Møller-Plesset perturbation theory: example "o5"

Molecule H2O. 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 -76.478 859  -76.478 859 
2  0.208 023  -76.270 836 
3  0.004 839  -76.265 997 
4  0.007 302  -76.258 695 
5 -0.000 523  -76.259 218 
6  0.001 214  -76.258 004 
7 -0.000 531  -76.258 535 
8  0.000 517  -76.258 018 
9 -0.000 366  -76.258 384 
10  0.000 313  -76.258 071 
11 -0.000 257  -76.258 328 
12  0.000 223  -76.258 105 
13 -0.000 195  -76.258 3 
14  0.000 175  -76.258 125 
15 -0.000 159  -76.258 284 
16  0.000 147  -76.258 137 
17 -0.000 138  -76.258 275 
18  0.000 131  -76.258 144 
19 -0.000 126  -76.258 27 
20  0.000 123  -76.258 147 
21 -0.000 121  -76.258 268 
22  0.000 12  -76.258 148 
23 -0.000 12  -76.258 268 
24  0.000 12  -76.258 148 
25 -0.000 122  -76.258 27 
26  0.000 125  -76.258 145 
27 -0.000 128  -76.258 273 
28  0.000 133  -76.258 14 
29 -0.000 14  -76.258 28 
30  0.000 148  -76.258 132 
31 -0.000 157  -76.258 289 
Exact energy -76.258 208 
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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 =  1.2360, b = -4.6439 and c =  1.7611
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -76.48 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


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Designed by A. Sergeev.