Møller-Plesset perturbation theory: example "a2"

Molecule BH. Basis cc-pVDZ. 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 -25.125 186 608 9  -25.125 186 608 9 
2 -0.060 723 555 4  -25.185 910 164 3 
3 -0.017 835 390 9  -25.203 745 555 2 
4 -0.006 351 053  -25.210 096 608 2 
5 -0.002 655 811 4  -25.212 752 419 6 
6 -0.001 256 028 1  -25.214 008 447 7 
7 -0.000 638 342 5  -25.214 646 790 2 
8 -0.000 334 340 6  -25.214 981 130 8 
9 -0.000 175 292 2  -25.215 156 423 
10 -0.000 090 215 5  -25.215 246 638 5 
11 -0.000 044 855 7  -25.215 291 494 2 
12 -0.000 021 155 8  -25.215 312 65 
13 -0.000 009 185 6  -25.215 321 835 6 
14 -0.000 003 431 5  -25.215 325 267 1 
15 -0.000 000 864  -25.215 326 131 1 
16  0.000 000 144 6  -25.215 325 986 5 
17  0.000 000 440 3  -25.215 325 546 2 
18  0.000 000 443 8  -25.215 325 102 4 
19  0.000 000 352 1  -25.215 324 750 3 
20  0.000 000 248 6  -25.215 324 501 7 
21  0.000 000 163 1  -25.215 324 338 6 
22  0.000 000 101 1  -25.215 324 237 5 
23  0.000 000 059 8  -25.215 324 177 7 
24  0.000 000 034  -25.215 324 143 7 
25  0.000 000 018 5  -25.215 324 125 2 
26  0.000 000 009 6  -25.215 324 115 6 
27  0.000 000 004 8  -25.215 324 110 8 
28  0.000 000 002 2  -25.215 324 108 6 
29  0.000 000 001  -25.215 324 107 6 
Exact energy -25.215 324 107 282 
Top of Page  Top of the page         Previous Example  Prev. (a1)     Next Example  Next (a8)          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. (a1)     Next Example  Next (a8)          PDF format for printing  PDF format     Mathematica program  Mathematica program

Scaled coefficients of Møller-Plesset perturbation theory.
Parameters a =  0.6574, b = -2.2444 and c =  0.7499
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. (a1)     Next Example  Next (a8)          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. (a1)     Next Example  Next (a8)          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 = 1.65 + 0.43 i and a subdominant z'c = -3.6 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. (a1)     Next Example  Next (a8)          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. (a1)     Next Example  Next (a8)          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.