cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3

Moller-Plesset perturbation theory: example "CH3"

System CH3 (class A)

Content


Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-39.570629-39.57063
2-0.125321-39.69595
3-0.018901-39.71485
4-0.00438-39.71923
5-0.001211-39.72044
6-0.000424-39.72087
Exact energy-39.72121
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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 Moller-Plesset perturbation theory.
Parameters a =  0.8148, b = -4.7488 and c =  6.5834
are chosen so that scaled coefficients remain of order of one in magnitude for all n.
Coefficient E1 = -39.57 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 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).
Plot of number of accurate digits
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Singularities of approximants in the complex plane
are not shown for this example (CH3)
because number of available coefficients of the series (6)
is too small to construct a meaningful approximant
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cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3
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Designed by A. Sergeev.