Singularities of Møller-Plesset series: example "BH cc-pVQZ 1.5Re"

Molecule X 1^Sigma+ State of BH. Basis CC-PVQZ. 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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Quadratic approximants

[n1n2n3] approximant is defined as a solution of the quadratic equation
A(z)f2 +  B(z)f +  C(z) = 0
with polynomial coefficients A(z), B(z) and C(z) of degree n3, n2 and n1 respectively.

Square-root singularities are determined as zeroes of the discriminant
D(z) = B2(z) - 4A(z)C(z).
The weight c of the singularity zc is defined so that
f ~ c(1 - z/zc)1/2 at z -> zc.
The weight is calculated by formula
c = 1/2[-z(D/A2)']1/2
where r. h. s. of the above equation is evaluated at z = zc.

Table 1. Singularities with their weights for the quadratic approximant [1, 0, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.1393
0.187
Singularities of quadratic [1, 0, 0] approximant
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Table 2. Singularities with their weights for the quadratic approximant [1, 1, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.0849
0.169
Singularities of quadratic [1, 1, 0] approximant
2
1857.9511
7.01 i
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Table 3. Singularities with their weights for the quadratic approximant [1, 1, 1]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5098
0.708
Singularities of quadratic [1, 1, 1] approximant
2
-3.863
0.325
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Table 4. Singularities with their weights for the quadratic approximant [2, 1, 1]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5721
0.898
Singularities of quadratic [2, 1, 1] approximant
2
-4.7954
0.397
3
13.0159
0.371 i
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Table 5. Singularities with their weights for the quadratic approximant [2, 2, 1]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.894
2.98e4
Singularities of quadratic [2, 2, 1] approximant
2
-2.1983
0.0631
3
-4.3881
0.0786 i
4
9.1321
0.24 i
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Table 6. Singularities with their weights for the quadratic approximant [2, 2, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.7343 + 0.6044 i
0.573 - 0.0942 i
Singularities of quadratic [2, 2, 2] approximant
2
1.7343 - 0.6044 i
0.573 + 0.0942 i
3
3.1691
1.46
4
-3.3344
0.181
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Table 7. Singularities with their weights for the quadratic approximant [3, 2, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.3392 + 0.1177 i
0.108 - 0.0747 i
Singularities of quadratic [3, 2, 2] approximant
2
1.3392 - 0.1177 i
0.108 + 0.0747 i
3
2.1651
0.653
4
-4.3677
24.9
5
-5.5107
0.724 i
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Table 8. Singularities with their weights for the quadratic approximant [3, 3, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5855 + 0.4335 i
0.404 - 0.687 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5855 - 0.4335 i
0.404 + 0.687 i
3
1.9336
0.464
4
-3.1331
0.167
5
-15.4714
0.216 i
6
50.6626
0.477 i
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Table 9. Singularities with their weights for the quadratic approximant [3, 3, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5794 + 0.4612 i
0.454 - 0.447 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5794 - 0.4612 i
0.454 + 0.447 i
3
1.9092
0.445
4
-3.1056
0.151
5
14.1375
0.457 i
6
-46.1227
0.176 i
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Table 10. Singularities with their weights for the quadratic approximant [4, 3, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5844 + 0.4349 i
0.368 - 0.694 i
Singularities of quadratic [4, 3, 3] approximant
2
1.5844 - 0.4349 i
0.368 + 0.694 i
3
1.9598
0.465
4
-3.1789
0.186
5
-10.9509
0.242 i
6
20.6654
0.466 i
7
929.0668
380.
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Table 11. Singularities with their weights for the quadratic approximant [4, 4, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.3553 + 0.e-5 i
0.000145 + 0.000145 i
Singularities of quadratic [4, 4, 3] approximant
2
-0.3553 - 0.e-5 i
0.000145 - 0.000145 i
3
1.5867 + 0.45 i
0.501 - 0.537 i
4
1.5867 - 0.45 i
0.501 + 0.537 i
5
1.91
0.451
6
-3.1631
0.183
7
-14.1935
0.211 i
8
49.1702
0.475 i
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Table 12. Singularities with their weights for the quadratic approximant [4, 4, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2009
0.0506
Singularities of quadratic [4, 4, 4] approximant
2
1.2214
0.0509 i
3
1.6337 + 0.4014 i
2.78 - 1.02 i
4
1.6337 - 0.4014 i
2.78 + 1.02 i
5
1.7745
