Møller-Plesset perturbation theory: example "a69"

Molecule HF. 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 -100.019 277 933 369 88  -100.019 277 933 369 88 
2 -0.201 768 338 228  -100.221 046 271 597 88 
3 -0.002 885 555 191 33  -100.223 931 826 789 21 
4 -0.004 224 410 022 73  -100.228 156 236 811 94 
5 -0.000 060 851 894 43  -100.228 217 088 706 37 
6 -0.000 442 613 806 02  -100.228 659 702 512 39 
7  0.000 079 736 036 41  -100.228 579 966 475 98 
8 -0.000 085 487 417 43  -100.228 665 453 893 41 
9  0.000 027 489 452 05  -100.228 637 964 441 36 
10 -0.000 019 583 863 24  -100.228 657 548 304 6 
11  0.000 009 031 064 07  -100.228 648 517 240 53 
12 -0.000 005 821 509 43  -100.228 654 338 749 96 
13  0.000 003 270 992 92  -100.228 651 067 757 04 
14 -0.000 002 073 887 08  -100.228 653 141 644 12 
15  0.000 001 280 319 5  -100.228 651 861 324 62 
16 -0.000 000 825 547 72  -100.228 652 686 872 34 
17  0.000 000 534 840 44  -100.228 652 152 031 9 
18 -0.000 000 352 939 59  -100.228 652 504 971 49 
19  0.000 000 235 254 35  -100.228 652 269 717 14 
20 -0.000 000 158 469 99  -100.228 652 428 187 13 
21  0.000 000 107 711 19  -100.228 652 320 475 94 
22 -0.000 000 073 765 57  -100.228 652 394 241 51 
23  0.000 000 050 876 67  -100.228 652 343 364 84 
24 -0.000 000 035 297 12  -100.228 652 378 661 96 
25  0.000 000 024 622 39  -100.228 652 354 039 57 
26 -0.000 000 017 256 25  -100.228 652 371 295 82 
27  0.000 000 012 145 16  -100.228 652 359 150 66 
28 -0.000 000 008 579 62  -100.228 652 367 730 28 
29  0.000 000 006 081 04  -100.228 652 361 649 24 
30 -0.000 000 004 322 83  -100.228 652 365 972 07 
31  0.000 000 003 081 1  -100.228 652 362 890 97 
32 -0.000 000 002 201 26  -100.228 652 365 092 23 
33  0.000 000 001 576 04  -100.228 652 363 516 19 
34 -0.000 000 001 130 56  -100.228 652 364 646 75 
35  0.000 000 000 812 44  -100.228 652 363 834 31 
36 -0.000 000 000 584 75  -100.228 652 364 419 06 
37  0.000 000 000 421 49  -100.228 652 363 997 57 
38 -0.000 000 000 304 23  -100.228 652 364 301 8 
39  0.000 000 000 219 86  -100.228 652 364 081 94 
Exact energy -100.228 652 363 23 
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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 =  0.8427, b = -4.6151 and c =  4.3743
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -100.02 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 = -1.31 and a subdominant z'c = 2.5 + 0.4 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


Molecule - icon for Allen-dataBlankExamples of MP seriesBlankSource code of Mathematica programBlankMathematica programsBlankWork in UMass DartmouthWork in UMassDBlankWaste iconUnpublished reports

Designed by A. Sergeev.