987 988  -24.993 152 771 987 988 
2 -0.072 478 443 461 968  -25.065 631 215 449 956 
3 -0.024 740 760 139 692  -25.090 371 975 589 648 
4 -0.013 272 378 455 587  -25.103 644 354 045 235 
5 -0.007 058 177 995 344  -25.110 702 532 040 579 
6 -0.003 794 848 960 28  -25.114 497 381 000 859 
7 -0.001 921 563 826 192  -25.116 418 944 827 051 
8 -0.000 867 622 300 585  -25.117 286 567 127 636 
9 -0.000 299 286 253 718  -25.117 585 853 381 354 
10 -0.000 016 456 375 883  -25.117 602 309 757 237 
11  0.000 102 938 154 753  -25.117 499 371 602 484 
12  0.000 134 076 368 34  -25.117 365 295 234 144 
13  0.000 122 231 184 117  -25.117 243 064 050 027 
14  0.000 093 695 321 435  -25.117 149 368 728 592 
15  0.000 062 749 672 93  -25.117 086 619 055 662 
16  0.000 036 233 518 548  -25.117 050 385 537 114 
17  0.000 016 566 044 928  -25.117 033 819 492 186 
18  0.000 003 732 687 242  -25.117 030 086 804 944 
19 -0.000 003 438 036 018  -25.117 033 524 840 962 
20 -0.000 006 492 041 5  -25.117 040 016 882 462 
21 -0.000 006 909 481 684  -25.117 046 926 364 146 
22 -0.000 005 894 776 381  -25.117 052 821 140 527 
23 -0.000 004 312 984 939  -25.117 057 134 125 466 
24 -0.000 002 710 677 266  -25.117 059 844 802 732 
25 -0.000 001 377 605 697  -25.117 061 222 408 429 
26 -0.000 000 420 363 441  -25.117 061 642 771 87 
27  0.000 000 169 049 257  -25.117 061 473 722 613 
28  0.000 000 458 138 674  -25.117 061 015 583 939 
29  0.000 000 534 777 871  -25.117 060 480 806 068 
30  0.000 000 482 889 606  -25.117 059 997 916 462 
31  0.000 000 370 032 564  -25.117 059 627 883 898 
32  0.000 000 243 431 957  -25.117 059 384 451 941 
33  0.000 000 131 231 846  -25.117 059 253 220 095 
34  0.000 000 046 377 402  -25.117 059 206 842 693 
35 -0.000 000 008 711 524  -25.117 059 215 554 217 
36 -0.000 000 037 809 314  -25.117 059 253 363 531 
37 -0.000 000 047 461 376  -25.117 059 300 824 907 
38 -0.000 000 044 630 51  -25.117 059 345 455 417 
39 -0.000 000 035 325 86  -25.117 059 380 781 277 
40 -0.000 000 024 004 259  -25.117 059 404 785 536 
41 -0.000 000 013 499 849  -25.117 059 418 285 385 
42 -0.000 000 005 259 009  -25.117 059 423 544 394 
43  0.000 000 000 294 093  -25.117 059 423 250 301 
44  0.000 000 003 380 345  -25.117 059 419 869 956 
45  0.000 000 004 545 35  -25.117 059 415 324 606 
46  0.000 000 004 424 704  -25.117 059 410 899 902 
47  0.000 000 003 596 761  -25.117 059 407 303 141 
48  0.000 000 002 509 349  -25.117 059 404 793 792 
49  0.000 000 001 460 459  -25.117 059 403 333 333 
Exact energy -25.117 059 404 623 3 
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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 =  0.8023, b = -2.3246 and c =  0.6303
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -24.99 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.