Møller-Plesset perturbation theory: example "BH-cc-pVQZ-Re"

Molecule X 1^Sigma+ State of BH. Basis CC-PVQZ. 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 -25.131 295 405 160 681  -25.131 295 405 160 681 
2 -0.078 145 387 510 342  -25.209 440 792 671 023 
3 -0.015 110 378 592 481  -25.224 551 171 263 504 
4 -0.005 868 326 136 459  -25.230 419 497 399 963 
5 -0.002 505 919 488 595  -25.232 925 416 888 558 
6 -0.001 233 748 830 341  -25.234 159 165 718 899 
7 -0.000 641 545 181 663  -25.234 800 710 900 562 
8 -0.000 347 191 042 445  -25.235 147 901 943 007 
9 -0.000 190 699 644 428  -25.235 338 601 587 435 
10 -0.000 105 183 884 991  -25.235 443 785 472 426 
11 -0.000 057 758 964 774  -25.235 501 544 437 2 
12 -0.000 031 411 320 013  -25.235 532 955 757 213 
13 -0.000 016 841 836 204  -25.235 549 797 593 417 
14 -0.000 008 864 652 905  -25.235 558 662 246 322 
15 -0.000 004 555 933 471  -25.235 563 218 179 793 
16 -0.000 002 268 652 267  -25.235 565 486 832 06 
17 -0.000 001 080 382 252  -25.235 566 567 214 312 
18 -0.000 000 479 867 92  -25.235 567 047 082 232 
19 -0.000 000 187 456 269  -25.235 567 234 538 501 
20 -0.000 000 052 613 458  -25.235 567 287 151 959 
21  0.000 000 004 176 001  -25.235 567 282 975 958 
22  0.000 000 023 972 375  -25.235 567 259 003 583 
23  0.000 000 027 389 727  -25.235 567 231 613 856 
24  0.000 000 024 399 461  -25.235 567 207 214 395 
25  0.000 000 019 573 216  -25.235 567 187 641 179 
26  0.000 000 014 830 092  -25.235 567 172 811 087 
27  0.000 000 010 842 326  -25.235 567 161 968 761 
28  0.000 000 007 733 926  -25.235 567 154 234 835 
29  0.000 000 005 415 092  -25.235 567 148 819 743 
30  0.000 000 003 733 969  -25.235 567 145 085 774 
31  0.000 000 002 539 805  -25.235 567 142 545 969 
32  0.000 000 001 705 016  -25.235 567 140 840 953 
33  0.000 000 001 129 422  -25.235 567 139 711 531 
34  0.000 000 000 737 603  -25.235 567 138 973 928 
35  0.000 000 000 474 269  -25.235 567 138 499 659 
36  0.000 000 000 299 635  -25.235 567 138 200 024 
37  0.000 000 000 185 482  -25.235 567 138 014 542 
38  0.000 000 000 112 048  -25.235 567 137 902 494 
39  0.000 000 000 065 66  -25.235 567 137 836 834 
40  0.000 000 000 036 969  -25.235 567 137 799 865 
41  0.000 000 000 019 67  -25.235 567 137 780 195 
42  0.000 000 000 009 565  -25.235 567 137 770 63 
43  0.000 000 000 003 905  -25.235 567 137 766 725 
44  0.000 000 000 000 92  -25.235 567 137 765 805 
45 -0.000 000 000 000 508  -25.235 567 137 766 313 
46 -0.000 000 000 001 069  -25.235 567 137 767 382 
47 -0.000 000 000 001 177  -25.235 567 137 768 559 
48 -0.000 000 000 001 073  -25.235 567 137 769 632 
49 -0.000 000 000 000 888  -25.235 567 137 770 52 
Exact energy -25.235 567 137 772 9 
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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 =  0.7319, b = -3.6371 and c =  6.5289
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.13 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.