cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3

Moller-Plesset perturbation theory: example "cc1C2"

System cc1C2 (class B)

Content


Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-75.386457-75.38646
2-0.31296-75.69942
30.034658-75.66476
4-0.073156-75.73792
50.040188-75.69773
6-0.042455-75.74018
70.028168-75.71201
8-0.025416-75.73743
90.016017-75.72141
10-0.011894-75.73331
110.005528-75.72778
12-0.001849-75.72963
13-0.001938-75.73157
140.0042-75.72737
15-0.005749-75.73312
160.006377-75.72674
17-0.006209-75.73295
180.005538-75.72741
19-0.004347-75.73176
200.003005-75.72875
21-0.001512-75.73026
220.00015-75.73011
230.001056-75.72906
24-0.001959-75.73102
250.002549-75.72847
26-0.002795-75.73126
270.002722-75.72854
28-0.002384-75.73092
290.001838-75.72909
30-0.001173-75.73026
310.000461-75.72980
320.000214-75.72958
33-0.000796-75.73038
340.001231-75.72915
35-0.001494-75.73064
360.001574-75.72907
37-0.001484-75.73055
380.001248-75.72931
39-0.000905-75.73021
Exact energy-75.72985
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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 = -1.9942 and c =  0.9786
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 quadratic approximants,
right panel to differential approximants.
To view an individual approximant, click on the right bar.
Location of singularities in the  complex plane
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cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3
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Designed by A. Sergeev.