Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 1.9r_e"

Molecule X 1^Sigma+ State of BH. Basis AUG-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 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 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-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 [5, 5, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.1488
0.0138
Singularities of quadratic [5, 5, 4] approximant
2
1.1742
0.0147 i
3
1.2386 + 0.4334 i
0.0158 - 0.0754 i
4
1.2386 - 0.4334 i
0.0158 + 0.0754 i
5
-2.6173 + 0.3602 i
0.225 - 0.09 i
6
-2.6173 - 0.3602 i
0.225 + 0.09 i
7
3.1364
1.42
8
-5.0038
0.119
9
6.9352
0.549 i
10
-26.0318
0.296 i
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Table 2. 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
1.1502
0.0151
Singularities of quadratic [5, 5, 5] approximant
2
1.1798
0.0162 i
3
1.2362 + 0.4321 i
0.0134 - 0.0748 i
4
1.2362 - 0.4321 i
0.0134 + 0.0748 i
5
-2.677 + 0.4295 i
0.193 - 0.275 i
6
-2.677 - 0.4295 i
0.193 + 0.275 i
7
3.7713 + 0.7619 i
0.973 - 1.46 i
8
3.7713 - 0.7619 i
0.973 + 1.46 i
9
-5.6022
0.162
10
26.55
516.
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Table 3. 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
1.321
0.0561
Singularities of quadratic [6, 5, 5] approximant
2
1.2519 + 0.4405 i
0.0309 - 0.106 i
3
1.2519 - 0.4405 i
0.0309 + 0.106 i
4
1.409
0.076 i
5
-2.7667 + 0.6178 i
0.242 + 0.175 i
6
-2.7667 - 0.6178 i
0.242 - 0.175 i
7
2.6114 + 1.4364 i
0.0984 + 0.261 i
8
2.6114 - 1.4364 i
0.0984 - 0.261 i
9
7.6035
0.291
10
-7.6092 + 1.0287 i
1.25 + 1.62 i
11
-7.6092 - 1.0287 i
1.25 - 1.62 i
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Table 4. 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
1.2654 + 0.4427 i
0.0399 - 0.151 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2654 - 0.4427 i
0.0399 + 0.151 i
3
1.4651
0.147
4
1.892 + 0.2121 i
0.907 - 0.136 i
5
1.892 - 0.2121 i
0.907 + 0.136 i
6
2.0311 + 1.0217 i
0.251 + 0.0339 i
7
2.0311 - 1.0217 i
0.251 - 0.0339 i
8
-2.7511 + 0.5455 i
0.196 + 0.348 i
9
-2.7511 - 0.5455 i
0.196 - 0.348 i
10
-5.4343
0.255
11
-21.1425
0.322 i
12
28.2362
0.398 i
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Table 5. 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
-0.6353 + 0.e-5 i
0.0000184 + 0.0000184 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.6353 - 0.e-5 i
0.0000184 - 0.0000184 i
3
1.2582 + 0.4266 i
0.0324 + 0.12 i
4
1.2582 - 0.4266 i
0.0324 - 0.12 i
5
1.5445
0.348
6
1.9205 + 0.6533 i
0.0169 + 0.204 i
7
1.9205 - 0.6533 i
0.0169 - 0.204 i
8
1.842 + 1.2411 i
0.091 + 0.0434 i
9
1.842 - 1.2411 i
0.091 - 0.0434 i
10
-2.6852 + 0.4583 i
0.109 - 0.255 i
11
-2.6852 - 0.4583 i
0.109 + 0.255 i
12
-7.4833
0.344
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Table 6. 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
1.2912 + 0.4285 i
0.158 + 0.264 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2912 - 0.4285 i
0.158 - 0.264 i
3
