cc1C2 cc1H2O cc2BH cc3BH cc4BH cc4x2BH cca2BH cca3BH cca4BH ccaAr ccaClm ccaFm ccaHCl ccaHF ccaNe cc+C2 ccCNp ccFm cc+H2O ccH2O ccH2Op ccHF ccN2 ccNe cctCH2B cctFm cctHF cctNe CH3

# Moller-Plesset perturbation theory: example "cca4BH"

### Content

Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-25.13136-25.13136
2-0.078637-25.21000
3-0.014823-25.22482
4-0.005861-25.23068
5-0.002511-25.23319
6-0.001238-25.23443
7-0.000643-25.23507
8-0.000348-25.23542
9-0.000192-25.23561
10-0.000105-25.23572
11-0.000059-25.23578
12-0.000031-25.23581
13-0.000017-25.23582
14-9.e-6-25.23583
15-5.e-6-25.23584
16-2.e-6-25.23584
17-1.e-6-25.23584
Exact energy-25.23584
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Coefficients of Moller-Plesset perturbation theory, semilogarithmic plot.
Red/blue dots correspond to positive/negative coefficients
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Scaled coefficients of Moller-Plesset perturbation theory.
Parameters a =  0.6231, b = -1.3408 and c =  0.2519
are chosen so that scaled coefficients remain 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
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Convergence of summation approximants for the Moller - 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),
cubic, quartic, fifth and sixth degree approximants
(triangles, diamonds, pentagonal and hexagonal stars respectively).
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Location of singularities in the complex plane of the parameter z.
Left panel refers to diagonal quadratic approximants,
right panel to differential approximants.
N is number of coefficients used for construction of the approximant.
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 cc1C2 cc1H2O cc2BH cc3BH cc4BH cc4x2BH cca2BH cca3BH cca4BH ccaAr ccaClm ccaFm ccaHCl ccaHF ccaNe cc+C2 ccCNp ccFm cc+H2O ccH2O ccH2Op ccHF ccN2 ccNe cctCH2B cctFm cctHF cctNe CH3
 List of examples of MP series Mathematica programs Work in UMassD Unpublished reports

Designed by A. Sergeev.