cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3

Moller-Plesset perturbation theory: example "cc+H2O"

Content


Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-76.037557-76.03756
2-0.208023-76.24558
3-0.004839-76.25042
4-0.007302-76.25772
50.000523-76.25720
6-0.001214-76.25841
70.000531-76.25788
8-0.000517-76.25840
90.000366-76.25803
10-0.000313-76.25834
110.000257-76.25809
12-0.000223-76.25831
130.000195-76.25812
14-0.000175-76.25829
150.000159-76.25813
16-0.000147-76.25828
170.000138-76.25814
18-0.000131-76.25827
190.000126-76.25815
20-0.000123-76.25827
210.000121-76.25815
22-0.00012-76.25827
230.00012-76.25815
24-0.00012-76.25827
250.000122-76.25815
26-0.000125-76.25827
270.000128-76.25814
28-0.000133-76.25828
290.00014-76.25814
30-0.000148-76.25828
310.000157-76.25813
Exact energy-76.25821
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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 =  1.2360, b = -4.6439 and c =  1.7611
are chosen so that scaled coefficients remain of order of one in magnitude for all n.
Coefficient E1 = -76.04 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.