1.3971 + 0.5274 i
0.291 - 0.133 i
4
1.3971 - 0.5274 i
0.291 + 0.133 i
5
1.5743 + 0.5148 i
1.26 + 0.731 i
6
1.5743 - 0.5148 i
1.26 - 0.731 i
7
2.1493
0.461
8
-2.7593 + 0.6125 i
0.249 + 0.182 i
9
-2.7593 - 0.6125 i
0.249 - 0.182 i
10
-5.6658
0.869
11
6.8537
1.16 i
12
-7.4889
1.69 i
13
119.8042
7.79
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Table 7. 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
1.2677 + 0.4647 i
0.107 - 0.0996 i
Singularities of quadratic [7, 7, 6] approximant
2
1.2677 - 0.4647 i
0.107 + 0.0996 i
3
-1.4907
0.00162
4
-1.4911
0.00162 i
5
1.6188 + 0.2522 i
0.173 - 0.109 i
6
1.6188 - 0.2522 i
0.173 + 0.109 i
7
1.6509
0.146
8
1.9205 + 0.4932 i
1.62 + 0.452 i
9
1.9205 - 0.4932 i
1.62 - 0.452 i
10
-2.802 + 0.5953 i
0.524 + 0.125 i
11
-2.802 - 0.5953 i
0.524 - 0.125 i
12
-4.4502
0.202
13
13.4357
0.3 i
14
-14.7748
0.22 i
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Table 8. Singularities with their weights for the quadratic approximant [7, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-1.0118
0.000141
Singularities of quadratic [7, 7, 7] approximant
2
-1.0118
0.000141 i
3
1.2664 + 0.4654 i
0.105 - 0.0914 i
4
1.2664 - 0.4654 i
0.105 + 0.0914 i
5
1.5752
0.0928
6
1.6499 + 0.1845 i
0.0936 - 0.148 i
7
1.6499 - 0.1845 i
0.0936 + 0.148 i
8
1.9511 + 0.5759 i
1.17 - 0.33 i
9
1.9511 - 0.5759 i
1.17 + 0.33 i
10
-2.7963 + 0.6276 i
0.394 + 0.0494 i
11
-2.7963 - 0.6276 i
0.394 - 0.0494 i
12
-4.3442
0.24
13
-10.4768
0.204 i
14
20.0683
0.292 i
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Table 9. Singularities with their weights for the quadratic approximant [8, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2751 + 0.4627 i
0.129 - 0.142 i
Singularities of quadratic [8, 7, 7] approximant
2
1.2751 - 0.4627 i
0.129 + 0.142 i
3
1.5115 + 0.3778 i
0.275 + 0.0874 i
4
1.5115 - 0.3778 i
0.275 - 0.0874 i
5
1.6362 + 0.3795 i
0.0401 - 1.85 i
6
1.6362 - 0.3795 i
0.0401 + 1.85 i
7
-2.2175
0.38
8
-2.2243
0.375 i
9
2.2795
0.505
10
-2.7155 + 0.5146 i
0.0507 + 0.399 i
11
-2.7155 - 0.5146 i
0.0507 - 0.399 i
12
-5.2843
0.207
13
6.2602
0.763 i
14
-23.9836
0.418 i
15
30.2095
36.8
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Table 10. Singularities with their weights for the quadratic approximant [8, 8, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2738 + 0.4626 i
0.122 - 0.136 i
Singularities of quadratic [8, 8, 7] approximant
2
1.2738 - 0.4626 i
0.122 + 0.136 i
3
1.5319 + 0.3691 i
0.278 + 0.0535 i
4
1.5319 - 0.3691 i
0.278 - 0.0535 i
5
1.6743 + 0.3796 i
1.11 + 1.86 i
6
1.6743 - 0.3796 i
1.11 - 1.86 i
7
2.1618
0.463
8
-2.5774 + 0.5641 i
0.0239 + 0.126 i
9
-2.5774 - 0.5641 i
0.0239 - 0.126 i
10
-2.672 + 0.1525 i
0.146 + 0.0393 i
11
-2.672 - 0.1525 i
0.146 - 0.0393 i
12
-5.0017 + 2.6472 i
0.129 - 0.116 i
13
-5.0017 - 2.6472 i
0.129 + 0.116 i
14
8.9584
0.351 i
15
-7.355 + 6.5412 i
0.144 + 0.0837 i
16
-7.355 - 6.5412 i
0.144 - 0.0837 i
