Singularities of Møller-Plesset series: example "bh cc-pvqz re"

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 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
1.2278 + 0.0049 i
0.0215 - 0.0217 i
Singularities of quadratic [5, 5, 4] approximant
2
1.2278 - 0.0049 i
0.0215 + 0.0217 i
3
1.6425 + 0.3744 i
0.321 + 0.121 i
4
1.6425 - 0.3744 i
0.321 - 0.121 i
5
2.3726
1.51
6
-3.1568
0.0429
7
-3.3453
0.0445 i
8
-5.5642
181.
9
-9.8315
0.22 i
10
82.9303
0.695 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
1.2942 + 0.0094 i
0.0303 - 0.0307 i
Singularities of quadratic [5, 5, 5] approximant
2
1.2942 - 0.0094 i
0.0303 + 0.0307 i
3
1.6568 + 0.3847 i
0.293 + 0.182 i
4
1.6568 - 0.3847 i
0.293 - 0.182 i
5
2.3818
1.85
6
-3.5478
0.0492
7
-4.7808
0.0541 i
8
-4.9641 + 3.2827 i
0.0704 - 0.111 i
9
-4.9641 - 3.2827 i
0.0704 + 0.111 i
10
-22.0044
4.01
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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
1.3942 + 0.0369 i
0.034 - 0.0299 i
Singularities of quadratic [6, 5, 5] approximant
2
1.3942 - 0.0369 i
0.034 + 0.0299 i
3
1.7339 + 0.4595 i
0.0819 - 0.276 i
4
1.7339 - 0.4595 i
0.0819 + 0.276 i
5
2.081
1.33
6
-3.0611 + 0.0724 i
0.017 + 0.0172 i
7
-3.0611 - 0.0724 i
0.017 - 0.0172 i
8
-4.3966
0.0962
9
4.7811
30. i
10
7.2777
0.625
11
-11.1261
0.482 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
1.4412 + 0.0658 i
0.0497 - 0.0376 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4412 - 0.0658 i
0.0497 + 0.0376 i
3
1.6888 + 0.5347 i
0.0323 - 0.146 i
4
1.6888 - 0.5347 i
0.0323 + 0.146 i
5
2.0551 + 0.2311 i
0.675 + 0.0237 i
6
2.0551 - 0.2311 i
0.675 - 0.0237 i
7
3.0301
180.
8
-3.2458
0.201
9
-3.3189
0.197 i
10
-5.1778
0.956
11
-9.9524
0.29 i
12
156.374
1.06 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
1.5739 + 0.1599 i
1.42 - 3.9 i
Singularities of quadratic [6, 6, 6] approximant
2
1.5739 - 0.1599 i
1.42 + 3.9 i
3
1.577 + 0.436 i
0.159 - 0.0536 i
4
1.577 - 0.436 i
0.159 + 0.0536 i
5
1.6681 + 0.1793 i
0.0138 - 0.205 i
6
1.6681 - 0.1793 i
0.0138 + 0.205 i
7
1.9698
0.184
8
-3.1442
0.0333
9
-3.3514
0.0359 i
10
-5.2287
5.81
11
17.7283
0.469 i
12
-17.7717
0.176 i
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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
1.4637
0.0518
Singularities of quadratic [7, 6, 6] approximant
2
1.4787 + 0.3166 i
0.0286 + 0.00635 i
3
1.4787 - 0.3166 i
0.0286 - 0.00635 i
4
1.4699 + 0.4284 i
0.0145 - 0.0223 i
5
1.4699 - 0.4284 i
0.0145 + 0.0223 i
6
1.945 + 0.5207 i
0.0749 + 0.122 i
7
1.945 - 0.5207 i
0.0749 - 0.122 i
8
-3.1085
0.0136
9
