Møller-Plesset perturbation theory: example "o8"

Molecule C2. Basis cc-pVDZ(+). Structure ""

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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

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -76.072 454  -76.072 454 
2  0.311 51  -75.760 944 
3 -0.032 487  -75.793 431 
4  0.069 69  -75.723 741 
5 -0.036 201  -75.759 942 
6  0.038 162  -75.721 78 
7 -0.023 812  -75.745 592 
8  0.021 2  -75.724 392 
9 -0.012 347  -75.736 739 
10  0.008 83  -75.727 909 
11 -0.003 413  -75.731 322 
12  0.000 6  -75.730 722 
13  0.002 179  -75.728 543 
14 -0.003 635  -75.732 178 
15  0.004 442  -75.727 736 
16 -0.004 595  -75.732 331 
17  0.004 143  -75.728 188 
18 -0.003 449  -75.731 637 
19  0.002 439  -75.729 198 
20 -0.001 46  -75.730 658 
21  0.000 46  -75.730 198 
22  0.000 35  -75.729 848 
23 -0.000 993  -75.730 841 
24  0.001 395  -75.729 446 
25 -0.001 578  -75.731 024 
Exact energy -75.730 209 
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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 =  1.0098, b = -2.2828 and c =  1.4033
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -76.07 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.