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

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 -25.129 932 842 002 877  -25.129 932 842 002 877 
2 -0.073 513 001 044 73  -25.203 445 843 047 607 
3 -0.016 552 091 338 476  -25.219 997 934 386 083 
4 -0.005 973 167 964 101  -25.225 971 102 350 184 
5 -0.002 541 078 428 981  -25.228 512 180 779 165 
6 -0.001 231 735 756 507  -25.229 743 916 535 672 
7 -0.000 638 609 621 398  -25.230 382 526 157 07 
8 -0.000 343 473 079 854  -25.230 725 999 236 924 
9 -0.000 187 481 147 816  -25.230 913 480 384 74 
10 -0.000 102 510 784 537  -25.231 015 991 169 277 
11 -0.000 055 652 798 837  -25.231 071 643 968 114 
12 -0.000 029 811 467 541  -25.231 101 455 435 655 
13 -0.000 015 669 160 392  -25.231 117 124 596 047 
14 -0.000 008 032 324 059  -25.231 125 156 920 106 
15 -0.000 003 982 671 06  -25.231 129 139 591 166 
16 -0.000 001 884 678 849  -25.231 131 024 270 015 
17 -0.000 000 829 887 594  -25.231 131 854 157 609 
18 -0.000 000 320 552 828  -25.231 132 174 710 437 
19 -0.000 000 088 665 46  -25.231 132 263 375 897 
20  0.000 000 007 056 063  -25.231 132 256 319 834 
21  0.000 000 039 191 889  -25.231 132 217 127 945 
22  0.000 000 043 838 167  -25.231 132 173 289 778 
23  0.000 000 038 186 392  -25.231 132 135 103 386 
24  0.000 000 029 922 226  -25.231 132 105 181 16 
25  0.000 000 022 132 83  -25.231 132 083 048 33 
26  0.000 000 015 797 454  -25.231 132 067 250 876 
27  0.000 000 011 007 513  -25.231 132 056 243 363 
28  0.000 000 007 536 632  -25.231 132 048 706 731 
29  0.000 000 005 088 957  -25.231 132 043 617 774 
30  0.000 000 003 394 907  -25.231 132 040 222 867 
31  0.000 000 002 238 811  -25.231 132 037 984 056 
32  0.000 000 001 458 96  -25.231 132 036 525 096 
33  0.000 000 000 938 496  -25.231 132 035 586 6 
34  0.000 000 000 594 864  -25.231 132 034 991 736 
35  0.000 000 000 370 605  -25.231 132 034 621 131 
36  0.000 000 000 226 154  -25.231 132 034 394 977 
37  0.000 000 000 134 51  -25.231 132 034 260 467 
38  0.000 000 000 077 402  -25.231 132 034 183 065 
39  0.000 000 000 042 577  -25.231 132 034 140 488 
40  0.000 000 000 021 907  -25.231 132 034 118 581 
41  0.000 000 000 010 059  -25.231 132 034 108 522 
42  0.000 000 000 003 586  -25.231 132 034 104 936 
43  0.000 000 000 000 296  -25.231 132 034 104 64 
44 -0.000 000 000 001 177  -25.231 132 034 105 817 
45 -0.000 000 000 001 665  -25.231 132 034 107 482 
46 -0.000 000 000 001 659  -25.231 132 034 109 141 
47 -0.000 000 000 001 439  -25.231 132 034 110 58 
48 -0.000 000 000 001 153  -25.231 132 034 111 733 
49 -0.000 000 000 000 877  -25.231 132 034 112 61 
Exact energy -25.231 132 034 114 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 =  0.7723, b = -4.8347 and c =  60.0387
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
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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.