-3.5649
0.0164 i
10
-9.1147
0.0587
11
-4.308 + 8.2387 i
0.000402 - 0.0676 i
12
-4.308 - 8.2387 i
0.000402 + 0.0676 i
13
-15.6356
0.0712 i
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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
1.3974 + 0.1935 i
0.0621 + 0.0671 i
Singularities of quadratic [7, 7, 6] approximant
2
1.3974 - 0.1935 i
0.0621 - 0.0671 i
3
1.4374 + 0.2004 i
0.0639 - 0.055 i
4
1.4374 - 0.2004 i
0.0639 + 0.055 i
5
1.675 + 0.4223 i
0.108 + 0.359 i
6
1.675 - 0.4223 i
0.108 - 0.359 i
7
2.0809
0.672
8
-3.2214
0.388
9
-3.2618
0.412 i
10
4.3581
11.7 i
11
-4.9857
0.519
12
5.3763
0.82
13
-10.6449
0.302 i
14
279.2109
1.55 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
0.8397 + 0.2386 i
1.42e-6 - 0.0000276 i
Singularities of quadratic [7, 7, 7] approximant
2
0.8397 - 0.2386 i
1.42e-6 + 0.0000276 i
3
0.8398 + 0.2386 i
0.0000276 + 1.41e-6 i
4
0.8398 - 0.2386 i
0.0000276 - 1.41e-6 i
5
1.3616
0.0102
6
1.6181 + 0.5922 i
0.0148 - 0.028 i
7
1.6181 - 0.5922 i
0.0148 + 0.028 i
8
1.732
6.15 i
9
2.894
3.64
10
-3.089
0.0119
11
-3.5458
0.0156 i
12
-6.2577
0.359
13
8.0821
0.974 i
14
98.6258
0.309
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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
1.4306 + 0.2991 i
0.0229 - 0.00474 i
Singularities of quadratic [8, 7, 7] approximant
2
1.4306 - 0.2991 i
0.0229 + 0.00474 i
3
1.4764
0.0506
4
1.4518 + 0.3849 i
0.00145 - 0.0252 i
5
1.4518 - 0.3849 i
0.00145 + 0.0252 i
6
1.9052 + 0.5188 i
0.107 + 0.104 i
7
1.9052 - 0.5188 i
0.107 - 0.104 i
8
-3.1309 + 0.1575 i
0.00659 + 0.00848 i
9
-3.1309 - 0.1575 i
0.00659 - 0.00848 i
10
-3.8582
0.016
11
-5.8226
0.195 i
12
0.2827 + 6.4164 i
0.0404 + 0.00452 i
13
0.2827 - 6.4164 i
0.0404 - 0.00452 i
14
-0.1129 + 7.4633 i
0.0107 - 0.0429 i
15
-0.1129 - 7.4633 i
0.0107 + 0.0429 i
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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
1.4359 + 0.2825 i
0.0293 - 0.012 i
Singularities of quadratic [8, 8, 7] approximant
2
1.4359 - 0.2825 i
0.0293 + 0.012 i
3
1.5014
0.0678
4
1.4668 + 0.3702 i
0.00484 + 0.0344 i
5
1.4668 - 0.3702 i
0.00484 - 0.0344 i
6
1.8931 + 0.4808 i
0.132 + 0.105 i
7
1.8931 - 0.4808 i
0.132 - 0.105 i
8
-3.1495 + 0.174 i
0.00725 + 0.00775 i
9
-3.1495 - 0.174 i
0.00725 - 0.00775 i
10
0.859 + 3.8522 i
0.00359 - 0.0151 i
11
0.859 - 3.8522 i
0.00359 + 0.0151 i
12
0.9291 + 3.9272 i
0.0155 + 0.00385 i
13
0.9291 - 3.9272 i
0.0155 - 0.00385 i
14
-4.1046
0.0248
15
-7.0877
25.1 i
16
691.3508
3.26 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
0.7939
7.1e-6