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Table 11. Singularities with their weights for the quadratic approximant [8, 8, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2839
0.0197
Singularities of quadratic [8, 8, 8] approximant
2
1.2917
0.0203 i
3
1.2661 + 0.4596 i
0.0741 - 0.103 i
4
1.2661 - 0.4596 i
0.0741 + 0.103 i
5
1.5331 + 0.492 i
0.999 - 0.994 i
6
1.5331 - 0.492 i
0.999 + 0.994 i
7
1.5372 + 0.5741 i
0.0776 - 0.532 i
8
1.5372 - 0.5741 i
0.0776 + 0.532 i
9
-2.3448
0.139
10
-2.3879
0.149 i
11
-2.7026 + 0.4807 i
0.163 - 0.471 i
12
-2.7026 - 0.4807 i
0.163 + 0.471 i
13
2.8001
1.06
14
-5.0425
0.157
15
5.3824
0.861 i
16
44.1509
2.13
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Table 12. Singularities with their weights for the quadratic approximant [9, 8, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2697 + 0.4603 i
0.0925 - 0.12 i
Singularities of quadratic [9, 8, 8] approximant
2
1.2697 - 0.4603 i
0.0925 + 0.12 i
3
1.4161
0.0548
4
1.4377
0.0612 i
5
1.5629 + 0.4854 i
0.809 - 0.243 i
6
1.5629 - 0.4854 i
0.809 + 0.243 i
7
1.5781 + 0.5546 i
0.0399 + 1.3 i
8
1.5781 - 0.5546 i
0.0399 - 1.3 i
9
-2.3563 + 0.0028 i
1.85 + 1.73 i
10
-2.3563 - 0.0028 i
1.85 - 1.73 i
11
2.7321
0.863
12
-2.6902 + 0.4992 i
0.041 - 0.361 i
13
-2.6902 - 0.4992 i
0.041 + 0.361 i
14
5.254
1.2 i
15
-5.2846
0.185
16
24.0443
38.7
17
-38.6172
0.455 i
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Table 13. Singularities with their weights for the quadratic approximant [9, 9, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2743 + 0.457 i
0.0844 - 0.171 i
Singularities of quadratic [9, 9, 8] approximant
2
1.2743 - 0.457 i
0.0844 + 0.171 i
3
1.5447 + 0.3851 i
0.234 + 0.441 i
4
1.5447 - 0.3851 i
0.234 - 0.441 i
5
1.5398 + 0.4427 i
0.341 + 0.126 i
6
1.5398 - 0.4427 i
0.341 - 0.126 i
7
-2.1416 + 0.0145 i
0.00771 + 0.0074 i
8
-2.1416 - 0.0145 i
0.00771 - 0.0074 i
9
2.5
0.804
10
-2.6205 + 0.5939 i
0.032 + 0.0833 i
11
-2.6205 - 0.5939 i
0.032 - 0.0833 i
12
0.1571 + 4.221 i
0.00741 - 0.0179 i
13
0.1571 - 4.221 i
0.00741 + 0.0179 i
14
0.119 + 4.4646 i
0.0178 + 0.00823 i
15
0.119 - 4.4646 i
0.0178 - 0.00823 i
16
-6.2438 + 3.1037 i
0.149 + 0.0326 i
17
-6.2438 - 3.1037 i
0.149 - 0.0326 i
18
16.818
0.21 i
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Table 14. Singularities with their weights for the quadratic approximant [9, 9, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.274 + 0.4574 i
0.0874 - 0.167 i
Singularities of quadratic [9, 9, 9] approximant
2
1.274 - 0.4574 i
0.0874 + 0.167 i
3
1.5516 + 0.3859 i
0.239 + 0.381 i
4
1.5516 - 0.3859 i
0.239 - 0.381 i
5
1.5496 + 0.4387 i
0.362 + 0.0881 i
6
1.5496 - 0.4387 i
0.362 - 0.0881 i
7
-1.6854 + 0.0006 i
0.000519 + 0.000519 i
8
-1.6854 - 0.0006 i
0.000519 - 0.000519 i
9
2.4435
0.775
10
-2.4887 + 0.5126 i
0.0321 - 0.0274 i
11
-2.4887 - 0.5126 i
0.0321 + 0.0274 i
12
-2.882
0.949
13
-3.847 + 0.8806 i
0.0569 - 0.0344 i
14
-3.847 - 0.8806 i
0.0569 + 0.0344 i
15
3.8916 + 3.3018 i
0.165 - 0.009 i
16
3.8916 - 3.3018 i
