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

Molecule X 1^Sigma+ State of HF. 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 -100.019 418 409 917 748  -100.019 418 409 917 748 
2 -0.201 619 181 365 082  -100.221 037 591 282 83 
3 -0.002 909 956 975 082  -100.223 947 548 257 912 
4 -0.004 199 520 355 299  -100.228 147 068 613 211 
5 -0.000 061 232 756 48  -100.228 208 301 369 691 
6 -0.000 438 246 849 547  -100.228 646 548 219 238 
7  0.000 078 691 820 312  -100.228 567 856 398 926 
8 -0.000 084 114 801 069  -100.228 651 971 199 995 
9  0.000 026 939 135 579  -100.228 625 032 064 416 
10 -0.000 019 143 976 835  -100.228 644 176 041 251 
11  0.000 008 797 330 617  -100.228 635 378 710 634 
12 -0.000 005 656 443 509  -100.228 641 035 154 143 
13  0.000 003 168 258 801  -100.228 637 866 895 342 
14 -0.000 002 003 325 477  -100.228 639 870 220 819 
15  0.000 001 233 070 289  -100.228 638 637 150 53 
16 -0.000 000 792 839 777  -100.228 639 429 990 307 
17  0.000 000 512 127 82  -100.228 638 917 862 487 
18 -0.000 000 336 959 079  -100.228 639 254 821 566 
19  0.000 000 223 922 701  -100.228 639 030 898 865 
20 -0.000 000 150 376 468  -100.228 639 181 275 333 
21  0.000 000 101 891 428  -100.228 639 079 383 905 
22 -0.000 000 069 559 438  -100.228 639 148 943 343 
23  0.000 000 047 821 572  -100.228 639 101 121 771 
24 -0.000 000 033 069 549  -100.228 639 134 191 32 
25  0.000 000 022 992 406  -100.228 639 111 198 914 
26 -0.000 000 016 060 13  -100.228 639 127 259 044 
27  0.000 000 011 265 205  -100.228 639 115 993 839 
28 -0.000 000 007 930 91  -100.228 639 123 924 749 
29  0.000 000 005 601 962  -100.228 639 118 322 787 
30 -0.000 000 003 968 504  -100.228 639 122 291 291 
31  0.000 000 002 818 729  -100.228 639 119 472 562 
32 -0.000 000 002 006 782  -100.228 639 121 479 344 
33  0.000 000 001 431 75  -100.228 639 120 047 594 
34 -0.000 000 001 023 448  -100.228 639 121 071 042 
35  0.000 000 000 732 859  -100.228 639 120 338 183 
36 -0.000 000 000 525 613  -100.228 639 120 863 796 
37  0.000 000 000 377 525  -100.228 639 120 486 271 
38 -0.000 000 000 271 525  -100.228 639 120 757 796 
39  0.000 000 000 195 533  -100.228 639 120 562 263 
40 -0.000 000 000 140 974  -100.228 639 120 703 237 
41  0.000 000 000 101 75  -100.228 639 120 601 487 
42 -0.000 000 000 073 516  -100.228 639 120 675 003 
43  0.000 000 000 053 169  -100.228 639 120 621 834 
44 -0.000 000 000 038 49  -100.228 639 120 660 324 
45  0.000 000 000 027 888  -100.228 639 120 632 436 
46 -0.000 000 000 020 225  -100.228 639 120 652 661 
47  0.000 000 000 014 679  -100.228 639 120 637 982 
48 -0.000 000 000 010 663  -100.228 639 120 648 645 
49  0.000 000 000 007 752  -100.228 639 120 640 893 
Exact energy -100.228 639 120 640 893 
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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 =  0.8342, b = -4.5927 and c =  4.6143
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -100.02 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.