Møller-Plesset perturbation theory: example "a90"

Molecule OH-. 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 -75.395 884 323 005 35  -75.395 884 323 005 35 
2 -0.241 056 315 219 28  -75.636 940 638 224 63 
3  0.007 632 415 012 96  -75.629 308 223 211 67 
4 -0.019 784 643 683 43  -75.649 092 866 895 1 
5  0.010 918 614 271 87  -75.638 174 252 623 23 
6 -0.013 053 314 200 47  -75.651 227 566 823 7 
7  0.014 033 547 800 1  -75.637 194 019 023 6 
8 -0.016 704 563 093 12  -75.653 898 582 116 72 
9  0.020 117 693 095 14  -75.633 780 889 021 58 
10 -0.024 907 842 168 42  -75.658 688 731 19 
11  0.031 394 768 075 73  -75.627 293 963 114 27 
12 -0.040 233 800 554 03  -75.667 527 763 668 3 
13  0.052 279 476 693 8  -75.615 248 286 974 5 
14 -0.068 762 333 073 56  -75.684 010 620 048 06 
15  0.091 419 211 243 64  -75.592 591 408 804 42 
16 -0.122 730 147 805 73  -75.715 321 556 610 15 
17  0.166 252 379 009 76  -75.549 069 177 600 39 
18 -0.227 126 365 582 84  -75.776 195 543 183 23 
19  0.312 836 527 795 23  -75.463 359 015 388 
20 -0.434 371 543 878 55  -75.897 730 559 266 55 
21  0.608 010 034 609 74  -75.289 720 524 656 81 
22 -0.858 098 652 123 93  -76.147 819 176 780 74 
23  1.221 419 895 098 2  -74.926 399 281 682 54 
24 -1.754 132 280 751 9  -76.680 531 562 434 44 
25  2.542 912 171 736 22  -74.137 619 390 698 22 
26 -3.723 019 534 288 64  -77.860 638 924 986 86 
27  5.507 867 624 682 48  -72.352 771 300 304 38 
Exact energy -75.644 864 708 427 
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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 =  1.6338, b = -3.0431 and c =  0.2186
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -75.40 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 = -0.67 and a subdominant z'c = 2.8 + 1. 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.