cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3

Moller-Plesset perturbation theory: example "cc+C2"

Content


Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-75.387964-75.38796
2-0.31151-75.69947
30.032487-75.66699
4-0.06969-75.73668
50.036201-75.70048
6-0.038162-75.73864
70.023812-75.71483
8-0.0212-75.73603
90.012347-75.72368
10-0.00883-75.73251
110.003413-75.72910
12-0.0006-75.72970
13-0.002179-75.73188
140.003635-75.72824
15-0.004442-75.73268
160.004595-75.72809
17-0.004143-75.73223
180.003449-75.72878
19-0.002439-75.73122
200.00146-75.72976
21-0.00046-75.73022
22-0.00035-75.73057
230.000993-75.72958
24-0.001395-75.73097
250.001578-75.72939
Exact energy-75.73021
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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 =  1.0098, b = -2.2828 and c =  1.4033
are chosen so that scaled coefficients remain of order of one in magnitude for all n.
Coefficient E1 = -75.39 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.