Møller-Plesset perturbation theory: example "HF aug-cc-pVDZ r_e"

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

Content


ExamplesAr cc-pVDZBH aug-cc-pVQZ 0.9r_eBH aug-cc-pVQZ 1.0r_eBH aug-cc-pVQZ 1.1r_eBH aug-cc-pVQZ 1.2r_eBH aug-cc-pVQZ 1.3r_eBH aug-cc-pVQZ 1.4r_eBH aug-cc-pVQZ 1.5r_eBH aug-cc-pVQZ 1.6r_eBH aug-cc-pVQZ 1.7r_eBH aug-cc-pVQZ 1.8r_eBH aug-cc-pVQZ 1.9r_eBH aug-cc-pVQZ 2.0r_eBH aug-cc-pVQZ 2.1r_eBH aug-cc-pVQZ 2.2r_eBH 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 aug-cc-pVDZ 1.5r_eHF aug-cc-pVDZ 2.0r_eHF aug-cc-pVDZ r_eHF cc-pVDZ 1.5ReHF cc-pVDZ 2ReHF cc-pVDZ Rena-pl aug-cc-pvdzNe cc-pVDZO2- aug-cc-pVDZ
MoleculeArX 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 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 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 HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

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Coefficients of Møller-Plesset perturbation series
nEnPartial sum
1 -100.033 473 873 073 063  -100.033 473 873 073 063 
2 -0.222 260 157 591 536  -100.255 734 030 664 599 
3 -0.000 705 301 228 362  -100.256 439 331 892 961 
4 -0.008 539 165 149 872  -100.264 978 497 042 833 
5  0.002 551 103 176 088  -100.262 427 393 866 745 
6 -0.002 655 181 676 017  -100.265 082 575 542 762 
7  0.001 850 914 212 447  -100.263 231 661 330 315 
8 -0.001 590 474 230 324  -100.264 822 135 560 639 
9  0.001 348 380 935 392  -100.263 473 754 625 247 
10 -0.001 219 002 079 691  -100.264 692 756 704 938 
11  0.001 133 746 958 868  -100.263 559 009 746 07 
12 -0.001 089 875 839 582  -100.264 648 885 585 652 
13  0.001 074 710 068 298  -100.263 574 175 517 354 
14 -0.001 084 535 525 294  -100.264 658 711 042 648 
15  0.001 116 535 546 781  -100.263 542 175 495 867 
16 -0.001 170 078 727 417  -100.264 712 254 223 284 
17  0.001 245 688 654 845  -100.263 466 565 568 439 
18 -0.001 345 061 440 193  -100.264 811 627 008 632 
19  0.001 470 949 566 979  -100.263 340 677 441 653 
20 -0.001 627 229 105 125  -100.264 967 906 546 778 
21  0.001 819 019 458 267  -100.263 148 887 088 511 
22 -0.002 052 888 546 001  -100.265 201 775 634 512 
23  0.002 337 136 498 894  -100.262 864 639 135 618 
24 -0.002 682 173 047 174  -100.265 546 812 182 792 
25  0.003 101 006 275 277  -100.262 445 805 907 515 
26 -0.003 609 868 767 173  -100.266 055 674 674 688 
27  0.004 229 015 723 845  -100.261 826 658 950 843 
28 -0.004 983 740 240 285  -100.266 810 399 191 128 
29  0.005 905 664 515 819  -100.260 904 734 675 309 
30 -0.007 034 383 034 645  -100.267 939 117 709 954 
31  0.008 419 556 137 699  -100.259 519 561 572 255 
32 -0.010 123 581 416 617  -100.269 643 142 988 872 
33  0.012 225 008 173 452  -100.257 418 134 815 42 
34 -0.014 822 909 587 081  -100.272 241 044 402 501 
35  0.018 042 491 946 131  -100.254 198 552 456 37 
36 -0.022 042 305 308 885  -100.276 240 857 765 255 
37  0.027 023 531 867 779  -100.249 217 325 897 476 
38 -0.033 241 976 014 764  -100.282 459 301 912 24 
39  0.041 023 575 557 308  -100.241 435 726 354 932 
40 -0.050 784 512 788 173  -100.292 220 239 143 105 
41  0.063 057 348 844 604  -100.229 162 890 298 501 
42 -0.078 525 064 328 173  -100.307 687 954 626 674 
43  0.098 065 503 251 065  -100.209 622 451 375 609 
44 -0.122 809 540 046 782  -100.332 431 991 422 391 
45  0.154 217 394 192 882  -100.178 214 597 229 509 
46 -0.194 179 004 322 511  -100.372 393 601 552 02 
47  0.245 146 380 815 768  -100.127 247 220 736 252 
48 -0.310 308 570 837 397  -100.437 555 791 573 649 
49  0.393 823 550 808 282  -100.043 732 240 765 367 
Exact energy -100.264 111 144 733 62 
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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 =  1.3877, b = -4.4877 and c =  1.5180
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -100.03 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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ExamplesAr cc-pVDZBH aug-cc-pVQZ 0.9r_eBH aug-cc-pVQZ 1.0r_eBH aug-cc-pVQZ 1.1r_eBH aug-cc-pVQZ 1.2r_eBH aug-cc-pVQZ 1.3r_eBH aug-cc-pVQZ 1.4r_eBH aug-cc-pVQZ 1.5r_eBH aug-cc-pVQZ 1.6r_eBH aug-cc-pVQZ 1.7r_eBH aug-cc-pVQZ 1.8r_eBH aug-cc-pVQZ 1.9r_eBH aug-cc-pVQZ 2.0r_eBH aug-cc-pVQZ 2.1r_eBH aug-cc-pVQZ 2.2r_eBH 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 aug-cc-pVDZ 1.5r_eHF aug-cc-pVDZ 2.0r_eHF aug-cc-pVDZ r_eHF cc-pVDZ 1.5ReHF cc-pVDZ 2ReHF cc-pVDZ Rena-pl aug-cc-pvdzNe cc-pVDZO2- aug-cc-pVDZ
MoleculeArX 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 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 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 HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

Known inaccuracies


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Designed by A. Sergeev.