Møller-Plesset perturbation theory: example "BH aug-cc-pVQZ 1.5r_e"

Molecule X 1^Sigma+ State of BH. Basis AUG-CC-PVQZ. Structure ""

Content


ExamplesAr cc-pVDZBH aug-cc-pVQZ 0.9r_eBH aug-cc-pVQZ 1.0r_eBH aug-cc-pVQZ 1.1r_eBH aug-cc-pVQZ 1.2r_eBH aug-cc-pVQZ 1.3r_eBH aug-cc-pVQZ 1.4r_eBH aug-cc-pVQZ 1.5r_eBH aug-cc-pVQZ 1.6r_eBH aug-cc-pVQZ 1.7r_eBH aug-cc-pVQZ 1.8r_eBH aug-cc-pVQZ 1.9r_eBH aug-cc-pVQZ 2.0r_eBH aug-cc-pVQZ 2.1r_eBH aug-cc-pVQZ 2.2r_eBH 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 aug-cc-pVDZ 1.5r_eHF aug-cc-pVDZ 2.0r_eHF aug-cc-pVDZ r_eHF cc-pVDZ 1.5ReHF cc-pVDZ 2ReHF cc-pVDZ Rena-pl aug-cc-pvdzNe cc-pVDZO2- aug-cc-pVDZ
MoleculeArX 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 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 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 HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -25.068 187 436 594 365  -25.068 187 436 594 365 
2 -0.082 668 726 661 57  -25.150 856 163 255 935 
3 -0.017 659 698 082 893  -25.168 515 861 338 828 
4 -0.008 250 343 124 204  -25.176 766 204 463 032 
5 -0.003 653 606 276 814  -25.180 419 810 739 846 
6 -0.001 781 890 242 15  -25.182 201 700 981 996 
7 -0.000 837 042 574 266  -25.183 038 743 556 262 
8 -0.000 389 255 140 891  -25.183 427 998 697 153 
9 -0.000 169 454 977 638  -25.183 597 453 674 791 
10 -0.000 066 892 331 054  -25.183 664 346 005 845 
11 -0.000 020 910 711 381  -25.183 685 256 717 226 
12 -0.000 002 284 220 124  -25.183 687 540 937 35 
13  0.000 003 955 422 335  -25.183 683 585 515 015 
14  0.000 004 981 919 753  -25.183 678 603 595 262 
15  0.000 004 164 740 978  -25.183 674 438 854 284 
16  0.000 002 949 000 927  -25.183 671 489 853 357 
17  0.000 001 880 160 821  -25.183 669 609 692 536 
18  0.000 001 098 770 725  -25.183 668 510 921 811 
19  0.000 000 587 247 817  -25.183 667 923 673 994 
20  0.000 000 280 138 789  -25.183 667 643 535 205 
21  0.000 000 110 732 631  -25.183 667 532 802 574 
22  0.000 000 026 248 833  -25.183 667 506 553 741 
23 -0.000 000 009 945 649  -25.183 667 516 499 39 
24 -0.000 000 021 089 673  -25.183 667 537 589 063 
25 -0.000 000 020 785 481  -25.183 667 558 374 544 
26 -0.000 000 016 350 774  -25.183 667 574 725 318 
27 -0.000 000 011 313 444  -25.183 667 586 038 762 
28 -0.000 000 007 094 216  -25.183 667 593 132 978 
29 -0.000 000 004 049 245  -25.183 667 597 182 223 
30 -0.000 000 002 069 52  -25.183 667 599 251 743 
31 -0.000 000 000 896 001  -25.183 667 600 147 744 
32 -0.000 000 000 266 755  -25.183 667 600 414 499 
33  0.000 000 000 027 859  -25.183 667 600 386 64 
34  0.000 000 000 135 191  -25.183 667 600 251 449 
35  0.000 000 000 149 191  -25.183 667 600 102 258 
36  0.000 000 000 124 559  -25.183 667 599 977 699 
37  0.000 000 000 090 018  -25.183 667 599 887 681 
38  0.000 000 000 058 588  -25.183 667 599 829 093 
39  0.000 000 000 034 66  -25.183 667 599 794 433 
40  0.000 000 000 018 425  -25.183 667 599 776 008 
41  0.000 000 000 008 42  -25.183 667 599 767 588 
42  0.000 000 000 002 835  -25.183 667 599 764 753 
43  0.000 000 000 000 086  -25.183 667 599 764 667 
44 -0.000 000 000 001 009  -25.183 667 599 765 676 
45 -0.000 000 000 001 239  -25.183 667 599 766 915 
46 -0.000 000 000 001 084  -25.183 667 599 767 999 
47 -0.000 000 000 000 809  -25.183 667 599 768 808 
48 -0.000 000 000 000 541  -25.183 667 599 769 349 
49 -0.000 000 000 000 328  -25.183 667 599 769 677 
50 -0.000 000 000 000 179  -25.183 667 599 769 856 
51 -0.000 000 000 000 085  -25.183 667 599 769 941 
52 -0.000 000 000 000 031  -25.183 667 599 769 972 
53 -0.000 000 000 000 003  -25.183 667 599 769 975 
54  0.000 000 000 000 008  -25.183 667 599 769 967 
55  0.000 000 000 000 011  -25.183 667 599 769 956 
56  -14  0. x 10  -25.183 667 599 769 946 
57  0.000 000 000 000 008  -25.183 667 599 769 938 
58  0.000 000 000 000 005  -25.183 667 599 769 933 
59  0.000 000 000 000 003  -25.183 667 599 769 93 
60  0.000 000 000 000 002  -25.183 667 599 769 928 
61  -15  0. x 10  -25.183 667 599 769 927 
Exact energy -25.183 667 599 769 927 
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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 =  0.6574, b = -2.0641 and c =  0.5795
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.07 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.
Encircled areas are subjectively estimated locations of
the dominant zc = -2.23 and a subdominant z'c = 1.48 + 0.47 i singularities.
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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ExamplesAr cc-pVDZBH aug-cc-pVQZ 0.9r_eBH aug-cc-pVQZ 1.0r_eBH aug-cc-pVQZ 1.1r_eBH aug-cc-pVQZ 1.2r_eBH aug-cc-pVQZ 1.3r_eBH aug-cc-pVQZ 1.4r_eBH aug-cc-pVQZ 1.5r_eBH aug-cc-pVQZ 1.6r_eBH aug-cc-pVQZ 1.7r_eBH aug-cc-pVQZ 1.8r_eBH aug-cc-pVQZ 1.9r_eBH aug-cc-pVQZ 2.0r_eBH aug-cc-pVQZ 2.1r_eBH aug-cc-pVQZ 2.2r_eBH 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 aug-cc-pVDZ 1.5r_eHF aug-cc-pVDZ 2.0r_eHF aug-cc-pVDZ r_eHF cc-pVDZ 1.5ReHF cc-pVDZ 2ReHF cc-pVDZ Rena-pl aug-cc-pvdzNe cc-pVDZO2- aug-cc-pVDZ
MoleculeArX 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 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 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 HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

Known inaccuracies


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Designed by A. Sergeev.