Møller-Plesset perturbation theory: example "a38"

Molecule BH. Basis aug-cc-pVQZ. 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 -25.131 366 039 3  -25.131 366 039 3 
2 -0.078 635 551 6  -25.210 001 590 9 
3 -0.014 820 453  -25.224 822 043 9 
4 -0.005 859 359 1  -25.230 681 403 
5 -0.002 510 736  -25.233 192 139 
6 -0.001 237 247 5  -25.234 429 386 5 
7 -0.000 643 019 9  -25.235 072 406 4 
8 -0.000 348 435 6  -25.235 420 842 
9 -0.000 191 607 4  -25.235 612 449 4 
10 -0.000 105 883 4  -25.235 718 332 8 
11 -0.000 058 252 3  -25.235 776 585 1 
12 -0.000 031 752 3  -25.235 808 337 4 
13 -0.000 017 066 1  -25.235 825 403 5 
14 -0.000 009 008 6  -25.235 834 412 1 
15 -0.000 004 645 1  -25.235 839 057 2 
16 -0.000 002 322 7  -25.235 841 379 9 
17 -0.000 001 112 2  -25.235 842 492 1 
18 -0.000 000 498 2  -25.235 842 990 3 
19 -0.000 000 197 8  -25.235 843 188 1 
20 -0.000 000 058 4  -25.235 843 246 5 
21  0.000 000 001  -25.235 843 245 5 
22  0.000 000 022 2  -25.235 843 223 3 
23  0.000 000 026 4  -25.235 843 196 9 
24  0.000 000 023 9  -25.235 843 173 
25  0.000 000 019 3  -25.235 843 153 7 
26  0.000 000 014 7  -25.235 843 139 
27  0.000 000 010 7  -25.235 843 128 3 
28  0.000 000 007 7  -25.235 843 120 6 
29  0.000 000 005 4  -25.235 843 115 2 
30  0.000 000 003 8  -25.235 843 111 4 
31  0.000 000 002 5  -25.235 843 108 9 
32  0.000 000 001 7  -25.235 843 107 2 
33  0.000 000 001 2  -25.235 843 106 
34  0.000 000 000 7  -25.235 843 105 3 
35  0.000 000 000 5  -25.235 843 104 8 
36  0.000 000 000 3  -25.235 843 104 5 
37  0.000 000 000 2  -25.235 843 104 3 
38  -10  0. x 10  -25.235 843 104 2 
39  -10  0. x 10  -25.235 843 104 1 
Exact energy -25.235 843 243 994 
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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 =  0.7319, b = -3.5878 and c =  6.4716
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.13 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 = 1.61 + 0.35 i and a subdominant z'c = -3.5 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.
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.