Møller-Plesset perturbation theory: example "BH-cc-pVTZ-1.5Re"

Molecule X 1^Sigma+ State of BH. Basis CC-PVTZ. 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 -25.067 027 554 150 322  -25.067 027 554 150 322 
2 -0.077 488 944 347 376  -25.144 516 498 497 698 
3 -0.019 386 629 417 005  -25.163 903 127 914 703 
4 -0.008 376 178 509 513  -25.172 279 306 424 216 
5 -0.003 721 927 496 214  -25.176 001 233 920 43 
6 -0.001 786 197 964 814  -25.177 787 431 885 244 
7 -0.000 843 894 482 388  -25.178 631 326 367 632 
8 -0.000 389 079 133 476  -25.179 020 405 501 108 
9 -0.000 168 072 359 499  -25.179 188 477 860 607 
10 -0.000 064 587 167 463  -25.179 253 065 028 07 
11 -0.000 018 792 484 055  -25.179 271 857 512 125 
12 -0.000 000 598 267 291  -25.179 272 455 779 416 
13  0.000 005 125 595 892  -25.179 267 330 183 524 
14  0.000 005 720 792 02  -25.179 261 609 391 504 
15  0.000 004 584 666 939  -25.179 257 024 724 565 
16  0.000 003 159 578 781  -25.179 253 865 145 784 
17  0.000 001 965 424 715  -25.179 251 899 721 069 
18  0.000 001 117 140 393  -25.179 250 782 580 676 
19  0.000 000 575 061 548  -25.179 250 207 519 128 
20  0.000 000 257 996 556  -25.179 249 949 522 572 
21  0.000 000 088 844 016  -25.179 249 860 678 556 
22  0.000 000 008 698 043  -25.179 249 851 980 513 
23 -0.000 000 022 348 161  -25.179 249 874 328 674 
24 -0.000 000 029 006 872  -25.179 249 903 335 546 
25 -0.000 000 025 351 862  -25.179 249 928 687 408 
26 -0.000 000 018 672 483  -25.179 249 947 359 891 
27 -0.000 000 012 272 835  -25.179 249 959 632 726 
28 -0.000 000 007 312 773  -25.179 249 966 945 499 
29 -0.000 000 003 922 92  -25.179 249 970 868 419 
30 -0.000 000 001 826 252  -25.179 249 972 694 671 
31 -0.000 000 000 651 44  -25.179 249 973 346 111 
32 -0.000 000 000 068 484  -25.179 249 973 414 595 
33  0.000 000 000 169 207  -25.179 249 973 245 388 
34  0.000 000 000 226 148  -25.179 249 973 019 24 
35  0.000 000 000 202 073  -25.179 249 972 817 167 
36  0.000 000 000 151 696  -25.179 249 972 665 471 
37  0.000 000 000 101 392  -25.179 249 972 564 079 
38  0.000 000 000 061 311  -25.179 249 972 502 768 
39  0.000 000 000 033 305  -25.179 249 972 469 463 
40  0.000 000 000 015 652  -25.179 249 972 453 811 
41  0.000 000 000 005 593  -25.179 249 972 448 218 
42  0.000 000 000 000 526  -25.179 249 972 447 692 
43 -0.000 000 000 001 57  -25.179 249 972 449 262 
44 -0.000 000 000 002 079  -25.179 249 972 451 341 
45 -0.000 000 000 001 864  -25.179 249 972 453 205 
46 -0.000 000 000 001 406  -25.179 249 972 454 611 
47 -0.000 000 000 000 944  -25.179 249 972 455 555 
48 -0.000 000 000 000 573  -25.179 249 972 456 128 
49 -0.000 000 000 000 312  -25.179 249 972 456 44 
Exact energy -25.179 249 972 456 6 
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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 =  0.6937, b = -3.0666 and c =  3.2363
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -25.07 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.