Møller-Plesset perturbation theory: example "HF aug-cc-pVDZ 2.0r_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 -99.808 202 895 235 695  -99.808 202 895 235 695 
2 -0.269 539 961 488 477  -100.077 742 856 724 172 
3  0.009 021 221 318 783  -100.068 721 635 405 389 
4 -0.029 788 355 147 68  -100.098 509 990 553 069 
5  0.014 425 788 271 134  -100.084 084 202 281 935 
6 -0.021 747 869 382 371  -100.105 832 071 664 306 
7  0.021 267 117 590 349  -100.084 564 954 073 957 
8 -0.026 380 448 308 389  -100.110 945 402 382 346 
9  0.031 250 387 040 127  -100.079 695 015 342 219 
10 -0.039 177 539 635 508  -100.118 872 554 977 727 
11  0.050 316 325 331 803  -100.068 556 229 645 924 
12 -0.066 120 898 659 121  -100.134 677 128 305 045 
13  0.089 120 676 324 91  -100.045 556 451 980 135 
14 -0.122 289 506 574 286  -100.167 845 958 554 421 
15  0.171 078 284 000 309  -99.996 767 674 554 112 
16 -0.243 152 177 856 427  -100.239 919 852 410 539 
17  0.350 927 034 722 371  -99.888 992 817 688 168 
18 -0.513 521 573 747 891  -100.402 514 391 436 059 
19  0.761 262 046 252 112  -99.641 252 345 183 947 
20 -1.142 302 310 584 152  -100.783 554 655 768 099 
21  1.733 806 224 985 021  -99.049 748 430 783 078 
22 -2.660 375 590 863 79  -101.710 124 021 646 868 
23  4.124 649 491 824 312  -97.585 474 529 822 556 
24 -6.458 656 920 063 07  -104.044 131 449 885 626 
25  10.210 228 705 860 242  -93.833 902 744 025 384 
26 -16.289 542 538 512 457  -110.123 445 282 537 841 
27  26.218 853 443 355 513  -83.904 591 839 182 328 
28 -42.560 543 346 029 938  -126.465 135 185 212 266 
29  69.654 595 653 389 833  -56.810 539 531 822 433 
30 -114.895 595 805 914 894  -171.706 135 337 737 327 
31  190.954 566 140 513 776   19.248 430 802 776 449 
32 -319.662 350 704 452 138  -300.413 919 901 675 689 
33  538.826 575 458 017 032   238.412 655 556 341 343 
34 -914.247 534 624 160 949  -675.834 879 067 819 606 
35  1 560.980 659 246 258 483   885.145 780 178 438 877 
36 -2 681.100 249 834 946 226  -1 795.954 469 656 507 349 
37  4 631.005 576 417 332 122   2 835.051 106 760 824 773 
38 -8 041.777 845 190 846 165  -5 206.726 738 430 021 392 
39  14 035.078 328 290 534 046   8 828.351 589 860 512 654 
40 -24 611.580 825 693 159 568  -15 783.229 235 832 646 914 
41  43 351.787 610 202 125 506   27 568.558 374 369 478 592 
42 -76 683.832 351 968 536 386  -49 115.273 977 599 057 794 
43  136 182.808 180 405 350 868   87 067.534 202 806 293 074 
44 -242 750.977 959 011 011 99  -155 683.443 756 204 718 916 
45  434 234.954 455 776 663 963   278 551.510 699 571 945 047 
46 -779 336.250 173 936 248 757  -500 784.739 474 364 303 71 
47  1 403 068.283 435 751 218 349   902 283.543 961 386 914 639 
48 -2 533 438.009 473 737 329 245  -1 631 154.465 512 350 414 606 
49  4 587 214.172 980 102 710 426   2 956 059.707 467 752 295 82 
Exact energy  2 956 059.707 467 752 295 82 
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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 =  2.0224, b = -5.8184 and c =  26.8732
are chosen to make scaled coefficients of order of one in magnitude for all n.
Coefficient E1 = -99.81 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.