Møller-Plesset perturbation theory: example "BH-cc-pVTZ-2Re"

Molecule X 1^Sigma+ State of BH. Basis CC-PVTZ. 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

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -24.997 241 660 105 667  -24.997 241 660 105 667 
2 -0.082 964 936 592 995  -25.080 206 596 698 662 
3 -0.022 884 816 311 958  -25.103 091 413 010 62 
4 -0.012 809 990 579 489  -25.115 901 403 590 109 
5 -0.006 461 711 981 243  -25.122 363 115 571 352 
6 -0.003 669 130 350 012  -25.126 032 245 921 364 
7 -0.001 890 302 399 394  -25.127 922 548 320 758 
8 -0.000 931 582 249 164  -25.128 854 130 569 922 
9 -0.000 379 651 599 687  -25.129 233 782 169 609 
10 -0.000 093 784 901 962  -25.129 327 567 071 571 
11  0.000 042 409 885 972  -25.129 285 157 185 599 
12  0.000 092 521 136 362  -25.129 192 636 049 237 
13  0.000 097 854 701 286  -25.129 094 781 347 951 
14  0.000 082 622 605 373  -25.129 012 158 742 578 
15  0.000 060 756 608 959  -25.128 951 402 133 619 
16  0.000 039 564 359 711  -25.128 911 837 773 908 
17  0.000 022 300 492 513  -25.128 889 537 281 395 
18  0.000 009 865 139 711  -25.128 879 672 141 684 
19  0.000 001 906 307 426  -25.128 877 765 834 258 
20 -0.000 002 476 107 57  -25.128 880 241 941 828 
21 -0.000 004 312 670 158  -25.128 884 554 611 986 
22 -0.000 004 538 111 784  -25.128 889 092 723 77 
23 -0.000 003 892 257 046  -25.128 892 984 980 816 
24 -0.000 002 898 725 418  -25.128 895 883 706 234 
25 -0.000 001 886 720 543  -25.128 897 770 426 777 
26 -0.000 001 031 989 04  -25.128 898 802 415 817 
27 -0.000 000 401 820 298  -25.128 899 204 236 115 
28  0.000 000 004 498 005  -25.128 899 199 738 11 
29  0.000 000 223 691 054  -25.128 898 976 047 056 
30  0.000 000 305 848 751  -25.128 898 670 198 305 
31  0.000 000 300 219 699  -25.128 898 369 978 606 
32  0.000 000 247 713 172  -25.128 898 122 265 434 
33  0.000 000 178 169 978  -25.128 897 944 095 456 
34  0.000 000 110 633 678  -25.128 897 833 461 778 
35  0.000 000 055 206 867  -25.128 897 778 254 911 
36  0.000 000 015 480 372  -25.128 897 762 774 539 
37 -0.000 000 009 104 764  -25.128 897 771 879 303 
38 -0.000 000 021 302 314  -25.128 897 793 181 617 
39 -0.000 000 024 636 314  -25.128 897 817 817 931 
40 -0.000 000 022 492 513  -25.128 897 840 310 444 
41 -0.000 000 017 637 682  -25.128 897 857 948 126 
42 -0.000 000 012 051 399  -25.128 897 869 999 525 
43 -0.000 000 006 957 698  -25.128 897 876 957 223 
44 -0.000 000 002 962 821  -25.128 897 879 920 044 
45 -0.000 000 000 230 341  -25.128 897 880 150 385 
46  0.000 000 001 350 509  -25.128 897 878 799 876 
47  0.000 000 002 026 881  -25.128 897 876 772 995 
48  0.000 000 002 083 192  -25.128 897 874 689 803 
49  0.000 000 001 779 452  -25.128 897 872 910 351 
Exact energy -25.128 897 871 005 1 
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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 =  0.7988, b = -2.3044 and c =  0.6009
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25 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.