Møller-Plesset perturbation theory: example "o7"

Molecule CH2. Basis cc-pVTZ-(f/d). Structure "theta=104.5`256"

Content


Exampleso1o2o3o4o5o6o7o8o9
MoleculeNeNeF-HFH2OCH2CH2C2N2
Basiscc-pVDZcc-pVTZ-(f)cc-pVTZ-(f)cc-pVTZ-(f/d)cc-pVDZ(+)aug-cc-pVDZcc-pVTZ-(f/d)cc-pVDZ(+)cc-pVDZ

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -39.208 267  -39.208 267 
2  0.126 792  -39.081 475 
3  0.019 942  -39.061 533 
4  0.006 603  -39.054 93 
5  0.002 017  -39.052 913 
6  0.001 023  -39.051 89 
7  0.000 541  -39.051 349 
8  0.000 356  -39.050 993 
9  0.000 244  -39.050 749 
10  0.000 179  -39.050 57 
11  0.000 134  -39.050 436 
12  0.000 104  -39.050 332 
13  0.000 08  -39.050 252 
14  0.000 064  -39.050 188 
15  0.000 05  -39.050 138 
16  0.000 04  -39.050 098 
17  0.000 032  -39.050 066 
18  0.000 025  -39.050 041 
19  0.000 021  -39.050 02 
20  0.000 016  -39.050 004 
21  0.000 013  -39.049 991 
22  0.000 011  -39.049 98 
23  0.000 008  -39.049 972 
24  0.000 007  -39.049 965 
25  0.000 005  -39.049 96 
26  0.000 004  -39.049 956 
27  0.000 004  -39.049 952 
28  0.000 002  -39.049 95 
29  0.000 002  -39.049 948 
30  0.000 002  -39.049 946 
31  0.000 001  -39.049 945 
32  0.000 001  -39.049 944 
33  0.000 001  -39.049 943 
Exact energy -39.049 94 
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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 =  0.9571, b = -3.2686 and c =  0.5941
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -39.21 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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Exampleso1o2o3o4o5o6o7o8o9
MoleculeNeNeF-HFH2OCH2CH2C2N2
Basiscc-pVDZcc-pVTZ-(f)cc-pVTZ-(f)cc-pVTZ-(f/d)cc-pVDZ(+)aug-cc-pVDZcc-pVTZ-(f/d)cc-pVDZ(+)cc-pVDZ

Known inaccuracies


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Designed by A. Sergeev.