0.377
6
-3.4916
0.605
7
-4.8645
0.604 i
8
-9.7798
1.51
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Table 13. Singularities with their weights for the quadratic approximant [5, 4, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4674 + 0.4456 i
0.0649 - 0.173 i
Singularities of quadratic [5, 4, 4] approximant
2
1.4674 - 0.4456 i
0.0649 + 0.173 i
3
1.5604 + 0.0641 i
0.102 - 0.0631 i
4
1.5604 - 0.0641 i
0.102 + 0.0631 i
5
2.6557
0.603
6
-3.2853
0.24
7
-6.4305
0.408 i
8
11.0398
0.692 i
9
-25.9189
2.44
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Table 14. Singularities with their weights for the quadratic approximant [5, 5, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4434 + 0.0105 i
0.0175 - 0.0163 i
Singularities of quadratic [5, 5, 4] approximant
2
1.4434 - 0.0105 i
0.0175 + 0.0163 i
3
1.4413 + 0.4564 i
0.0432 - 0.103 i
4
1.4413 - 0.4564 i
0.0432 + 0.103 i
5
2.8647
0.877
6
-3.2077
0.14
7
-4.4561
4.08 i
8
-6.038
0.178
9
13.1907
0.356 i
10
-28.6331
0.277 i
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Table 15. Singularities with their weights for the quadratic approximant [5, 5, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-1.113
0.000349
Singularities of quadratic [5, 5, 5] approximant
2
-1.1132
0.000349 i
3
1.2098
0.0065
4
1.2239
0.0067 i
5
1.4159 + 0.4474 i
0.012 - 0.0697 i
6
1.4159 - 0.4474 i
0.012 + 0.0697 i
7
2.8505
1.06
8
-3.4411
0.987
9
-9.3884
0.162 i
10
37.1937
0.26 i
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Table 16. Singularities with their weights for the quadratic approximant [6, 5, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2015
0.00621
Singularities of quadratic [6, 5, 5] approximant
2
1.215
0.00639 i
3
-1.2761
0.000604
4
-1.2765
0.000604 i
5
1.415 + 0.4463 i
0.0104 - 0.0692 i
6
1.415 - 0.4463 i
0.0104 + 0.0692 i
7
2.8618
1.09
8
-3.4682
1.41
9
-10.0322
0.154 i
10
40.8416 + 39.7368 i
0.124 + 0.275 i
11
40.8416 - 39.7368 i
0.124 - 0.275 i
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Table 17. Singularities with their weights for the quadratic approximant [6, 6, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.366
0.0226
Singularities of quadratic [6, 6, 5] approximant
2
1.4063
0.0253 i
3
1.4249 + 0.4565 i
0.0273 - 0.0833 i
4
1.4249 - 0.4565 i
0.0273 + 0.0833 i
5
-1.1142 + 1.2434 i
0.000936 - 0.00208 i
6
-1.1142 - 1.2434 i
0.000936 + 0.00208 i
7
-1.1159 + 1.2423 i
0.00208 + 0.000936 i
8
-1.1159 - 1.2423 i
0.00208 - 0.000936 i
9
3.0617
1.38
10
-3.4342
1.11
11
13.1585
0.3 i
12
-13.9113
0.163 i
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Table 18. Singularities with their weights for the quadratic approximant [6, 6, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4603 + 0.4638 i
0.0693 - 0.179 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4603 - 0.4638 i
0.0693 + 0.179 i
3
1.7208
0.205
4
2.1394 + 0.3208 i
0.805 + 0.343 i
5
2.1394 - 0.3208 i
0.805 - 0.343 i
6
2.252 + 1.0212 i
0.311 + 0.055 i
7
2.252 - 1.0212 i
0.311 - 0.055 i
8
-2.477 + 0.0066 i
0.129 + 0.132 i
9
-2.477 - 0.0066 i
0.129 - 0.132 i
10
-3.5252
0.548
11
-4.7991
0.838 i
12
-10.0505
1.16
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Table 19. Singularities with their weights for the quadratic approximant [7, 6, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4614 + 0.4794 i
0.125 - 0.123 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4614 - 0.4794 i
0.125 + 0.123 i
3
1.7848 + 0.0502 i
0.095 - 0.0665 i
4
1.7848 - 0.0502 i
0.095 + 0.0665 i
5
2.3672
10.4
6
2.2606 + 0.7648 i
0.707 - 0.343 i
7
2.2606 - 0.7648 i
0.707 + 0.343 i
8
-2.5194
0.0176
9
-2.6197
0.0184 i
10
-4.1125
0.44
11
-7.5446
0.103 i
12
-5.5406 + 10.7287 i
0.0879 - 0.175 i
13
-5.5406 - 10.7287 i
0.0879 + 0.175 i
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Table 20. Singularities with their weights for the quadratic approximant [7, 7, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4616 + 0.4791 i
0.125 - 0.124 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4616 - 0.4791 i
0.125 + 0.124 i
3
1.791 + 0.0446 i
0.0889 - 0.065 i
4
1.791 - 0.0446 i
0.0889 + 0.065 i
5
2.3473
8.16
6
2.2588 + 0.7677 i
0.703 - 0.33 i
7
2.2588 - 0.7677 i
0.703 + 0.33 i
8
-2.5203
0.0178
9
-2.6203
0.0186 i
10
-4.109
0.45
11
-7.4151
0.103 i
12
-5.8065 + 10.748 i
0.0919 - 0.178 i
13
-5.8065 - 10.748 i
0.0919 + 0.178 i
14
145732.3828
52.9 i
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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

Plot of singularities Blank Molecule - icon for Allen-dataList of examples Blank Mathematica programs Blank Work in UMassD Blank Waste iconUnpublished reports

Designed by A. Sergeev.