Møller-Plesset perturbation theory: example "a86"

Molecule Cl-. 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 -459.542 220 318 845 64  -459.542 220 318 845 64 
2 -0.134 405 350 425 19  -459.676 625 669 270 83 
3 -0.011 848 758 475 03  -459.688 474 427 745 86 
4 -0.001 032 616 281 18  -459.689 507 044 027 04 
5 -0.000 282 070 308 36  -459.689 789 114 335 4 
6 -0.000 106 328 989 2  -459.689 895 443 324 6 
7 -0.000 031 361 675 6  -459.689 926 805 000 2 
8 -0.000 007 682 729 97  -459.689 934 487 730 17 
9 -0.000 002 112 179 13  -459.689 936 599 909 3 
10 -0.000 000 728 980 06  -459.689 937 328 889 36 
11 -0.000 000 251 669 69  -459.689 937 580 559 05 
12 -0.000 000 078 739 39  -459.689 937 659 298 44 
13 -0.000 000 023 480 96  -459.689 937 682 779 4 
14 -0.000 000 007 156 4  -459.689 937 689 935 8 
15 -0.000 000 002 250 65  -459.689 937 692 186 45 
16 -0.000 000 000 701 65  -459.689 937 692 888 1 
17 -0.000 000 000 211 2  -459.689 937 693 099 3 
18 -0.000 000 000 061 7  -459.689 937 693 161 
19 -0.000 000 000 017 7  -459.689 937 693 178 7 
20 -0.000 000 000 004 9  -459.689 937 693 183 6 
21 -0.000 000 000 001 25  -459.689 937 693 184 85 
22 -0.000 000 000 000 28  -459.689 937 693 185 13 
23 -0.000 000 000 000 07  -459.689 937 693 185 2 
Exact energy -459.689 937 693 185 1 
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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 =  0.3529, b = -1.9273 and c =  2.0114
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -459.54 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 = 2.6 + 0.2 i and a subdominant z'c = -2.7 + 3.6 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.
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.