Møller-Plesset perturbation theory: example "a51"

Molecule CN+. Basis 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 -91.617 491 879 7  -91.617 491 879 7 
2 -0.355 497 960 1  -91.972 989 839 8 
3  0.059 129 699  -91.913 860 140 8 
4 -0.106 018 924 1  -92.019 879 064 9 
5  0.082 917 117 3  -91.936 961 947 6 
6 -0.110 745 657 6  -92.047 707 605 2 
7  0.128 461 189 3  -91.919 246 415 9 
8 -0.174 396 284 6  -92.093 642 700 5 
9  0.227 849 615 2  -91.865 793 085 3 
10 -0.307 066 645 7  -92.172 859 731 
11  0.406 806 592 4  -91.766 053 138 6 
12 -0.536 560 427 2  -92.302 613 565 8 
13  0.697 793 095 8  -91.604 820 47 
Exact energy -91.997 968 947 642 
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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 =  1.6366, b = -2.0652 and c =  0.2577
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -91.62 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 = -0.6 and a subdominant z'c = 1.1 + 0.2 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.
Red circle marks the lowest excited energy level 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.