Møller-Plesset perturbation theory: example "BH aug-cc-pVQZ 1.2r_e"

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

Content


ExamplesAr cc-pVDZBH aug-cc-pVQZ 0.9r_eBH aug-cc-pVQZ 1.0r_eBH aug-cc-pVQZ 1.1r_eBH aug-cc-pVQZ 1.2r_eBH aug-cc-pVQZ 1.3r_eBH aug-cc-pVQZ 1.4r_eBH aug-cc-pVQZ 1.5r_eBH aug-cc-pVQZ 1.6r_eBH aug-cc-pVQZ 1.7r_eBH aug-cc-pVQZ 1.8r_eBH aug-cc-pVQZ 1.9r_eBH aug-cc-pVQZ 2.0r_eBH aug-cc-pVQZ 2.1r_eBH aug-cc-pVQZ 2.2r_eBH 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 aug-cc-pVDZ 1.5r_eHF aug-cc-pVDZ 2.0r_eHF aug-cc-pVDZ r_eHF cc-pVDZ 1.5ReHF cc-pVDZ 2ReHF cc-pVDZ Rena-pl aug-cc-pvdzNe cc-pVDZO2- aug-cc-pVDZ
MoleculeArX 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 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 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 HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-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 -25.114 092 913 312 717  -25.114 092 913 312 717 
2 -0.079 903 850 711 077  -25.193 996 764 023 794 
3 -0.015 789 731 496 336  -25.209 786 495 520 13 
4 -0.006 598 486 128 814  -25.216 384 981 648 944 
5 -0.002 825 354 351 522  -25.219 210 336 000 466 
6 -0.001 358 559 728 615  -25.220 568 895 729 081 
7 -0.000 666 194 423 179  -25.221 235 090 152 26 
8 -0.000 334 553 023 068  -25.221 569 643 175 328 
9 -0.000 166 813 591 309  -25.221 736 456 766 637 
10 -0.000 081 700 834 903  -25.221 818 157 601 54 
11 -0.000 038 462 948 11  -25.221 856 620 549 65 
12 -0.000 016 969 934 327  -25.221 873 590 483 977 
13 -0.000 006 642 673 303  -25.221 880 233 157 28 
14 -0.000 001 974 218 031  -25.221 882 207 375 311 
15 -0.000 000 070 490 932  -25.221 882 277 866 243 
16  0.000 000 550 634 689  -25.221 881 727 231 554 
17  0.000 000 630 012 188  -25.221 881 097 219 366 
18  0.000 000 518 138 841  -25.221 880 579 080 525 
19  0.000 000 368 627 754  -25.221 880 210 452 771 
20  0.000 000 239 138 237  -25.221 879 971 314 534 
21  0.000 000 144 228 394  -25.221 879 827 086 14 
22  0.000 000 081 253 273  -25.221 879 745 832 867 
23  0.000 000 042 504 312  -25.221 879 703 328 555 
24  0.000 000 020 224 905  -25.221 879 683 103 65 
25  0.000 000 008 294 197  -25.221 879 674 809 453 
26  0.000 000 002 436 887  -25.221 879 672 372 566 
27 -0.000 000 000 092 621  -25.221 879 672 465 187 
28 -0.000 000 000 939 823  -25.221 879 673 405 01 
29 -0.000 000 001 026 746  -25.221 879 674 431 756 
30 -0.000 000 000 832 597  -25.221 879 675 264 353 
31 -0.000 000 000 582 84  -25.221 879 675 847 193 
32 -0.000 000 000 367 577  -25.221 879 676 214 77 
33 -0.000 000 000 210 862  -25.221 879 676 425 632 
34 -0.000 000 000 108 638  -25.221 879 676 534 27 
35 -0.000 000 000 047 847  -25.221 879 676 582 117 
36 -0.000 000 000 015 028  -25.221 879 676 597 145 
37  0.000 000 000 000 585  -25.221 879 676 596 56 
38  0.000 000 000 006 527  -25.221 879 676 590 033 
39  0.000 000 000 007 587  -25.221 879 676 582 446 
40  0.000 000 000 006 557  -25.221 879 676 575 889 
41  0.000 000 000 004 914  -25.221 879 676 570 975 
42  0.000 000 000 003 346  -25.221 879 676 567 629 
43  0.000 000 000 002 106  -25.221 879 676 565 523 
44  0.000 000 000 001 226  -25.221 879 676 564 297 
45  0.000 000 000 000 653  -25.221 879 676 563 644 
46  0.000 000 000 000 307  -25.221 879 676 563 337 
47  0.000 000 000 000 114  -25.221 879 676 563 223 
48  0.000 000 000 000 017  -25.221 879 676 563 206 
49 -0.000 000 000 000 024  -25.221 879 676 563 23 
50 -0.000 000 000 000 036  -25.221 879 676 563 266 
51 -0.000 000 000 000 035  -25.221 879 676 563 301 
52 -0.000 000 000 000 028  -25.221 879 676 563 329 
53 -0.000 000 000 000 02  -25.221 879 676 563 349 
54 -0.000 000 000 000 013  -25.221 879 676 563 362 
55 -0.000 000 000 000 008  -25.221 879 676 563 37 
56 -0.000 000 000 000 005  -25.221 879 676 563 375 
57 -0.000 000 000 000 003  -25.221 879 676 563 378 
58  -15 -0. x 10  -25.221 879 676 563 379 
59  -15 -0. x 10  -25.221 879 676 563 38 
Exact energy -25.221 879 676 563 38 
Top of Page  Top of the page         Previous Example  Prev. (BH aug-cc-pVQZ 1.1r_e)     Top oftable  Top of this table (BH aug-cc-pVQZ 1.2r_e)     Next Example  Next (BH aug-cc-pVQZ 1.3r_e)          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 aug-cc-pVQZ 1.1r_e)     Next Example  Next (BH aug-cc-pVQZ 1.3r_e)          PDF format for printing  PDF format     Mathematica program  Mathematica program

