Møller-Plesset perturbation theory: example "a16"

Molecule BH. Basis cc-pVQZ. 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 -25.131 285 139 026 172  -25.131 285 139 026 172 
2 -0.078 149 198 363 374  -25.209 434 337 389 546 
3 -0.015 114 005 254 244  -25.224 548 342 643 79 
4 -0.005 870 928 562 224  -25.230 419 271 206 014 
5 -0.002 506 915 994 772  -25.232 926 187 200 786 
6 -0.001 234 063 534 514  -25.234 160 250 735 3 
7 -0.000 641 540 531 795  -25.234 801 791 267 095 
8 -0.000 347 078 706 505  -25.235 148 869 973 6 
9 -0.000 190 566 382 688  -25.235 339 436 356 288 
10 -0.000 105 064 984 602  -25.235 444 501 340 89 
11 -0.000 057 664 435 25  -25.235 502 165 776 14 
12 -0.000 031 341 029 505  -25.235 533 506 805 645 
13 -0.000 016 791 916 657  -25.235 550 298 722 302 
14 -0.000 008 830 469 138  -25.235 559 129 191 44 
15 -0.000 004 533 257 52  -25.235 563 662 448 96 
16 -0.000 002 254 055 6  -25.235 565 916 504 56 
17 -0.000 001 071 267 315  -25.235 566 987 771 875 
18 -0.000 000 474 359 175  -25.235 567 462 131 05 
19 -0.000 000 184 249 982  -25.235 567 646 381 032 
20 -0.000 000 050 832 742  -25.235 567 697 213 774 
21  0.000 000 005 103 206  -25.235 567 692 110 568 
22  0.000 000 024 408 248  -25.235 567 667 702 32 
23  0.000 000 027 556 51  -25.235 567 640 145 81 
24  0.000 000 024 428 893  -25.235 567 615 716 917 
25  0.000 000 019 540 241  -25.235 567 596 176 676 
26  0.000 000 014 775 129  -25.235 567 581 401 547 
27  0.000 000 010 785 547  -25.235 567 570 616 
28  0.000 000 007 684 137  -25.235 567 562 931 863 
29  0.000 000 005 375 061  -25.235 567 557 556 802 
Exact energy -25.235 567 546 576 
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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 = -2.7824 and c =  1.5886
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 + 0.31 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.