Møller-Plesset perturbation theory: example "a30"

Molecule BH. Basis aug-cc-pVTZ. Structure "mpn_Rfci"

Content


Examplesa1a2a8a16a22a30a38a44a45a51a62a69a75a83a84a85a86a87a88a90a91
MoleculeArBHBHBHBHBHBHBO+C2CN+N2HFHFHClHClF-Cl-Cl-NeOH-SH-
Basisaug-cc-pVDZcc-pVDZcc-pVTZcc-pVQZaug-cc-pVDZaug-cc-pVTZaug-cc-pVQZcc-pVDZcc-pVDZcc-pVDZcc-pVDZcc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-pVDZ

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

Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -25.130 170 396 7  -25.130 170 396 7 
2 -0.074 402 909 4  -25.204 573 306 1 
3 -0.016 333 114 1  -25.220 906 420 2 
4 -0.005 934 607 4  -25.226 841 027 6 
5 -0.002 538 088 9  -25.229 379 116 5 
6 -0.001 235 818 8  -25.230 614 935 3 
7 -0.000 641 343 4  -25.231 256 278 7 
8 -0.000 345 326  -25.231 601 604 7 
9 -0.000 188 696 6  -25.231 790 301 3 
10 -0.000 103 391  -25.231 893 692 3 
11 -0.000 056 295  -25.231 949 987 3 
12 -0.000 030 282 7  -25.231 980 27 
13 -0.000 016 006 4  -25.231 996 276 4 
14 -0.000 008 267 4  -25.232 004 543 8 
15 -0.000 004 141 7  -25.232 008 685 5 
16 -0.000 001 989 3  -25.232 010 674 8 
17 -0.000 000 897  -25.232 011 571 8 
18 -0.000 000 362 7  -25.232 011 934 5 
19 -0.000 000 114 7  -25.232 012 049 2 
20 -0.000 000 008 8  -25.232 012 058 
21  0.000 000 029 6  -25.232 012 028 4 
22  0.000 000 038 1  -25.232 011 990 3 
23  0.000 000 034 7  -25.232 011 955 6 
24  0.000 000 027 9  -25.232 011 927 7 
25  0.000 000 021  -25.232 011 906 7 
26  0.000 000 015 1  -25.232 011 891 6 
27  0.000 000 010 6  -25.232 011 881 
28  0.000 000 007 4  -25.232 011 873 6 
29  0.000 000 005  -25.232 011 868 6 
30  0.000 000 003 3  -25.232 011 865 3 
31  0.000 000 002 3  -25.232 011 863 
32  0.000 000 001 4  -25.232 011 861 6 
33  0.000 000 001  -25.232 011 860 6 
34  0.000 000 000 6  -25.232 011 86 
35  0.000 000 000 4  -25.232 011 859 6 
36  0.000 000 000 2  -25.232 011 859 4 
37  0.000 000 000 2  -25.232 011 859 2 
38  -10  0. x 10  -25.232 011 859 1 
Exact energy -25.232 011 858 97 
Top of Page  Top of the page         Previous Example  Prev. (a22)     Top oftable  Top of this table (a30)     Next Example  Next (a38)          Mathematica program  Mathematica program

Coefficients of Moller-Plesset perturbation theory, semilogarithmic plot.
Red/blue dots correspond to positive/negative coefficients
Plot of MP coefficients
Top of Page  Top of the page         Previous Example  Prev. (a22)     Next Example  Next (a38)          PDF format for printing  PDF format     Mathematica program  Mathematica program

Scaled coefficients of Møller-Plesset perturbation theory.
Parameters a =  0.7723, b = -4.8281 and c =  70.0056
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.13 is not shown because it is too small and out of scale
Plot of MP coefficients
Top of Page  Top of the page         Previous Example  Prev. (a22)     Next Example  Next (a38)          PDF format for printing  PDF format     Mathematica program  Mathematica program

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
Top of Page  Top of the page         Previous Example  Prev. (a22)     Next Example  Next (a38)          PDF format for printing  PDF format     Mathematica program  Mathematica program

Location of singularities in the complex plane of the parameter z.
Left panel refers to quadratic approximants,
right panel to differential approximants.
Encircled areas are subjectively estimated locations of
the dominant zc = 1.59 + 0.36 i and a subdominant z'c = -3.5 singularities.
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
Top of Page  Top of the page         Previous Example  Prev. (a22)     Next Example  Next (a38)          Mathematica program  Mathematica program

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.
Red circle marks the lowest excited energy level 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
Top of Page  Top of the page         Previous Example  Prev. (a22)     Next Example  Next (a38)          Mathematica program  Mathematica program


Examplesa1a2a8a16a22a30a38a44a45a51a62a69a75a83a84a85a86a87a88a90a91
MoleculeArBHBHBHBHBHBHBO+C2CN+N2HFHFHClHClF-Cl-Cl-NeOH-SH-
Basisaug-cc-pVDZcc-pVDZcc-pVTZcc-pVQZaug-cc-pVDZaug-cc-pVTZaug-cc-pVQZcc-pVDZcc-pVDZcc-pVDZcc-pVDZcc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-pVDZaug-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.