Møller-Plesset perturbation theory: example "a44"

Molecule BO+. 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 -99.030 054 115 982 45  -99.030 054 115 982 45 
2 -0.271 838 618 315 19  -99.301 892 734 297 64 
3  0.023 829 776 776 25  -99.278 062 957 521 39 
4 -0.045 620 861 629 7  -99.323 683 819 151 09 
5  0.037 502 684 725 49  -99.286 181 134 425 6 
6 -0.056 858 618 707 75  -99.343 039 753 133 35 
7  0.081 069 226 505 16  -99.261 970 526 628 19 
8 -0.129 427 518 259 89  -99.391 398 044 888 08 
9  0.210 809 142 140 61  -99.180 588 902 747 47 
10 -0.358 088 189 655 42  -99.538 677 092 402 89 
11  0.622 264 391 613 38  -98.916 412 700 789 51 
12 -1.105 645 506 944 68  -100.022 058 207 734 19 
13  1.995 171 142 457 04  -98.026 887 065 277 15 
14 -3.646 079 794 538 91  -101.672 966 859 816 06 
15  6.725 767 713 599 91  -94.947 199 146 216 15 
16 -12.496 742 686 602 45  -107.443 941 832 818 6 
17  23.345 843 345 867 68  -84.098 098 486 950 92 
18 -43.792 905 949 066 59  -127.891 004 436 017 51 
19  82.400 702 840 592 19  -45.490 301 595 425 32 
20 -155.400 483 220 519 55  -200.890 784 815 944 87 
21  293.568 765 060 555 96   92.677 980 244 611 09 
22 -555.274 405 930 821 56  -462.596 425 686 210 47 
23  1 051.228 884 747 022 37   588.632 459 060 811 9 
Exact energy -99.313 343 244 659 9 
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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 =  2.2738, b = -3.0584 and c =  0.1216
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -99.03 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 = -0.5 and a subdominant z'c = 1.25 + 0.23 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


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

Designed by A. Sergeev.