Scaled coefficients of Møller-Plesset perturbation theory.
Parameters a =  0.6937, b = -4.3089 and c =  82.5358
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.11 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 aug-cc-pVQZ 1.1r_e)     Next Example  Next (BH aug-cc-pVQZ 1.3r_e)          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 aug-cc-pVQZ 1.1r_e)     Next Example  Next (BH aug-cc-pVQZ 1.3r_e)          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 = -2.5 and a subdominant z'c = 1.51 + 0.46 i 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. (BH aug-cc-pVQZ 1.1r_e)     Next Example  Next (BH aug-cc-pVQZ 1.3r_e)          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 aug-cc-pVQZ 1.1r_e)     Next Example  Next (BH aug-cc-pVQZ 1.3r_e)          Mathematica program  Mathematica program


ExamplesAr cc-pVDZBH aug-cc-pVQZ 0.9r_eBH aug-cc-pVQZ 1.0r_eBH aug-cc-pVQZ 1.1r_eBH aug-cc-pVQZ 1.2r_eBH aug-cc-pVQZ 1.3r_eBH aug-cc-pVQZ 1.4r_eBH aug-cc-pVQZ 1.5r_eBH aug-cc-pVQZ 1.6r_eBH aug-cc-pVQZ 1.7r_eBH aug-cc-pVQZ 1.8r_eBH aug-cc-pVQZ 1.9r_eBH aug-cc-pVQZ 2.0r_eBH aug-cc-pVQZ 2.1r_eBH aug-cc-pVQZ 2.2r_eBH 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 aug-cc-pVDZ 1.5r_eHF aug-cc-pVDZ 2.0r_eHF aug-cc-pVDZ r_eHF cc-pVDZ 1.5ReHF cc-pVDZ 2ReHF cc-pVDZ Rena-pl aug-cc-pvdzNe cc-pVDZO2- aug-cc-pVDZ
MoleculeArX 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 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 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 HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-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.