cc1C2cc1H2Occ2BHcc3BHcc4BHcc4x2BHcca2BHcca3BHcca4BHccaArccaClmccaFmccaHClccaHFccaNecc+C2ccCNpccFmcc+H2OccH2OccH2OpccHFccN2ccNecctCH2BcctFmcctHFcctNeCH3

Moller-Plesset perturbation theory: example "ccaHF"

System ccaHF (class B)

Content


Coefficients of Moller-Plesset perturbation series
nEnPartial sum
1-100.033094-100.03309
2-0.222711-100.25581
3-0.000612-100.25642
4-0.008642-100.26506
50.002597-100.26246
6-0.002709-100.26517
70.001897-100.26327
8-0.001636-100.26491
90.001393-100.26352
10-0.001264-100.26478
110.001179-100.26360
12-0.001137-100.26474
130.001125-100.26361
14-0.001139-100.26475
150.001176-100.26358
16-0.001236-100.26481
170.00132-100.26349
18-0.00143-100.26492
190.001569-100.26335
20-0.00174-100.26509
210.00195-100.26314
Exact energy-100.26418
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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 =  1.4485, b = -4.7613 and c =  1.6369
are chosen so that scaled coefficients remain of order of one in magnitude for all n.
Coefficient E1 = -100.03 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.