Møller-Plesset perturbation theory: example "a8"

Molecule BH. Basis cc-pVTZ. 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 -25.129 904 309 206 978  -25.129 904 309 206 978 
2 -0.073 524 861 963 044  -25.203 429 171 170 022 
3 -0.016 562 627 140 836  -25.219 991 798 310 858 
4 -0.005 980 816 849 122  -25.225 972 615 159 98 
5 -0.002 544 123 911 326  -25.228 516 739 071 306 
6 -0.001 232 664 635 762  -25.229 749 403 707 068 
7 -0.000 638 608 332 65  -25.230 388 012 039 718 
8 -0.000 343 148 478 468  -25.230 731 160 518 186 
9 -0.000 187 094 220 276  -25.230 918 254 738 462 
10 -0.000 102 164 569 182  -25.231 020 419 307 644 
11 -0.000 055 377 582 551  -25.231 075 796 890 195 
12 -0.000 029 607 158 489  -25.231 105 404 048 684 
13 -0.000 015 524 553 138  -25.231 120 928 601 822 
14 -0.000 007 933 804 543  -25.231 128 862 406 365 
15 -0.000 003 917 776 858  -25.231 132 780 183 223 
16 -0.000 001 843 292 84  -25.231 134 623 476 063 
17 -0.000 000 804 354 987  -25.231 135 427 831 05 
18 -0.000 000 305 364 15  -25.231 135 733 195 2 
19 -0.000 000 080 010 706  -25.231 135 813 205 906 
20  0.000 000 011 721 042  -25.231 135 801 484 864 
21  0.000 000 041 511 096  -25.231 135 759 973 768 
22  0.000 000 044 839 692  -25.231 135 715 134 076 
23  0.000 000 038 491 166  -25.231 135 676 642 91 
24  0.000 000 029 890 738  -25.231 135 646 752 172 
25  0.000 000 021 964 425  -25.231 135 624 787 747 
26  0.000 000 015 595 283  -25.231 135 609 192 464 
27  0.000 000 010 819 644  -25.231 135 598 372 82 
28  0.000 000 007 381 19  -25.231 135 590 991 63 
29  0.000 000 004 968 952  -25.231 135 586 022 678 
Exact energy -25.231 135 576 759 
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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 = -2.8217 and c =  1.6992
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.13 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 = 1.6 + 0.4 i and a subdominant z'c = -3.5 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.