Møller-Plesset perturbation theory: example "a62"

Molecule N2. 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 -108.949 557 544 626 97  -108.949 557 544 626 97 
2 -0.313 176 209 736 85  -109.262 733 754 363 82 
3  0.007 234 572 368 26  -109.255 499 181 995 56 
4 -0.025 062 086 619 84  -109.280 561 268 615 4 
5  0.006 174 127 742 43  -109.274 387 140 872 97 
6 -0.004 502 831 327 16  -109.278 889 972 200 13 
7  0.001 256 425 932 72  -109.277 633 546 267 41 
8 -0.000 711 809 420 35  -109.278 345 355 687 76 
9  0.000 090 138 508 17  -109.278 255 217 179 59 
10 -0.000 038 647 214 34  -109.278 293 864 393 93 
11 -0.000 048 920 630 25  -109.278 342 785 024 18 
12  0.000 023 533 470 18  -109.278 319 251 554 
13 -0.000 024 931 481 83  -109.278 344 183 035 83 
14  0.000 009 216 638 32  -109.278 334 966 397 51 
15 -0.000 005 700 259 93  -109.278 340 666 657 44 
16  0.000 000 971 797 79  -109.278 339 694 859 65 
17 -0.000 000 082 747 55  -109.278 339 777 607 2 
18 -0.000 000 616 488 15  -109.278 340 394 095 35 
19  0.000 000 522 825 53  -109.278 339 871 269 82 
Exact energy -109.278 340 103 367 
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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 =  0.6937, b = -3.4094 and c =  9.6346
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -108.95 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 = -1.5 + 0.64 i and a subdominant z'c = 1.64 + 0.31 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.