Møller-Plesset perturbation theory: example "HF-cc-pVDZ-1.5Re"

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

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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

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -99.907 938 589 855 675  -99.907 938 589 855 675 
2 -0.220 575 479 538 505  -100.128 514 069 394 18 
3 -0.000 432 036 016 865  -100.128 946 105 411 045 
4 -0.009 032 010 740 26  -100.137 978 116 151 305 
5 -0.000 399 780 864 801  -100.138 377 897 016 106 
6 -0.001 559 586 637 953  -100.139 937 483 654 059 
7  0.000 084 746 625 967  -100.139 852 737 028 092 
8 -0.000 443 102 147 721  -100.140 295 839 175 813 
9  0.000 099 035 354 61  -100.140 196 803 821 203 
10 -0.000 134 591 977 004  -100.140 331 395 798 207 
11  0.000 059 947 341 852  -100.140 271 448 456 355 
12 -0.000 049 334 882 033  -100.140 320 783 338 388 
13  0.000 033 896 171 26  -100.140 286 887 167 128 
14 -0.000 023 512 408 432  -100.140 310 399 575 56 
15  0.000 019 458 975 678  -100.140 290 940 599 882 
16 -0.000 013 830 489 918  -100.140 304 771 089 8 
17  0.000 011 941 078 655  -100.140 292 830 011 145 
18 -0.000 009 245 991 013  -100.140 302 076 002 158 
19  0.000 008 025 483 309  -100.140 294 050 518 849 
20 -0.000 006 708 820 786  -100.140 300 759 339 635 
21  0.000 005 900 478 404  -100.140 294 858 861 231 
22 -0.000 005 200 831 157  -100.140 300 059 692 388 
23  0.000 004 685 404 513  -100.140 295 374 287 875 
24 -0.000 004 282 765 033  -100.140 299 657 052 908 
25  0.000 003 965 445 156  -100.140 295 691 607 752 
26 -0.000 003 726 729 651  -100.140 299 418 337 403 
27  0.000 003 540 329 14  -100.140 295 878 008 263 
28 -0.000 003 405 337 523  -100.140 299 283 345 786 
29  0.000 003 307 995 025  -100.140 295 975 350 761 
30 -0.000 003 246 157 005  -100.140 299 221 507 766 
31  0.000 003 213 658 872  -100.140 296 007 848 894 
32 -0.000 003 208 257 822  -100.140 299 216 106 716 
33  0.000 003 227 284 516  -100.140 295 988 822 2 
34 -0.000 003 269 236 868  -100.140 299 258 059 068 
35  0.000 003 333 036 741  -100.140 295 925 022 327 
36 -0.000 003 418 024 083  -100.140 299 343 046 41 
37  0.000 003 523 978 464  -100.140 295 819 067 946 
38 -0.000 003 650 936 057  -100.140 299 470 004 003 
39  0.000 003 799 261 226  -100.140 295 670 742 777 
40 -0.000 003 969 542 563  -100.140 299 640 285 34 
41  0.000 004 162 622 085  -100.140 295 477 663 255 
42 -0.000 004 379 557 036  -100.140 299 857 220 291 
43  0.000 004 621 627 61  -100.140 295 235 592 681 
44 -0.000 004 890 329 72  -100.140 300 125 922 401 
45  0.000 005 187 380 004  -100.140 294 938 542 397 
46 -0.000 005 514 721 74  -100.140 300 453 264 137 
47  0.000 005 874 534 071  -100.140 294 578 730 066 
48 -0.000 006 269 244 86  -100.140 300 847 974 926 
49  0.000 006 701 545 588  -100.140 294 146 429 338 
Exact energy -100.140 294 146 429 338 
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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 =  1.2829, b = -7.9753 and c =  950.5291
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -99.91 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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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


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Designed by A. Sergeev.