cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3

Moller-Plesset perturbation theory: example "cc4x2BH"

Content


Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-25.131286-25.13129
2-0.078149-25.20944
3-0.015114-25.22455
4-0.005871-25.23042
5-0.002507-25.23293
6-0.001256-25.23418
7-0.000639-25.23482
8-0.000334-25.23516
9-0.000175-25.23533
10-0.000091-25.23542
11-0.000044-25.23547
12-0.000022-25.23549
13-9.e-6-25.23550
Exact energy-25.23557
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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 =  0.6292, b = -1.5245 and c =  0.3170
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
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.