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

Molecule X 1^Sigma+ State of BH. Basis 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 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
1.6234 + 0.4544 i
0.223 + 0.141 i
Singularities of quadratic [5, 5, 4] approximant
2
1.6234 - 0.4544 i
0.223 - 0.141 i
3
1.8381 + 0.141 i
0.495 - 0.348 i
4
1.8381 - 0.141 i
0.495 + 0.348 i
5
3.7863 + 1.6624 i
0.129 - 0.252 i
6
3.7863 - 1.6624 i
0.129 + 0.252 i
7
-4.8702
0.0119
8
-7.0615
0.0123 i
9
17.2497
0.0617
10
1175.9734
0.264 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
1.4305 + 0.0245 i
0.0328 - 0.0294 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4305 - 0.0245 i
0.0328 + 0.0294 i
3
1.616 + 0.3748 i
0.106 - 2.35 i
4
1.616 - 0.3748 i
0.106 + 2.35 i
5
2.7268 + 0.7745 i
0.0853 + 0.451 i
6
2.7268 - 0.7745 i
0.0853 - 0.451 i
7
4.2417
5.05
8
-4.4914 + 0.9966 i
0.00166 + 0.00286 i
9
-4.4914 - 0.9966 i
0.00166 - 0.00286 i
10
-6.7472
0.00325
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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
1.5419 + 0.0515 i
0.115 - 0.103 i
Singularities of quadratic [6, 5, 5] approximant
2
1.5419 - 0.0515 i
0.115 + 0.103 i
3
1.5966 + 0.3958 i
0.324 - 0.571 i
4
1.5966 - 0.3958 i
0.324 + 0.571 i
5
2.8341 + 0.9717 i
0.28 - 0.325 i
6
2.8341 - 0.9717 i
0.28 + 0.325 i
7
-4.3052 + 0.9079 i
0.000936 + 0.00239 i
8
-4.3052 - 0.9079 i
0.000936 - 0.00239 i
9
4.4592
72.9
10
-5.4452
0.00209
11
-36.0886
0.0134 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
1.53 + 0.0536 i
0.0908 - 0.0723 i
Singularities of quadratic [6, 6, 5] approximant
2
1.53 - 0.0536 i
0.0908 + 0.0723 i
3
1.5973 + 0.3867 i
0.108 - 0.701 i
4
1.5973 - 0.3867 i
0.108 + 0.701 i
5
-2.7265
0.00031
6
-2.754
0.000307 i
7
2.9683 + 1.0723 i
0.339 - 0.13 i
8
2.9683 - 1.0723 i
0.339 + 0.13 i
9
-4.1884
0.0019
10
5.6462
1.06
11
-14.2045
0.00809 i
12
1669.5855
0.185 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
1.2109 + 0.1945 i
0.000195 - 0.00316 i
Singularities of quadratic [6, 6, 6] approximant
2
1.2109 - 0.1945 i
0.000195 + 0.00316 i
3
1.2179 + 0.1875 i
0.00316 + 0.0000928 i
4
1.2179 - 0.1875 i
0.00316 - 0.0000928 i
5
1.6223 + 0.3194 i
0.349 - 0.779 i
6
1.6223 - 0.3194 i
0.349 + 0.779 i
7
2.9723 + 0.8504 i
0.357 - 0.401 i
8
2.9723 - 0.8504 i
0.357 + 0.401 i
9
-4.9102 + 0.8494 i
0.00369 + 0.00594 i
10
-4.9102 - 0.8494 i
0.00369 - 0.00594 i
11
5.1338
8.26
12
-8.9892
0.0071
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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
1.4985 + 0.5466 i
0.0325 + 0.0136 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4985 - 0.5466 i
0.0325 - 0.0136 i
3
1.5979 + 0.5759 i
