Møller-Plesset perturbation theory: example "a83"

Molecule HCl. 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 -460.089 433 045 457 44  -460.089 433 045 457 44 
2 -0.146 387 976 127 7  -460.235 821 021 585 14 
3 -0.015 577 563 995 86  -460.251 398 585 581 
4 -0.002 713 943 042 7  -460.254 112 528 623 7 
5 -0.000 645 473 426 74  -460.254 758 002 050 44 
6 -0.000 246 561 967 66  -460.255 004 564 018 1 
7 -0.000 066 155 856 7  -460.255 070 719 874 8 
8 -0.000 026 431 573 16  -460.255 097 151 447 96 
9 -0.000 006 325 020 7  -460.255 103 476 468 66 
10 -0.000 003 360 333 1  -460.255 106 836 801 76 
11 -0.000 000 530 404 64  -460.255 107 367 206 4 
12 -0.000 000 477 443 44  -460.255 107 844 649 84 
13  0.000 000 008 409 47  -460.255 107 836 240 37 
14 -0.000 000 082 450 3  -460.255 107 918 690 67 
15  0.000 000 022 955 47  -460.255 107 895 735 2 
16 -0.000 000 019 464 8  -460.255 107 915 2 
17  0.000 000 009 825 2  -460.255 107 905 374 8 
18 -0.000 000 006 035  -460.255 107 911 409 8 
19  0.000 000 003 629 54  -460.255 107 907 780 26 
20 -0.000 000 002 161 98  -460.255 107 909 942 24 
21  0.000 000 001 344 4  -460.255 107 908 597 84 
22 -0.000 000 000 824 16  -460.255 107 909 422 
23  0.000 000 000 515 4  -460.255 107 908 906 6 
24 -0.000 000 000 324 47  -460.255 107 909 231 07 
25  0.000 000 000 204 27  -460.255 107 909 026 8 
26 -0.000 000 000 130 6  -460.255 107 909 157 4 
27  0.000 000 000 083 05  -460.255 107 909 074 35 
28 -0.000 000 000 053 55  -460.255 107 909 127 9 
29  0.000 000 000 034 4  -460.255 107 909 093 5 
Exact energy -460.255 107 909 106 6 
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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 = -10.6904 and c =  100106.8582
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -460.09 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 = -1.58 and a subdominant z'c = 2.3 + 0.8 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.
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.