Møller-Plesset perturbation theory: example "BH aug-cc-pVQZ 1.3r_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 -25.099 585 716 709 079  -25.099 585 716 709 079 
2 -0.080 744 264 971 906  -25.180 329 981 680 985 
3 -0.016 371 464 856 284  -25.196 701 446 537 269 
4 -0.007 078 433 632 674  -25.203 779 880 169 943 
5 -0.003 051 636 895 339  -25.206 831 517 065 282 
6 -0.001 462 544 848 14  -25.208 294 061 913 422 
7 -0.000 700 979 860 011  -25.208 995 041 773 433 
8 -0.000 339 872 025 946  -25.209 334 913 799 379 
9 -0.000 160 767 713 898  -25.209 495 681 513 277 
10 -0.000 073 104 482 926  -25.209 568 785 996 203 
11 -0.000 030 685 943 594  -25.209 599 471 939 797 
12 -0.000 011 011 518 431  -25.209 610 483 458 228 
13 -0.000 002 476 202 335  -25.209 612 959 660 563 
14  0.000 000 756 404 759  -25.209 612 203 255 804 
15  0.000 001 626 041 761  -25.209 610 577 214 043 
16  0.000 001 552 130 811  -25.209 609 025 083 232 
17  0.000 001 189 489 894  -25.209 607 835 593 338 
18  0.000 000 810 234 898  -25.209 607 025 358 44 
19  0.000 000 507 213 697  -25.209 606 518 144 743 
20  0.000 000 294 779 551  -25.209 606 223 365 192 
21  0.000 000 158 530 545  -25.209 606 064 834 647 
22  0.000 000 077 407 009  -25.209 605 987 427 638 
23  0.000 000 032 562 802  -25.209 605 954 864 836 
24  0.000 000 009 846 237  -25.209 605 945 018 599 
25 -0.000 000 000 310 721  -25.209 605 945 329 32 
26 -0.000 000 003 891 13  -25.209 605 949 220 45 
27 -0.000 000 004 378 281  -25.209 605 953 598 731 
28 -0.000 000 003 653 003  -25.209 605 957 251 734 
29 -0.000 000 002 638 942  -25.209 605 959 890 676 
30 -0.000 000 001 728 057  -25.209 605 961 618 733 
31 -0.000 000 001 041 027  -25.209 605 962 659 76 
32 -0.000 000 000 576 003  -25.209 605 963 235 763 
33 -0.000 000 000 287 096  -25.209 605 963 522 859 
34 -0.000 000 000 121 726  -25.209 605 963 644 585 
35 -0.000 000 000 035 528  -25.209 605 963 680 113 
36  0.000 000 000 003 873  -25.209 605 963 676 24 
37  0.000 000 000 017 902  -25.209 605 963 658 338 
38  0.000 000 000 019 623  -25.209 605 963 638 715 
39  0.000 000 000 016 379  -25.209 605 963 622 336 
40  0.000 000 000 011 908  -25.209 605 963 610 428 
41  0.000 000 000 007 86  -25.209 605 963 602 568 
42  0.000 000 000 004 773  -25.209 605 963 597 795 
43  0.000 000 000 002 659  -25.209 605 963 595 136 
44  0.000 000 000 001 331  -25.209 605 963 593 805 
45  0.000 000 000 000 563  -25.209 605 963 593 242 
46  0.000 000 000 000 16  -25.209 605 963 593 082 
47 -0.000 000 000 000 026  -25.209 605 963 593 108 
48 -0.000 000 000 000 092  -25.209 605 963 593 2 
49 -0.000 000 000 000 1  -25.209 605 963 593 3 
50 -0.000 000 000 000 083  -25.209 605 963 593 383 
51 -0.000 000 000 000 06  -25.209 605 963 593 443 
52 -0.000 000 000 000 04  -25.209 605 963 593 483 
53 -0.000 000 000 000 024  -25.209 605 963 593 507 
54 -0.000 000 000 000 014  -25.209 605 963 593 521 
55 -0.000 000 000 000 007  -25.209 605 963 593 528 
56 -0.000 000 000 000 003  -25.209 605 963 593 531 
57  -15 -0. x 10  -25.209 605 963 593 532 
Exact energy -25.209 605 963 593 53 
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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 = -2.3397 and c =  0.8908
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.10 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 = -2.4 and a subdominant z'c = 1.47 + 0.48 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.