0.0244 - 0.0338 i
4
1.5979 - 0.5759 i
0.0244 + 0.0338 i
5
1.7554
0.162
6
2.234 + 0.5029 i
0.00208 - 0.171 i
7
2.234 - 0.5029 i
0.00208 + 0.171 i
8
-4.9089
0.0139
9
-6.6544
0.0157 i
10
7.0741
0.386 i
11
7.375 + 4.5985 i
0.219 + 0.42 i
12
7.375 - 4.5985 i
0.219 - 0.42 i
13
40.5827
0.157
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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
1.4761 + 0.5414 i
0.027 + 0.00921 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4761 - 0.5414 i
0.027 - 0.00921 i
3
1.5616 + 0.546 i
0.0161 - 0.0322 i
4
1.5616 - 0.546 i
0.0161 + 0.0322 i
5
1.7636
0.126
6
2.1261
0.141 i
7
2.5967
0.482
8
-4.6788
0.0065
9
7.2833
3.7 i
10
-6.9116 + 2.4758 i
0.00217 - 0.00905 i
11
-6.9116 - 2.4758 i
0.00217 + 0.00905 i
12
-9.966
0.0308 i
13
-10.4407 + 22.5971 i
0.0413 - 0.0044 i
14
-10.4407 - 22.5971 i
0.0413 + 0.0044 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
-0.1132
0
Singularities of quadratic [7, 7, 7] approximant
2
-0.1132
0
3
1.4714 + 0.5457 i
0.0196 + 0.0128 i
4
1.4714 - 0.5457 i
0.0196 - 0.0128 i
5
1.5625 + 0.5325 i
0.0201 - 0.0268 i
6
1.5625 - 0.5325 i
0.0201 + 0.0268 i
7
1.6986
0.0882
8
1.8673
0.145 i
9
3.0562
2.96e3
10
-4.8251
0.0118
11
-8.183
0.00631 i
12
-2.7187 + 9.575 i
0.0132 + 0.00363 i
13
-2.7187 - 9.575 i
0.0132 - 0.00363 i
14
19.7303
0.0392 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
-0.1821
2.17e-10
Singularities of quadratic [8, 7, 7] approximant
2
-0.1821
2.17e-10 i
3
1.472 + 0.5456 i
0.02 + 0.0128 i
4
1.472 - 0.5456 i
0.02 - 0.0128 i
5
1.5631 + 0.5338 i
0.0202 - 0.0272 i
6
1.5631 - 0.5338 i
0.0202 + 0.0272 i
7
1.702
0.0914
8
1.8803
0.149 i
9
3.0335
1.1e3
10
-4.8296
0.012
11
-8.0357
0.00665 i
12
-2.5226 + 9.7522 i
0.0139 + 0.00336 i
13
-2.5226 - 9.7522 i
0.0139 - 0.00336 i
14
21.9659
0.0283 i
15
79.4775
0.0124
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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
-0.6283
5.86e-8
Singularities of quadratic [8, 8, 7] approximant
2
-0.6283
5.86e-8 i
3
0.7256 + 0.e-5 i
1.31e-6 - 1.31e-6 i
4
0.7256 - 0.e-5 i
1.31e-6 + 1.31e-6 i
5
1.4577 + 0.52 i
0.0103 - 0.00188 i
6
1.4577 - 0.52 i
0.0103 + 0.00188 i
7
1.6555 + 0.5143 i
0.0194 - 0.0216 i
8
1.6555 - 0.5143 i
0.0194 + 0.0216 i
9
1.9616 + 1.5762 i
0.00427 + 0.00321 i
10
1.9616 - 1.5762 i
0.00427 - 0.00321 i
11
2.1995 + 1.7106 i
0.00583 - 0.0043 i
12
2.1995 - 1.7106 i
0.00583 + 0.0043 i
13
-5.0469
0.0467
14
-6.8478
0.00807 i
15
15.8457 + 14.9186 i
0.014 - 0.0165 i
16
15.8457 - 14.9186 i
0.014 + 0.0165 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
-0.8252
2.06e-7
Singularities of quadratic [8, 8, 8] approximant
2
-0.8252
2.06e-7 i
3
1.0027 + 0.e-4 i
0.0000255 - 0.0000255 i
