Møller-Plesset perturbation theory: example "o1"

Molecule O2-. Basis aug-cc-pVDZ. Structure ""

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Exampleso1
MoleculeO2-
Basisaug-cc-pVDZ

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -74.435 703 426 410 186  -74.435 703 426 410 186 
2 -0.301 643 761 470 571  -74.737 347 187 880 757 
3  0.055 905 599 398 757  -74.681 441 588 482 
4 -0.078 686 404 033 813  -74.760 127 992 515 813 
5  0.094 583 816 677 839  -74.665 544 175 837 974 
6 -0.149 300 027 524 308  -74.814 844 203 362 282 
7  0.241 948 259 909 253  -74.572 895 943 453 029 
8 -0.401 136 751 774 606  -74.974 032 695 227 635 
9  0.667 252 363 693 988  -74.306 780 331 533 647 
10 -1.112 020 343 918 861  -75.418 800 675 452 508 
11  1.851 774 093 021 33  -73.567 026 582 431 178 
12 -3.077 955 750 708 124  -76.644 982 333 139 302 
13  5.101 104 909 134 66  -71.543 877 424 004 642 
14 -8.422 731 698 764 311  -79.966 609 122 768 953 
15  13.846 114 413 511 405  -66.120 494 709 257 548 
16 -22.647 457 363 976 947  -88.767 952 073 234 495 
17  36.835 168 115 691 665  -51.932 783 957 542 83 
18 -59.535 943 871 016 002  -111.468 727 828 558 832 
19  95.556 247 289 482 371  -15.912 480 539 076 461 
20 -152.173 948 275 348 351  -168.086 428 814 424 812 
21  240.206 597 316 228 34   72.120 168 501 803 528 
22 -375.358 316 474 678 19  -303.238 147 972 874 662 
23  579.722 808 376 731 791   276.484 660 403 857 129 
24 -883.030 412 484 289 741  -606.545 752 080 432 612 
25  1 322.612 625 673 744 105   716.066 873 593 311 493 
26 -1 939.823 892 996 429 549  -1 223.757 019 403 118 056 
27  2 768.277 247 087 677 097   1 544.520 227 684 559 041 
28 -3 804.776 171 257 621 172  -2 260.255 943 573 062 131 
29  4 945.614 603 366 643 678   2 685.358 659 793 581 547 
30 -5 856.134 478 876 347 202  -3 170.775 819 082 765 655 
31  5 715.253 088 836 919 233   2 544.477 269 754 153 578 
32 -2 731.007 857 912 224 608  -186.530 588 158 071 03 
33 -6 755.384 534 705 881 379  -6 941.915 122 863 952 409 
34  29 892.763 632 927 490 107   22 950.848 510 063 537 698 
Exact energy -74.723 869 777 261 5 
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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 =  1.6198, b = -0.0821 and c =  0.0130
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -74.44 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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Exampleso1
MoleculeO2-
Basisaug-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.