Møller-Plesset perturbation theory: example "a91"

Molecule SH-. Basis aug-cc-pVDZ. Structure "mpn_Rfci"

Content


Examplesa1a2a8a16a22a30a38a44a45a51a62a69a75a83a84a85a86a87a88a90a91
MoleculeArBHBHBHBHBHBHBO+C2CN+N2HFHFHClHClF-Cl-Cl-NeOH-SH-
Basisaug-cc-pVDZcc-pVDZcc-pVTZcc-pVQZaug-cc-pVDZaug-cc-pVTZaug-cc-pVQZcc-pVDZcc-pVDZcc-pVDZcc-pVDZcc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-pVDZ

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -398.133 595 979 631 37  -398.133 595 979 631 37 
2 -0.159 633 804 331 33  -398.293 229 783 962 7 
3 -0.016 627 283 826 06  -398.309 857 067 788 76 
4 -0.005 562 037 925 14  -398.315 419 105 713 9 
5 -0.000 717 818 179 44  -398.316 136 923 893 34 
6 -0.000 669 531 803 66  -398.316 806 455 697 
7  0.000 058 202 839 44  -398.316 748 252 857 56 
8 -0.000 159 693 139 67  -398.316 907 945 997 23 
9  0.000 071 766 987 67  -398.316 836 179 009 56 
10 -0.000 065 244 776 57  -398.316 901 423 786 13 
11  0.000 043 843 490 03  -398.316 857 580 296 1 
12 -0.000 034 883 750 1  -398.316 892 464 046 2 
13  0.000 026 492 518 9  -398.316 865 971 527 3 
14 -0.000 021 125 396 1  -398.316 887 096 923 4 
15  0.000 016 888 161 97  -398.316 870 208 761 43 
16 -0.000 013 805 384 57  -398.316 884 014 146 
17  0.000 011 409 197 9  -398.316 872 604 948 1 
18 -0.000 009 575 460 7  -398.316 882 180 408 8 
19  0.000 008 132 555 7  -398.316 874 047 853 1 
20 -0.000 006 996 742 06  -398.316 881 044 595 16 
21  0.000 006 089 415 16  -398.316 874 955 18 
22 -0.000 005 361 621 8  -398.316 880 316 801 8 
23  0.000 004 772 774 7  -398.316 875 544 027 1 
24 -0.000 004 294 445 53  -398.316 879 838 472 63 
25  0.000 003 904 024 2  -398.316 875 934 448 43 
26 -0.000 003 584 662 92  -398.316 879 519 111 35 
27  0.000 003 323 071 61  -398.316 876 196 039 74 
28 -0.000 003 108 990 32  -398.316 879 305 030 06 
29  0.000 002 934 283 09  -398.316 876 370 746 97 
Exact energy -398.316 877 798 690 1 
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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 =  1.1470, b = -5.5080 and c =  5.7431
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -398.13 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.
Encircled areas are subjectively estimated locations of
the dominant zc = -1.1 and a subdominant z'c = 2.5 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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Examplesa1a2a8a16a22a30a38a44a45a51a62a69a75a83a84a85a86a87a88a90a91
MoleculeArBHBHBHBHBHBHBO+C2CN+N2HFHFHClHClF-Cl-Cl-NeOH-SH-
Basisaug-cc-pVDZcc-pVDZcc-pVTZcc-pVQZaug-cc-pVDZaug-cc-pVTZaug-cc-pVQZcc-pVDZcc-pVDZcc-pVDZcc-pVDZcc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-pVDZ

Known inaccuracies


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Designed by A. Sergeev.