4
1.0027 - 0.e-4 i
0.0000255 + 0.0000255 i
5
1.4474 + 0.5255 i
0.00829 + 0.000707 i
6
1.4474 - 0.5255 i
0.00829 - 0.000707 i
7
1.6256 + 0.4813 i
0.0145 - 0.0269 i
8
1.6256 - 0.4813 i
0.0145 + 0.0269 i
9
0.8794 + 2.1737 i
0.000244 + 0.000271 i
10
0.8794 - 2.1737 i
0.000244 - 0.000271 i
11
0.9036 + 2.1709 i
0.000273 - 0.000253 i
12
0.9036 - 2.1709 i
0.000273 + 0.000253 i
13
-5.5101
0.058
14
5.8661
3.17
15
-5.8806
0.0115 i
16
-28.271
7.77
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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
-0.8567
1.73e-7
Singularities of quadratic [9, 8, 8] approximant
2
-0.8567
1.73e-7 i
3
0.9047 + 0.e-4 i
7.25e-6 - 7.24e-6 i
4
0.9047 - 0.e-4 i
7.25e-6 + 7.24e-6 i
5
1.4454 + 0.5272 i
0.00788 + 0.000484 i
6
1.4454 - 0.5272 i
0.00788 - 0.000484 i
7
1.6266 + 0.492 i
0.015 - 0.0237 i
8
1.6266 - 0.492 i
0.015 + 0.0237 i
9
0.7763 + 2.4785 i
0.0000226 - 0.000339 i
10
0.7763 - 2.4785 i
0.0000226 + 0.000339 i
11
0.8163 + 2.5064 i
0.000355 + 0.0000273 i
12
0.8163 - 2.5064 i
0.000355 - 0.0000273 i
13
-5.7186 + 0.8406 i
0.00194 - 0.00452 i
14
-5.7186 - 0.8406 i
0.00194 + 0.00452 i
15
7.0081
0.282
16
-10.6335 + 8.1064 i
0.0061 - 0.00314 i
17
-10.6335 - 8.1064 i
0.0061 + 0.00314 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
-0.8707 + 0.2767 i
1.77e-8 - 1.33e-7 i
Singularities of quadratic [9, 9, 8] approximant
2
-0.8707 - 0.2767 i
1.77e-8 + 1.33e-7 i
3
-0.8707 + 0.2767 i
1.33e-7 + 1.77e-8 i
4
-0.8707 - 0.2767 i
1.33e-7 - 1.77e-8 i
5
1.3484 + 0.0011 i
0.0456 - 0.0572 i
6
1.3484 - 0.0011 i
0.0456 + 0.0572 i
7
1.4643 + 0.4786 i
0.0106 - 0.0115 i
8
1.4643 - 0.4786 i
0.0106 + 0.0115 i
9
1.6546 + 0.4072 i
0.00704 + 0.0744 i
10
1.6546 - 0.4072 i
0.00704 - 0.0744 i
11
1.6541 + 1.4634 i
0.00222 - 0.00102 i
12
1.6541 - 1.4634 i
0.00222 + 0.00102 i
13
1.7757 + 1.49 i
0.000993 + 0.0028 i
14
1.7757 - 1.49 i
0.000993 - 0.0028 i
15
-5.1436
0.567
16
-7.3579
0.00494 i
17
12.8052 + 9.3949 i
0.00776 - 0.019 i
18
12.8052 - 9.3949 i
0.00776 + 0.019 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
-0.895 + 0.2808 i
2.04e-8 - 1.51e-7 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.895 - 0.2808 i
2.04e-8 + 1.51e-7 i
3
-0.895 + 0.2808 i
1.51e-7 + 2.04e-8 i
4
-0.895 - 0.2808 i
1.51e-7 - 2.04e-8 i
5
1.42
0.0222
6
1.4439
0.0308 i
7
1.4623 + 0.4635 i
0.00605 - 0.0144 i
8
1.4623 - 0.4635 i
0.00605 + 0.0144 i
9
1.6607 + 0.3671 i
0.0483 + 0.113 i
10
1.6607 - 0.3671 i
0.0483 - 0.113 i
11
1.6863 + 1.3688 i
0.00209 - 0.0021 i
12
1.6863 - 1.3688 i
0.00209 + 0.0021 i
13
1.838 + 1.3459 i
0.0027 + 0.00286 i
14
1.838 - 1.3459 i
0.0027 - 0.00286 i
15
-5.1315
0.486
16
-7.5034
0.00474 i
17
9.9501 + 10.3789 i
0.00584 - 0.02 i
