Møller-Plesset perturbation theory: example "BH-cc-pVDZ-Re"

Molecule X 1^Sigma+ State of BH. Basis CC-PVDZ. Structure ""

Content


ExamplesBH-cc-pVDZ-1.5ReBH-cc-pVDZ-2ReBH-cc-pVDZ-ReBH-cc-pVQZ-1.5ReBH-cc-pVQZ-2ReBH-cc-pVQZ-ReBH-cc-pVTZ-1.5ReBH-cc-pVTZ-2ReBH-cc-pVTZ-ReH--cc-pV5ZH--cc-pVQZHF-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHH- ionH- ionX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-PVDZCC-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 -25.125 331 829 009 837  -25.125 331 829 009 837 
2 -0.060 531 882 975 89  -25.185 863 711 985 727 
3 -0.017 749 013 081 884  -25.203 612 725 067 611 
4 -0.006 300 312 496 743  -25.209 913 037 564 354 
5 -0.002 632 881 747 705  -25.212 545 919 312 059 
6 -0.001 248 961 324 413  -25.213 794 880 636 472 
7 -0.000 638 590 234 606  -25.214 433 470 871 078 
8 -0.000 337 184 984 143  -25.214 770 655 855 221 
9 -0.000 178 564 061 525  -25.214 949 219 916 746 
10 -0.000 093 069 478 22  -25.215 042 289 394 966 
11 -0.000 047 062 662 555  -25.215 089 352 057 521 
12 -0.000 022 742 462 102  -25.215 112 094 519 623 
13 -0.000 010 266 216 508  -25.215 122 360 736 131 
14 -0.000 004 134 288 063  -25.215 126 495 024 194 
15 -0.000 001 301 169 845  -25.215 127 796 194 039 
16 -0.000 000 114 978 465  -25.215 127 911 172 504 
17  0.000 000 294 238 201  -25.215 127 616 934 303 
18  0.000 000 367 208 888  -25.215 127 249 725 415 
19  0.000 000 315 842 462  -25.215 126 933 882 953 
20  0.000 000 234 511 722  -25.215 126 699 371 231 
21  0.000 000 160 080 09  -25.215 126 539 291 141 
22  0.000 000 103 143 502  -25.215 126 436 147 639 
23  0.000 000 063 567 545  -25.215 126 372 580 094 
24  0.000 000 037 746 75  -25.215 126 334 833 344 
25  0.000 000 021 683 701  -25.215 126 313 149 643 
26  0.000 000 012 074 352  -25.215 126 301 075 291 
27  0.000 000 006 519 902  -25.215 126 294 555 389 
28  0.000 000 003 409 767  -25.215 126 291 145 622 
29  0.000 000 001 721 127  -25.215 126 289 424 495 
30  0.000 000 000 832 456  -25.215 126 288 592 039 
31  0.000 000 000 380 072  -25.215 126 288 211 967 
32  0.000 000 000 158 322  -25.215 126 288 053 645 
33  0.000 000 000 054 623  -25.215 126 287 999 022 
34  0.000 000 000 009 272  -25.215 126 287 989 75 
35 -0.000 000 000 008 384  -25.215 126 287 998 134 
36 -0.000 000 000 013 561  -25.215 126 288 011 695 
37 -0.000 000 000 013 537  -25.215 126 288 025 232 
38 -0.000 000 000 011 647  -25.215 126 288 036 879 
39 -0.000 000 000 009 336  -25.215 126 288 046 215 
40 -0.000 000 000 007 176  -25.215 126 288 053 391 
41 -0.000 000 000 005 356  -25.215 126 288 058 747 
42 -0.000 000 000 003 902  -25.215 126 288 062 649 
43 -0.000 000 000 002 781  -25.215 126 288 065 43 
44 -0.000 000 000 001 939  -25.215 126 288 067 369 
45 -0.000 000 000 001 322  -25.215 126 288 068 691 
46 -0.000 000 000 000 88  -25.215 126 288 069 571 
47 -0.000 000 000 000 571  -25.215 126 288 070 142 
48 -0.000 000 000 000 36  -25.215 126 288 070 502 
49 -0.000 000 000 000 219  -25.215 126 288 070 721 
Exact energy -25.215 126 288 071 
Top of Page  Top of the page         Previous Example  Prev. (BH-cc-pVDZ-2Re)     Top oftable  Top of this table (BH-cc-pVDZ-Re)     Next Example  Next (BH-cc-pVQZ-1.5Re)          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. (BH-cc-pVDZ-2Re)     Next Example  Next (BH-cc-pVQZ-1.5Re)          PDF format for printing  PDF format     Mathematica program  Mathematica program

Scaled coefficients of Møller-Plesset perturbation theory.
Parameters a =  0.6574, b = -2.1900 and c =  0.6113
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. (BH-cc-pVDZ-2Re)     Next Example  Next (BH-cc-pVQZ-1.5Re)          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. (BH-cc-pVDZ-2Re)     Next Example  Next (BH-cc-pVQZ-1.5Re)          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.
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. (BH-cc-pVDZ-2Re)     Next Example  Next (BH-cc-pVQZ-1.5Re)          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.
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. (BH-cc-pVDZ-2Re)     Next Example  Next (BH-cc-pVQZ-1.5Re)          Mathematica program  Mathematica program


ExamplesBH-cc-pVDZ-1.5ReBH-cc-pVDZ-2ReBH-cc-pVDZ-ReBH-cc-pVQZ-1.5ReBH-cc-pVQZ-2ReBH-cc-pVQZ-ReBH-cc-pVTZ-1.5ReBH-cc-pVTZ-2ReBH-cc-pVTZ-ReH--cc-pV5ZH--cc-pVQZHF-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHH- ionH- ionX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-PVDZCC-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.