Møller-Plesset perturbation theory: example "o2"

Molecule Ne. Basis cc-pVTZ-(f). Structure ""

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 Examples o1 o2 o3 o4 o5 o6 o7 o8 o9 Molecule Ne Ne F- HF H2O CH2 CH2 C2 N2 Basis cc-pVDZ cc-pVTZ-(f) cc-pVTZ-(f) cc-pVTZ-(f/d) cc-pVDZ(+) aug-cc-pVDZ cc-pVTZ-(f/d) cc-pVDZ(+) cc-pVDZ

 Examples of MP seriesMathematica programsWork in UMassDUnpublished reports

Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -129.022 234  -129.022 234
2  0.240 879  -128.781 355
3 -0.001 007  -128.782 362
4  0.005 957  -128.776 405
5 -0.001 164  -128.777 569
6  0.000 697  -128.776 872
7 -0.000 279  -128.777 151
8  0.000 151  -128.777
9 -0.000 074  -128.777 074
10  0.000 039  -128.777 035
11 -0.000 02  -128.777 055
12  0.000 011  -128.777 044
13 -0.000 006  -128.777 05
14  0.000 003  -128.777 047
15 -0.000 006  -128.777 053
Exact energy -128.777 048
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Coefficients of Moller-Plesset perturbation theory, semilogarithmic plot.
Red/blue dots correspond to positive/negative coefficients
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Scaled coefficients of Møller-Plesset perturbation theory.
Parameters a =  1.1242, b = -6.4351 and c =  26.0270
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -129.02 is not shown because it is too small and out of scale
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Convergence of summation approximants for the Møller - 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),
cubic, quartic, fifth and sixth degree approximants
(triangles, diamonds, pentagonal and hexagonal stars respectively).
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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.
To view all singularities with their weights, see this table.
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The function E(z) found by summation of its power series.
Dashed line indicates that the approximant is complex valued.
Red dot marks exact physical energy at z = 1.
To view results of summation of a specific number of terms of the series, click on the right bar.
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 Examples o1 o2 o3 o4 o5 o6 o7 o8 o9 Molecule Ne Ne F- HF H2O CH2 CH2 C2 N2 Basis cc-pVDZ cc-pVTZ-(f) cc-pVTZ-(f) cc-pVTZ-(f/d) cc-pVDZ(+) aug-cc-pVDZ cc-pVTZ-(f/d) cc-pVDZ(+) cc-pVDZ

Known inaccuracies

• We always sum the series
F(z) = MP1 + (MP2-MP1) z + (MP3-MP2) z2 + ... rather than a complete Møller-Plesset series
E(z) = MP0 + (MP1-MP0) z + (MP2-MP1) z2 + ... where F(z) is expressed through E(z) by a formula
F(z) = MP0 + [E(z) - MP0] z-1.
• On the page, table of singularities with their weights for differential approximants is absent.

 Examples of MP seriesMathematica programsWork in UMassDUnpublished reports

Designed by A. Sergeev.