Møller-Plesset perturbation theory: example "a88"

Molecule Ne. 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 -128.496 349 730 5  -128.496 349 730 5 
2 -0.206 873 508 6  -128.703 223 239 1 
3 -0.001 547 443 2  -128.704 770 682 3 
4 -0.005 686 207 5  -128.710 456 889 8 
5  0.002 013 699 2  -128.708 443 190 6 
6 -0.001 582 384 8  -128.710 025 575 4 
7  0.000 959 125 5  -128.709 066 449 9 
8 -0.000 707 420 8  -128.709 773 870 7 
9  0.000 537 928 9  -128.709 235 941 8 
10 -0.000 439 802 3  -128.709 675 744 1 
11  0.000 375 500 1  -128.709 300 244 
12 -0.000 334 462 8  -128.709 634 706 8 
13  0.000 308 421 4  -128.709 326 285 4 
14 -0.000 293 243 4  -128.709 619 528 8 
15  0.000 286 368 6  -128.709 333 160 2 
16 -0.000 286 354 8  -128.709 619 515 
17  0.000 292 429 4  -128.709 327 085 6 
18 -0.000 304 288 5  -128.709 631 374 1 
19  0.000 321 979 6  -128.709 309 394 5 
20 -0.000 345 841 3  -128.709 655 235 8 
21  0.000 376 478 2  -128.709 278 757 6 
22 -0.000 414 758 8  -128.709 693 516 4 
23  0.000 461 831 5  -128.709 231 684 9 
24 -0.000 519 155 9  -128.709 750 840 8 
25  0.000 588 548 1  -128.709 162 292 7 
26 -0.000 672 240 7  -128.709 834 533 4 
27  0.000 772 958 8  -128.709 061 574 6 
28 -0.000 894 014 9  -128.709 955 589 5 
29  0.001 039 424 7  -128.708 916 164 8 
30 -0.001 214 048 6  -128.710 130 213 4 
31  0.001 423 764 2  -128.708 706 449 2 
32 -0.001 675 674 4  -128.710 382 123 6 
33  0.001 978 36  -128.708 403 763 6 
34 -0.002 342 185 6  -128.710 745 949 2 
35  0.002 779 668 9  -128.707 966 280 3 
36 -0.003 305 928  -128.711 272 208 3 
37  0.003 939 221 9  -128.707 332 986 4 
38 -0.004 701 603 7  -128.712 034 590 1 
39  0.005 619 710 7  -128.706 414 879 4 
40 -0.006 725 719 3  -128.713 140 598 7 
41  0.008 058 499 3  -128.705 082 099 4 
42 -0.009 665 009 6  -128.714 747 109 
43  0.011 601 985 2  -128.703 145 123 8 
44 -0.013 937 976 8  -128.717 083 100 6 
45  0.016 755 816 6  -128.700 327 284 
46 -0.020 155 599 5  -128.720 482 883 5 
47  0.024 258 287 1  -128.696 224 596 4 
48 -0.029 210 065  -128.725 434 661 4 
49  0.035 187 611 6  -128.690 247 049 8 
50 -0.042 404 467 7  -128.732 651 517 5 
51  0.051 118 737 7  -128.681 532 779 8 
52 -0.061 642 402 1  -128.743 175 181 9 
53  0.074 352 576 6  -128.668 822 605 3 
54 -0.089 705 125 3  -128.758 527 730 6 
55  0.108 251 122 2  -128.650 276 608 4 
Exact energy -128.709 475 548 753 5 
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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 =  1.3673, b = -4.8232 and c =  1.2601
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -128.50 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 = -0.83 and a subdominant z'c = 3. + 0.6 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.