18
9.9501 - 10.3789 i
0.00584 + 0.02 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
-0.0692
0
Singularities of quadratic [10, 9, 9] approximant
2
-0.0692
0
3
-0.9075 + 0.2896 i
1.8e-8 + 1.42e-8 i
4
-0.9075 - 0.2896 i
1.8e-8 - 1.42e-8 i
5
-0.9075 + 0.2896 i
1.42e-8 - 1.8e-8 i
6
-0.9075 - 0.2896 i
1.42e-8 + 1.8e-8 i
7
1.2863
0.000532
8
1.3038
0.000613 i
9
1.4239 + 0.4739 i
0.00106 - 0.00381 i
10
1.4239 - 0.4739 i
0.00106 + 0.00381 i
11
1.8355 + 0.464 i
0.0354 + 0.0174 i
12
1.8355 - 0.464 i
0.0354 - 0.0174 i
13
1.5843 + 1.4543 i
0.000816 + 0.0000642 i
14
1.5843 - 1.4543 i
0.000816 - 0.0000642 i
15
1.7721 + 1.3879 i
0.000043 + 0.00128 i
16
1.7721 - 1.3879 i
0.000043 - 0.00128 i
17
-4.274
0.000532
18
-4.9016
0.00156 i
19
-33.0435
0.0185
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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
-0.7229 + 0.4466 i
1.65e-9 - 4.28e-9 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.7229 - 0.4466 i
1.65e-9 + 4.28e-9 i
3
-0.7229 + 0.4466 i
4.28e-9 + 1.65e-9 i
4
-0.7229 - 0.4466 i
4.28e-9 - 1.65e-9 i
5
-0.8723
4.31e-9
6
-0.8724
4.31e-9 i
7
1.3163 + 0.3174 i
0.000177 + 0.000347 i
8
1.3163 - 0.3174 i
0.000177 - 0.000347 i
9
1.3948 + 0.2963 i
0.000733 - 0.0004 i
10
1.3948 - 0.2963 i
0.000733 + 0.0004 i
11
1.3928 + 0.5894 i
0.000261 + 0.000652 i
12
1.3928 - 0.5894 i
0.000261 - 0.000652 i
13
1.7269 + 1.5067 i
0.000417 + 0.000248 i
14
1.7269 - 1.5067 i
0.000417 - 0.000248 i
15
1.5259 + 1.7207 i
0.000261 - 0.000181 i
16
1.5259 - 1.7207 i
0.000261 + 0.000181 i
17
3.0666 + 1.0647 i
0.0268 - 0.00233 i
18
3.0666 - 1.0647 i
0.0268 + 0.00233 i
19
-6.2357
0.00291
20
-14.48
0.00279 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
0.8975 + 0.2013 i
3.e-7 - 3.7e-7 i
Singularities of quadratic [10, 10, 10] approximant
2
0.8975 - 0.2013 i
3.e-7 + 3.7e-7 i
3
0.8976 + 0.2012 i
3.7e-7 + 2.99e-7 i
4
0.8976 - 0.2012 i
3.7e-7 - 2.99e-7 i
5
-0.9622
6.16e-9
6
-0.9622
6.16e-9 i
7
-0.7904 + 0.562 i
2.1e-9 + 7.52e-9 i
8
-0.7904 - 0.562 i
2.1e-9 - 7.52e-9 i
9
-0.7904 + 0.562 i
7.52e-9 - 2.1e-9 i
10
-0.7904 - 0.562 i
7.52e-9 + 2.1e-9 i
11
1.3695 + 0.4927 i
0.000324 - 0.000736 i
12
1.3695 - 0.4927 i
0.000324 + 0.000736 i
13
1.4326 + 1.6122 i
0.00003 + 0.000187 i
14
1.4326 - 1.6122 i
0.00003 - 0.000187 i
15
2.1382 + 0.7117 i
0.00744 - 0.00447 i
16
2.1382 - 0.7117 i
0.00744 + 0.00447 i
17
1.6752 + 1.5278 i
0.000309 - 0.000132 i
18
1.6752 - 1.5278 i
0.000309 + 0.000132 i
19
-6.8311
0.00196
20
-22.1765
0.00442 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
-0.2273 + 0.9334 i
6.96e-9 - 1.22e-8 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.2273 - 0.9334 i
6.96e-9 + 1.22e-8 i
3
-0.2273 + 0.9334 i