0.165 + 0.009 i
17
4.8285 + 5.3506 i
0.0315 - 0.175 i
18
4.8285 - 5.3506 i
0.0315 + 0.175 i
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Table 15. Singularities with their weights for the quadratic approximant [10, 9, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.0592
0
Singularities of quadratic [10, 9, 9] approximant
2
0.0592
0
3
-1.2517 + 0.e-4 i
0.000012 + 0.000012 i
4
-1.2517 - 0.e-4 i
0.000012 - 0.000012 i
5
1.272 + 0.4568 i
0.0696 - 0.149 i
6
1.272 - 0.4568 i
0.0696 + 0.149 i
7
1.5177 + 0.4105 i
0.362 + 0.33 i
8
1.5177 - 0.4105 i
0.362 - 0.33 i
9
1.5638 + 0.4581 i
0.701 + 0.284 i
10
1.5638 - 0.4581 i
0.701 - 0.284 i
11
-1.8818 + 0.0071 i
0.000548 + 0.000527 i
12
-1.8818 - 0.0071 i
0.000548 - 0.000527 i
13
2.3871
0.611
14
-2.5549 + 0.6592 i
0.0246 + 0.029 i
15
-2.5549 - 0.6592 i
0.0246 - 0.029 i
16
5.8426
1.55 i
17
-6.0841 + 4.0388 i
0.163 + 0.0222 i
18
-6.0841 - 4.0388 i
0.163 - 0.0222 i
19
20.2286
0.889
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Table 16. Singularities with their weights for the quadratic approximant [10, 10, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.0171
0
Singularities of quadratic [10, 10, 9] approximant
2
-0.0171
0
3
-1.0837 + 0.e-5 i
3.94e-6 + 3.94e-6 i
4
-1.0837 - 0.e-5 i
3.94e-6 - 3.94e-6 i
5
1.272 + 0.4567 i
0.0692 - 0.149 i
6
1.272 - 0.4567 i
0.0692 + 0.149 i
7
1.5172 + 0.4106 i
0.367 + 0.329 i
8
1.5172 - 0.4106 i
0.367 - 0.329 i
9
1.5643 + 0.4587 i
0.707 + 0.302 i
10
1.5643 - 0.4587 i
0.707 - 0.302 i
11
-1.9075 + 0.0075 i
0.000705 + 0.00068 i
12
-1.9075 - 0.0075 i
0.000705 - 0.00068 i
13
2.3831
0.608
14
-2.556 + 0.6562 i
0.0243 + 0.0302 i
15
-2.556 - 0.6562 i
0.0243 - 0.0302 i
16
5.7338
1.83 i
17
-6.0557 + 4.0316 i
0.158 + 0.0206 i
18
-6.0557 - 4.0316 i
0.158 - 0.0206 i
19
17.8491
0.725
20
6183.5659
19.9 i
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Table 17. Singularities with their weights for the quadratic approximant [10, 10, 10]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5338 + 0.3578 i
1.98e-9 + 1.1e-7 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.5338 - 0.3578 i
1.98e-9 - 1.1e-7 i
3
-0.5338 + 0.3578 i
1.1e-7 - 1.98e-9 i
4
-0.5338 - 0.3578 i
1.1e-7 + 1.98e-9 i
5
1.2723 + 0.4568 i
0.0715 - 0.152 i
6
1.2723 - 0.4568 i
0.0715 + 0.152 i
7
1.5215 + 0.4069 i
0.344 + 0.317 i
8
1.5215 - 0.4069 i
0.344 - 0.317 i
9
1.5647 + 0.4549 i
0.673 + 0.22 i
10
1.5647 - 0.4549 i
0.673 - 0.22 i
11
-2.026 + 0.0125 i
0.00184 + 0.00174 i
12
-2.026 - 0.0125 i
0.00184 - 0.00174 i
13
2.3733
0.616
14
-2.5847 + 0.6433 i
0.0333 + 0.0389 i
15
-2.5847 - 0.6433 i
0.0333 - 0.0389 i
16
5.9805
1.97 i
17
-8.6492 + 3.573 i
0.362 - 0.176 i
18
-8.6492 - 3.573 i
0.362 + 0.176 i
19
13.4463 + 6.1757 i
0.35 - 0.283 i
20
13.4463 - 6.1757 i
0.35 + 0.283 i
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Table 18. Singularities with their weights for the quadratic approximant [11, 10, 10]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5899 + 0.3026 i
