Møller-Plesset perturbation theory: example "o9"

Molecule N2. Basis cc-pVDZ. Structure ""

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Exampleso1o2o3o4o5o6o7o8o9
MoleculeNeNeF-HFH2OCH2CH2C2N2
Basiscc-pVDZcc-pVTZ-(f)cc-pVTZ-(f)cc-pVTZ-(f/d)cc-pVDZ(+)aug-cc-pVDZcc-pVTZ-(f/d)cc-pVDZ(+)cc-pVDZ

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -109.598 501  -109.598 501 
2  0.305 288  -109.293 213 
3 -0.004 04  -109.297 253 
4  0.022 176  -109.275 077 
5 -0.004 694  -109.279 771 
6  0.003 565  -109.276 206 
7 -0.000 853  -109.277 059 
8  0.000 511  -109.276 548 
9 -0.000 042  -109.276 59 
10  0.000 029  -109.276 561 
11  0.000 033  -109.276 528 
12 -0.000 011  -109.276 539 
13  0.000 014  -109.276 525 
14 -0.000 004  -109.276 529 
15  0.000 003  -109.276 526 
Exact energy -109.276 527 
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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 Møller-Plesset perturbation theory.
Parameters a =  0.5305, b = -1.4253 and c =  1.3383
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -109.60 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 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),
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.
To view all singularities with their weights, see this table.
Location of singularities in the  complex plane
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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.
Partial sums, Pade and quadratic approximants
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Exampleso1o2o3o4o5o6o7o8o9
MoleculeNeNeF-HFH2OCH2CH2C2N2
Basiscc-pVDZcc-pVTZ-(f)cc-pVTZ-(f)cc-pVTZ-(f/d)cc-pVDZ(+)aug-cc-pVDZcc-pVTZ-(f/d)cc-pVDZ(+)cc-pVDZ

Known inaccuracies


Molecule - icon for Allen-dataBlankExamples of MP seriesBlankSource code of Mathematica programBlankMathematica programsBlankWork in UMass DartmouthWork in UMassDBlankWaste iconUnpublished reports

Designed by A. Sergeev.