Singularities of quadratic [8, 8, 8] approximant
2
0.7939
7.1e-6 i
3
1.4109
0.0105
4
1.4017 + 0.2953 i
0.00899 + 0.00251 i
5
1.4017 - 0.2953 i
0.00899 - 0.00251 i
6
1.4883 + 0.4145 i
0.0144 - 0.00993 i
7
1.4883 - 0.4145 i
0.0144 + 0.00993 i
8
1.7637
0.27 i
9
2.6637 + 0.2532 i
0.236 + 0.782 i
10
2.6637 - 0.2532 i
0.236 - 0.782 i
11
-2.9357 + 0.2363 i
0.000891 + 0.00189 i
12
-2.9357 - 0.2363 i
0.000891 - 0.00189 i
13
-3.1331
0.00181
14
4.4254
0.838
15
-4.9081
0.0404 i
16
-16.0574
0.244
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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
0.6077 + 0.2509 i
1.32e-7 - 3.35e-7 i
Singularities of quadratic [9, 8, 8] approximant
2
0.6077 - 0.2509 i
1.32e-7 + 3.35e-7 i
3
0.6077 + 0.2509 i
3.35e-7 + 1.32e-7 i
4
0.6077 - 0.2509 i
3.35e-7 - 1.32e-7 i
5
1.422 + 0.4494 i
0.00211 - 0.00638 i
6
1.422 - 0.4494 i
0.00211 + 0.00638 i
7
1.4948 + 0.2652 i
0.0155 - 0.0111 i
8
1.4948 - 0.2652 i
0.0155 + 0.0111 i
9
1.6289
11.2
10
-1.9821
0.0000245
11
-1.9824
0.0000245 i
12
1.953 + 0.7811 i
0.0155 - 0.0351 i
13
1.953 - 0.7811 i
0.0155 + 0.0351 i
14
-2.9263
0.00226
15
-4.2544
0.0154 i
16
-8.8792
0.189
17
-17.3778
0.624 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
-0.5844
1.13e-7
Singularities of quadratic [9, 9, 8] approximant
2
-0.5844
1.13e-7 i
3
1.4358 + 0.2674 i
0.0361 - 0.00821 i
4
1.4358 - 0.2674 i
0.0361 + 0.00821 i
5
1.5332
0.0655
6
1.5115 + 0.3625 i
0.00961 - 0.0584 i
7
1.5115 - 0.3625 i
0.00961 + 0.0584 i
8
1.8894 + 0.2997 i
0.212 + 0.279 i
9
1.8894 - 0.2997 i
0.212 - 0.279 i
10
-3.0664 + 0.2561 i
0.00304 + 0.00304 i
11
-3.0664 - 0.2561 i
0.00304 - 0.00304 i
12
-3.7495
0.008
13
2.1092 + 3.5801 i
0.0484 + 0.00662 i
14
2.1092 - 3.5801 i
0.0484 - 0.00662 i
15
2.3115 + 3.5652 i
0.0104 - 0.0546 i
16
2.3115 - 3.5652 i
0.0104 + 0.0546 i
17
-6.6535
2.31 i
18
264.9022
1.63 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
-0.6063 + 0.4951 i
5.79e-8 + 1.95e-7 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.6063 - 0.4951 i
5.79e-8 - 1.95e-7 i
3
-0.6063 + 0.4951 i
1.95e-7 - 5.79e-8 i
4
-0.6063 - 0.4951 i
1.95e-7 + 5.79e-8 i
5
1.4121 + 0.2553 i
0.0125 - 0.00184 i
6
1.4121 - 0.2553 i
0.0125 + 0.00184 i
7
1.4641 + 0.0377 i
0.0114 - 0.00522 i
8
1.4641 - 0.0377 i
0.0114 + 0.00522 i
9
1.5158 + 0.4397 i
0.0206 - 0.01 i
10
1.5158 - 0.4397 i
0.0206 + 0.01 i
11
2.4878 + 0.7879 i
0.123 + 0.102 i
12
2.4878 - 0.7879 i
0.123 - 0.102 i
13
-3.0255
0.00755
14
-3.2966
0.0331 i
15
3.6582
7.02
16
-3.6584
0.0168
17
-4.7603
0.0371 i
18
-14.4042
0.185
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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
