Møller-Plesset perturbation theory: example "a75"

Molecule HF. 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 -100.033 094 179 7  -100.033 094 179 7 
2 -0.222 710 218 9  -100.255 804 398 6 
3 -0.000 612 495 1  -100.256 416 893 7 
4 -0.008 641 640 3  -100.265 058 534 
5  0.002 596 994 3  -100.262 461 539 7 
6 -0.002 709 269 9  -100.265 170 809 6 
7  0.001 897 457 6  -100.263 273 352 
8 -0.001 636 691 9  -100.264 910 043 9 
9  0.001 392 925 6  -100.263 517 118 3 
10 -0.001 263 758 3  -100.264 780 876 6 
11  0.001 179 457 9  -100.263 601 418 7 
12 -0.001 137 611 8  -100.264 739 030 5 
13  0.001 125 435  -100.263 613 595 5 
14 -0.001 139 324 4  -100.264 752 919 9 
15  0.001 176 572  -100.263 576 347 9 
16 -0.001 236 728 1  -100.264 813 076 
17  0.001 320 552 6  -100.263 492 523 4 
18 -0.001 430 052 1  -100.264 922 575 5 
19  0.001 568 375 5  -100.263 354 2 
20 -0.001 739 902 4  -100.265 094 102 4 
21  0.001 950 388 6  -100.263 143 713 8 
Exact energy -100.264 176 805 368 
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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 =  1.4476, b = -4.7562 and c =  1.6290
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -100.03 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 = -0.78 and a subdominant z'c = 3. 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.