cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3

Moller-Plesset perturbation theory: example "cctNe"

System cctNe (class B)

Content


Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-128.531862-128.53186
2-0.240879-128.77274
30.001007-128.77173
4-0.005957-128.77769
50.001164-128.77653
6-0.000697-128.77722
70.000279-128.77694
8-0.000151-128.77710
90.000074-128.77702
10-0.000039-128.77706
110.00002-128.77704
12-0.000011-128.77705
136.e-6-128.77705
14-3.e-6-128.77705
156.e-6-128.77704
Exact energy-128.77705
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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 =  1.1242, b = -6.4351 and c =  26.0271
are chosen so that scaled coefficients remain of order of one in magnitude for all n.
Coefficient E1 = -128.53 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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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.
Location of singularities in the complex plane
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cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3
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Designed by A. Sergeev.