-0.7588 + 0.5989 i
3.22e-7 + 1.04e-6 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.7588 - 0.5989 i
3.22e-7 - 1.04e-6 i
3
-0.7588 + 0.5989 i
1.04e-6 - 3.22e-7 i
4
-0.7588 - 0.5989 i
1.04e-6 + 3.22e-7 i
5
1.4168 + 0.2489 i
0.0129 - 0.00298 i
6
1.4168 - 0.2489 i
0.0129 + 0.00298 i
7
1.4461 + 0.0471 i
0.0119 - 0.00441 i
8
1.4461 - 0.0471 i
0.0119 + 0.00441 i
9
1.508 + 0.4448 i
0.0185 - 0.00986 i
10
1.508 - 0.4448 i
0.0185 + 0.00986 i
11
-2.3205 + 0.0033 i
0.000212 + 0.000214 i
12
-2.3205 - 0.0033 i
0.000212 - 0.000214 i
13
2.2934 + 0.8144 i
0.102 + 0.0125 i
14
2.2934 - 0.8144 i
0.102 - 0.0125 i
15
2.8861
0.858
16
-2.9496
0.00256
17
-4.2027
0.0151 i
18
-9.5849
0.162
19
-26.3221
0.5 i
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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
0.0787
0
Singularities of quadratic [10, 10, 9] approximant
2
0.0787
0
3
-0.7495 + 0.5576 i
5.67e-8 + 1.54e-7 i
4
-0.7495 - 0.5576 i
5.67e-8 - 1.54e-7 i
5
-0.7495 + 0.5576 i
1.54e-7 - 5.67e-8 i
6
-0.7495 - 0.5576 i
1.54e-7 + 5.67e-8 i
7
1.3997 + 0.1881 i
0.00665 + 0.00655 i
8
1.3997 - 0.1881 i
0.00665 - 0.00655 i
9
1.4551 + 0.4064 i
0.00497 + 0.00778 i
10
1.4551 - 0.4064 i
0.00497 - 0.00778 i
11
1.8146 + 0.6467 i
0.00775 - 0.0148 i
12
1.8146 - 0.6467 i
0.00775 + 0.0148 i
13
1.8835 + 0.8185 i
0.00572 + 0.0138 i
14
1.8835 - 0.8185 i
0.00572 - 0.0138 i
15
2.3469
1.12
16
-2.902
0.00194
17
-4.7137
0.0244 i
18
-10.696 + 15.0916 i
0.181 + 0.0982 i
19
-10.696 - 15.0916 i
0.181 - 0.0982 i
20
27.2815
2.49 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
-0.5009 + 0.951 i
5.52e-7 - 1.64e-7 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.5009 - 0.951 i
5.52e-7 + 1.64e-7 i
3
-0.5009 + 0.951 i
1.64e-7 + 5.52e-7 i
4
-0.5009 - 0.951 i
1.64e-7 - 5.52e-7 i
5
1.3792
0.00165
6
-1.3016 + 0.4897 i
1.44e-7 + 1.62e-6 i
7
-1.3016 - 0.4897 i
1.44e-7 - 1.62e-6 i
8
-1.3017 + 0.4896 i
1.62e-6 - 1.44e-7 i
9
-1.3017 - 0.4896 i
1.62e-6 + 1.44e-7 i
10
1.3948
0.00187 i
11
1.3907 + 0.2511 i
0.00602 - 0.0021 i
12
1.3907 - 0.2511 i
0.00602 + 0.0021 i
13
1.5027 + 0.4542 i
0.0132 - 0.00516 i
14
1.5027 - 0.4542 i
0.0132 + 0.00516 i
15
2.5692 + 0.8255 i
0.0583 + 0.143 i
16
2.5692 - 0.8255 i
0.0583 - 0.143 i
17
-2.859
0.0013
18
3.9879
1.39
19
-4.833
0.0322 i
20
-17.3236
0.31
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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
-0.4858 + 0.9495 i
5.e-7 - 1.78e-7 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.4858 - 0.9495 i
5.e-7 + 1.78e-7 i
3
-0.4858 + 0.9495 i
1.78e-7 + 5.e-7 i
