Møller-Plesset perturbation theory: example "a84"

Molecule HCl. Basis aug-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 -460.092 602 266 664 1  -460.092 602 266 664 1 
2 -0.159 201 950 731 7  -460.251 804 217 395 8 
3 -0.016 250 285 565 35  -460.268 054 502 961 15 
4 -0.003 785 751 259 61  -460.271 840 254 220 76 
5 -0.000 660 742 601 78  -460.272 500 996 822 54 
6 -0.000 343 816 044 79  -460.272 844 812 867 33 
7 -0.000 031 760 782 01  -460.272 876 573 649 34 
8 -0.000 044 883 114 81  -460.272 921 456 764 15 
9  0.000 005 413 220 05  -460.272 916 043 544 1 
10 -0.000 009 612 342 4  -460.272 925 655 886 5 
11  0.000 003 605 666 1  -460.272 922 050 220 4 
12 -0.000 003 021 304 1  -460.272 925 071 524 5 
13  0.000 001 669 279 73  -460.272 923 402 244 77 
14 -0.000 001 207 781 23  -460.272 924 610 026 
15  0.000 000 778 077 1  -460.272 923 831 948 9 
16 -0.000 000 555 383 2  -460.272 924 387 332 1 
17  0.000 000 386 068 54  -460.272 924 001 263 56 
18 -0.000 000 281 066 24  -460.272 924 282 329 8 
19  0.000 000 205 022  -460.272 924 077 307 8 
20 -0.000 000 153 418 2  -460.272 924 230 726 
21  0.000 000 116 007 64  -460.272 924 114 718 36 
22 -0.000 000 089 251 11  -460.272 924 203 969 47 
23  0.000 000 069 498 37  -460.272 924 134 471 1 
24 -0.000 000 054 854 37  -460.272 924 189 325 47 
25  0.000 000 043 792 23  -460.272 924 145 533 24 
Exact energy -460.272 924 165 045 7 
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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 =  1.1242, b = -7.7476 and c =  143.1544
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 = -1.28 and a subdominant z'c = 2.2 + 0.3 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.