Møller-Plesset perturbation theory: example "o6"

Molecule CH2. Basis aug-cc-pVDZ. 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 -39.180 638  -39.180 638 
2  0.115 682  -39.064 956 
3  0.021 138  -39.043 818 
4  0.006 313  -39.037 505 
5  0.002 145  -39.035 36 
6  0.001 007  -39.034 353 
7  0.000 547  -39.033 806 
8  0.000 35  -39.033 456 
9  0.000 238  -39.033 218 
10  0.000 173  -39.033 045 
11  0.000 129  -39.032 916 
12  0.000 099  -39.032 817 
13  0.000 077  -39.032 74 
14  0.000 06  -39.032 68 
15  0.000 048  -39.032 632 
16  0.000 037  -39.032 595 
17  0.000 031  -39.032 564 
18  0.000 024  -39.032 54 
19  0.000 019  -39.032 521 
20  0.000 015  -39.032 506 
21  0.000 013  -39.032 493 
22  0.000 009  -39.032 484 
23  0.000 008  -39.032 476 
24  0.000 006  -39.032 47 
25  0.000 005  -39.032 465 
26  0.000 004  -39.032 461 
27  0.000 004  -39.032 457 
28  0.000 002  -39.032 455 
29  0.000 002  -39.032 453 
30  0.000 002  -39.032 451 
31  0.000 001  -39.032 45 
32  0.000 001  -39.032 449 
33  -353  0. x 10  -39.032 449 
Exact energy -39.032 446 
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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 =  0.9569, b = -3.2782 and c =  0.5764
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -39.18 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.