7.6e-8 + 9.32e-8 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.5899 - 0.3026 i
7.6e-8 - 9.32e-8 i
3
-0.5899 + 0.3026 i
9.32e-8 - 7.6e-8 i
4
-0.5899 - 0.3026 i
9.32e-8 + 7.6e-8 i
5
1.2725 + 0.4569 i
0.0736 - 0.153 i
6
1.2725 - 0.4569 i
0.0736 + 0.153 i
7
1.5257 + 0.4058 i
0.335 + 0.303 i
8
1.5257 - 0.4058 i
0.335 - 0.303 i
9
1.5665 + 0.4529 i
0.67 + 0.166 i
10
1.5665 - 0.4529 i
0.67 - 0.166 i
11
-1.997 + 0.011 i
0.00144 + 0.00137 i
12
-1.997 - 0.011 i
0.00144 - 0.00137 i
13
2.3448
0.639
14
-2.574 + 0.6472 i
0.0295 + 0.0357 i
15
-2.574 - 0.6472 i
0.0295 - 0.0357 i
16
3.216
2.51 i
17
3.4048
8.64
18
5.6623
1.34 i
19
-6.7237 + 3.8339 i
0.226 + 0.0271 i
20
-6.7237 - 3.8339 i
0.226 - 0.0271 i
21
20.065
1.17
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Table 19. Singularities with their weights for the quadratic approximant [11, 11, 10]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.6833 + 0.4998 i
4.46e-7 + 1.01e-6 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.6833 - 0.4998 i
4.46e-7 - 1.01e-6 i
3
-0.6833 + 0.4998 i
1.01e-6 - 4.46e-7 i
4
-0.6833 - 0.4998 i
1.01e-6 + 4.46e-7 i
5
1.2724 + 0.4568 i
0.072 - 0.154 i
6
1.2724 - 0.4568 i
0.072 + 0.154 i
7
1.5227 + 0.4048 i
0.346 + 0.313 i
8
1.5227 - 0.4048 i
0.346 - 0.313 i
9
1.5659 + 0.4553 i
0.665 + 0.228 i
10
1.5659 - 0.4553 i
0.665 - 0.228 i
11
-2.0954 + 0.0185 i
0.0029 + 0.00264 i
12
-2.0954 - 0.0185 i
0.0029 - 0.00264 i
13
2.3473
0.607
14
-2.6148 + 0.6404 i
0.0501 + 0.0411 i
15
-2.6148 - 0.6404 i
0.0501 - 0.0411 i
16
4.8538
484. i
17
-5.7431
0.268
18
7.1857
0.276
19
-4.759 + 8.0354 i
0.00347 - 0.141 i
20
-4.759 - 8.0354 i
0.00347 + 0.141 i
21
-19.7852
0.715 i
22
19.9729
0.229 i
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Table 20. Singularities with their weights for the quadratic approximant [11, 11, 11]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.0479
0
Singularities of quadratic [11, 11, 11] approximant
2
-0.0479
0
3
-0.6738 + 0.4671 i
5.85e-8 - 1.09e-6 i
4
-0.6738 - 0.4671 i
5.85e-8 + 1.09e-6 i
5
-0.6738 + 0.4671 i
1.09e-6 + 5.85e-8 i
6
-0.6738 - 0.4671 i
1.09e-6 - 5.85e-8 i
7
1.2724 + 0.4568 i
0.072 - 0.153 i
8
1.2724 - 0.4568 i
0.072 + 0.153 i
9
1.5222 + 0.4068 i
0.341 + 0.316 i
10
1.5222 - 0.4068 i
0.341 - 0.316 i
11
1.5645 + 0.4542 i
0.668 + 0.205 i
12
1.5645 - 0.4542 i
0.668 - 0.205 i
13
-2.0583 + 0.0144 i
0.00237 + 0.00222 i
14
-2.0583 - 0.0144 i
0.00237 - 0.00222 i
15
2.3751
0.619
16
-2.594 + 0.6384 i
0.0371 + 0.0424 i
17
-2.594 - 0.6384 i
0.0371 - 0.0424 i
18
6.1642
1.72 i
19
-10.1228 + 1.9856 i
0.275 - 0.623 i
20
-10.1228 - 1.9856 i
0.275 + 0.623 i
21
12.0058 + 5.9689 i
0.351 - 0.336 i
22
12.0058 - 5.9689 i
0.351 + 0.336 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 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 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-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

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Designed by A. Sergeev.