cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3

Moller-Plesset perturbation theory: example "ccaNe"

System ccaNe (class B)

Content


Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-128.49635-128.49635
2-0.206874-128.70322
3-0.001547-128.70477
4-0.005686-128.71046
50.002013-128.70844
6-0.001582-128.71003
70.000959-128.70907
8-0.000707-128.70977
90.000538-128.70924
10-0.00044-128.70968
110.000375-128.70930
12-0.000334-128.70964
130.000308-128.70933
14-0.000293-128.70962
150.000286-128.70933
16-0.000286-128.70962
170.000292-128.70933
18-0.000304-128.70963
190.000322-128.70931
20-0.000346-128.70966
210.000377-128.70928
22-0.000415-128.70969
230.000462-128.70923
24-0.000519-128.70975
250.000588-128.70916
26-0.000672-128.70984
270.000773-128.70906
28-0.000894-128.70996
290.001039-128.70892
30-0.001214-128.71013
310.001424-128.70871
32-0.001676-128.71038
330.001979-128.70840
34-0.002342-128.71075
350.002779-128.70797
36-0.003306-128.71127
370.00394-128.70733
38-0.004702-128.71203
390.00562-128.70642
40-0.006726-128.71314
410.008058-128.70508
42-0.009665-128.71475
430.011602-128.70315
44-0.013938-128.71708
450.016756-128.70033
46-0.020155-128.72048
470.024258-128.69622
48-0.02921-128.72544
490.035188-128.69025
50-0.042405-128.73265
510.051118-128.68153
52-0.061642-128.74318
530.074353-128.66882
54-0.089705-128.75853
550.108251-128.65028
56-0.130657-128.78093
570.157728-128.62321
58-0.190437-128.81364
590.229962-128.58368
60-0.277726-128.86141
610.335449-128.52596
62-0.405212-128.93117
630.48953-128.44164
64-0.591445-129.03308
650.714633-128.31845
Exact energy-128.70948
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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 =  1.3592, b = -4.7267 and c =  1.0408
are chosen so that scaled coefficients remain of order of one in magnitude for all n.
Coefficient E1 = -128.50 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.