Moller-Plesset perturbation theory: example "ccCNp"

System (class B)

Content

Table of coefficients and partial sums
Semilogarithmic plot of coefficients
Plot of scaled coefficients
Convergence of summation approximants
Singularities of approximants in complex plane

Coefficients of Moller-Plesset perturbation series
n	E_n	Partial sum
1	`-91.617515`	`-91.61752`
2	`-0.355498`	`-91.97301`
3	`0.05913`	`-91.91388`
4	`-0.106019`	`-92.01990`
5	`0.082917`	`-91.93698`
6	`-0.011223`	`-91.94821`
7	`0.028939`	`-91.91927`
8	`-0.174396`	`-92.09367`
9	`0.227849`	`-91.86582`
10	`-0.307066`	`-92.17288`
11	`0.406806`	`-91.76608`
12	`-0.53656`	`-92.30264`
13	`0.697793`	`-91.60484`
Exact energy		`-91.99797`

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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 = 1.6366, b = -2.0652 and c = 0.2256 are chosen so that scaled coefficients remain of order of one in magnitude for all n. Coefficient E₁ = -91.62 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),
Pade approximants (blue circles),
quadratic approximants (green boxes),
cubic, quartic, fifth and sixth degree approximants
(triangles, diamonds, pentagonal and hexagonal stars respectively).