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

Molecule X 1^Sigma+ State of HF. 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 -99.792 599 047 482 185  -99.792 599 047 482 185 
2 -0.243 612 035 859 46  -100.036 211 083 341 645 
3 -0.000 801 211 583 273  -100.037 012 294 924 918 
4 -0.018 640 993 996 257  -100.055 653 288 921 175 
5 -0.002 425 116 577 205  -100.058 078 405 498 38 
6 -0.004 883 909 879 625  -100.062 962 315 378 005 
7 -0.000 403 181 645 503  -100.063 365 497 023 508 
8 -0.001 241 414 336 999  -100.064 606 911 360 507 
9  0.000 330 875 460 583  -100.064 276 035 899 924 
10 -0.000 075 461 814 107  -100.064 351 497 714 031 
11  0.000 359 839 257 319  -100.063 991 658 456 712 
12  0.000 117 551 022 519  -100.063 874 107 434 193 
13  0.000 199 951 117 237  -100.063 674 156 316 956 
14  0.000 053 488 391 762  -100.063 620 667 925 194 
15  0.000 067 294 842 354  -100.063 553 373 082 84 
16 -0.000 010 114 914 017  -100.063 563 487 996 857 
17  0.000 007 232 770 378  -100.063 556 255 226 479 
18 -0.000 029 167 172 279  -100.063 585 422 398 758 
19 -0.000 004 434 189 22  -100.063 589 856 587 978 
20 -0.000 023 209 005 437  -100.063 613 065 593 415 
21  0.000 001 190 383 531  -100.063 611 875 209 884 
22 -0.000 013 182 394 099  -100.063 625 057 603 983 
23  0.000 007 260 127 649  -100.063 617 797 476 334 
24 -0.000 007 595 509 204  -100.063 625 392 985 538 
25  0.000 009 636 599 696  -100.063 615 756 385 842 
26 -0.000 006 560 940 771  -100.063 622 317 326 613 
27  0.000 009 761 809 49  -100.063 612 555 517 123 
28 -0.000 007 802 531 52  -100.063 620 358 048 643 
29  0.000 009 744 463 055  -100.063 610 613 585 588 
30 -0.000 009 738 416 714  -100.063 620 352 002 302 
31  0.000 010 716 458 988  -100.063 609 635 543 314 
32 -0.000 012 015 485 727  -100.063 621 651 029 041 
33  0.000 013 021 427 946  -100.063 608 629 601 095 
34 -0.000 015 050 238 972  -100.063 623 679 840 067 
35  0.000 016 849 472 307  -100.063 606 830 367 76 
36 -0.000 019 604 064 937  -100.063 626 434 432 697 
37  0.000 022 711 123 226  -100.063 603 723 309 471 
38 -0.000 026 716 290 451  -100.063 630 439 599 922 
39  0.000 031 729 259 446  -100.063 598 710 340 476 
40 -0.000 037 968 614 407  -100.063 636 678 954 883 
41  0.000 045 959 684 073  -100.063 590 719 270 81 
42 -0.000 056 034 677 309  -100.063 646 753 948 119 
43  0.000 068 992 820 077  -100.063 577 761 128 042 
44 -0.000 085 616 421 155  -100.063 663 377 549 197 
45  0.000 107 131 634 009  -100.063 556 245 915 188 
46 -0.000 135 094 778 619  -100.063 691 340 693 807 
47  0.000 171 613 295 818  -100.063 519 727 397 989 
48 -0.000 219 555 001 784  -100.063 739 282 399 773 
49  0.000 282 748 330 89  -100.063 456 534 068 883 
Exact energy -100.063 456 534 068 883 
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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 =  1.9224, b = -18.0600 and c =  8906146706294.6800
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -99.79 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.