1.22e-8 + 6.96e-9 i
4
-0.2273 - 0.9334 i
1.22e-8 - 6.96e-9 i
5
-1.3405
1.41e-8
6
-1.3467
1.38e-8 i
7
1.3875 + 0.3441 i
0.0000585 - 0.0016 i
8
1.3875 - 0.3441 i
0.0000585 + 0.0016 i
9
1.5063 + 0.1808 i
0.00183 + 0.00648 i
10
1.5063 - 0.1808 i
0.00183 - 0.00648 i
11
1.4924 + 0.6218 i
0.00196 - 0.00077 i
12
1.4924 - 0.6218 i
0.00196 + 0.00077 i
13
-1.6031 + 0.2578 i
2.58e-8 + 4.33e-8 i
14
-1.6031 - 0.2578 i
2.58e-8 - 4.33e-8 i
15
-1.6146 + 0.2376 i
4.38e-8 - 2.01e-8 i
16
-1.6146 - 0.2376 i
4.38e-8 + 2.01e-8 i
17
1.6638 + 1.3225 i
0.000116 + 0.000765 i
18
1.6638 - 1.3225 i
0.000116 - 0.000765 i
19
1.9705 + 1.4982 i
0.00136 + 0.00101 i
20
1.9705 - 1.4982 i
0.00136 - 0.00101 i
21
-19.3535
0.00522
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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
-0.1598 + 0.9542 i
1.7e-8 + 2.25e-9 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.1598 - 0.9542 i
1.7e-8 - 2.25e-9 i
3
-0.1598 + 0.9542 i
2.25e-9 - 1.7e-8 i
4
-0.1598 - 0.9542 i
2.25e-9 + 1.7e-8 i
5
-1.1834
1.43e-8
6
-1.1838
1.43e-8 i
7
1.4195 + 0.3537 i
0.000502 - 0.00316 i
8
1.4195 - 0.3537 i
0.000502 + 0.00316 i
9
1.4927 + 0.1125 i
0.00576 + 0.00263 i
10
1.4927 - 0.1125 i
0.00576 - 0.00263 i
11
-1.4004 + 0.6483 i
6.2e-8 - 5.87e-8 i
12
-1.4004 - 0.6483 i
6.2e-8 + 5.87e-8 i
13
-1.4021 + 0.6504 i
5.91e-8 + 6.25e-8 i
14
-1.4021 - 0.6504 i
5.91e-8 - 6.25e-8 i
15
1.5367 + 0.6007 i
0.00442 + 0.000231 i
16
1.5367 - 0.6007 i
0.00442 - 0.000231 i
17
1.6294 + 1.3376 i
0.000147 - 0.000708 i
18
1.6294 - 1.3376 i
0.000147 + 0.000708 i
19
1.9335 + 1.4026 i
0.00133 + 0.00108 i
20
1.9335 - 1.4026 i
0.00133 - 0.00108 i
21
-11.5843
0.00218
22
-157.4613
0.0469 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
-0.1754 + 0.9723 i
2.55e-8 + 8.64e-9 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.1754 - 0.9723 i
2.55e-8 - 8.64e-9 i
3
-0.1754 + 0.9723 i
8.64e-9 - 2.55e-8 i
4
-0.1754 - 0.9723 i
8.64e-9 + 2.55e-8 i
5
-1.2045
1.93e-8
6
-1.2051
1.93e-8 i
7
1.49 + 0.0597 i
0.0124 - 0.00164 i
8
1.49 - 0.0597 i
0.0124 + 0.00164 i
9
1.4542 + 0.3941 i
0.0092 - 0.00569 i
10
1.4542 - 0.3941 i
0.0092 + 0.00569 i
11
-1.4902 + 0.6064 i
1.18e-7 - 4.92e-8 i
12
-1.4902 - 0.6064 i
1.18e-7 + 4.92e-8 i
13
-1.4935 + 0.6086 i
4.92e-8 + 1.19e-7 i
14
-1.4935 - 0.6086 i
4.92e-8 - 1.19e-7 i
15
1.6477 + 0.5231 i
0.00672 + 0.0185 i
16
1.6477 - 0.5231 i
0.00672 - 0.0185 i
17
1.6611 + 1.2801 i
0.00029 - 0.00105 i
18
1.6611 - 1.2801 i
0.00029 + 0.00105 i
19
1.9896 + 1.1236 i
0.0032 + 0.000765 i
20
1.9896 - 1.1236 i
0.0032 - 0.000765 i
21
-12.222
0.00196
22
-34.226
0.00909 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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