Møller-Plesset perturbation theory: example "a85"

Molecule F-. 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 -99.428 282 432 9  -99.428 282 432 9 
2 -0.237 665 547 9  -99.665 947 980 8 
3  0.009 273 596 2  -99.656 674 384 6 
4 -0.018 196 154 5  -99.674 870 539 1 
5  0.013 402 814 5  -99.661 467 724 6 
6 -0.016 563 329 8  -99.678 031 054 4 
7  0.019 532 517 2  -99.658 498 537 2 
8 -0.024 841 587 2  -99.683 340 124 4 
9  0.032 653 047 7  -99.650 687 076 7 
10 -0.044 367 592 9  -99.695 054 669 6 
11  0.061 815 537 2  -99.633 239 132 4 
12 -0.087 896 115 1  -99.721 135 247 5 
13  0.127 058 036 3  -99.594 077 211 2 
14 -0.186 147 277  -99.780 224 488 2 
15  0.275 717 216 9  -99.504 507 271 3 
16 -0.412 052 628 1  -99.916 559 899 4 
17  0.620 316 821 3  -99.296 243 078 1 
18 -0.939 433 076 4  -100.235 676 154 5 
19  1.429 663 851 2  -98.806 012 303 3 
20 -2.184 379 388  -100.990 391 691 3 
21  3.348 335 115 7  -97.642 056 575 6 
Exact energy -99.669 368 843 136 7 
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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 =  1.8356, b = -2.9891 and c =  0.1161
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -99.43 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 = -0.6 and a subdominant z'c = 2. + 1. 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


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Designed by A. Sergeev.