4
-0.4858 - 0.9495 i
1.78e-7 - 5.e-7 i
5
-1.2534 + 0.503 i
3.04e-7 + 1.3e-6 i
6
-1.2534 - 0.503 i
3.04e-7 - 1.3e-6 i
7
-1.2534 + 0.5029 i
1.3e-6 - 3.04e-7 i
8
-1.2534 - 0.5029 i
1.3e-6 + 3.04e-7 i
9
1.3756
0.0016
10
1.3918
0.00183 i
11
1.3901 + 0.2508 i
0.00587 - 0.00212 i
12
1.3901 - 0.2508 i
0.00587 + 0.00212 i
13
1.5021 + 0.4546 i
0.0131 - 0.00508 i
14
1.5021 - 0.4546 i
0.0131 + 0.00508 i
15
2.5602 + 0.8258 i
0.0606 + 0.14 i
16
2.5602 - 0.8258 i
0.0606 - 0.14 i
17
-2.8653
0.00137
18
3.9318
1.61
19
-4.794
0.0303 i
20
-16.517
0.3
21
-274.1095
0.748 i
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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
-0.6314 + 0.935 i
1.19e-6 + 6.86e-7 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.6314 - 0.935 i
1.19e-6 - 6.86e-7 i
3
-0.6314 + 0.935 i
6.86e-7 - 1.19e-6 i
4
-0.6314 - 0.935 i
6.86e-7 + 1.19e-6 i
5
-1.2682 + 0.e-4 i
2.06e-6 + 2.06e-6 i
6
-1.2682 - 0.e-4 i
2.06e-6 - 2.06e-6 i
7
1.4103 + 0.191 i
0.00858 + 0.00807 i
8
1.4103 - 0.191 i
0.00858 - 0.00807 i
9
1.4442 + 0.39 i
0.00719 + 0.00558 i
10
1.4442 - 0.39 i
0.00719 - 0.00558 i
11
1.7205 + 0.7497 i
0.00275 + 0.00658 i
12
1.7205 - 0.7497 i
0.00275 - 0.00658 i
13
1.8596 + 0.8317 i
0.00902 + 0.00034 i
14
1.8596 - 0.8317 i
0.00902 - 0.00034 i
15
2.6434 + 1.2728 i
0.0554 + 0.0092 i
16
2.6434 - 1.2728 i
0.0554 - 0.0092 i
17
-2.9676 + 0.3314 i
0.00144 + 0.00151 i
18
-2.9676 - 0.3314 i
0.00144 - 0.00151 i
19
-3.5254
0.00332
20
4.3865
0.546
21
-7.3805
3.29 i
22
74.6047
0.624 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
-0.6166 + 0.9346 i
1.4e-6 + 2.87e-7 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.6166 - 0.9346 i
1.4e-6 - 2.87e-7 i
3
-0.6166 + 0.9347 i
2.87e-7 - 1.4e-6 i
4
-0.6166 - 0.9347 i
2.87e-7 + 1.4e-6 i
5
-1.31 + 0.e-5 i
0.0000102 + 0.0000102 i
6
-1.31 - 0.e-5 i
0.0000102 - 0.0000102 i
7
1.3974 + 0.1913 i
0.0053 + 0.00558 i
8
1.3974 - 0.1913 i
0.0053 - 0.00558 i
9
1.4228 + 0.4119 i
0.00279 + 0.00348 i
10
1.4228 - 0.4119 i
0.00279 - 0.00348 i
11
1.4624 + 0.7206 i
0.00142 - 0.000291 i
12
1.4624 - 0.7206 i
0.00142 + 0.000291 i
13
1.4917 + 0.6984 i
0.000469 + 0.00153 i
14
1.4917 - 0.6984 i
0.000469 - 0.00153 i
15
-2.7057 + 0.2703 i
0.00017 + 0.000486 i
16
-2.7057 - 0.2703 i
0.00017 - 0.000486 i
17
-2.726
0.000369
18
2.5923 + 0.9947 i
0.0472 - 0.0833 i
19
2.5923 - 0.9947 i
0.0472 + 0.0833 i
20
4.027
0.918
21
-5.8017
0.193 i
22
-40.1564
4.08
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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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