Singularities of Møller-Plesset series: example "bh cc-pvdz 2re"

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
1.1612 + 0.471 i
0.0433 - 0.105 i
Singularities of quadratic [5, 5, 4] approximant
2
1.1612 - 0.471 i
0.0433 + 0.105 i
3
1.2893
0.0779
4
1.4261
0.131 i
5
3.105 + 2.3237 i
0.0883 - 0.236 i
6
3.105 - 2.3237 i
0.0883 + 0.236 i
7
-2.9863 + 2.4893 i
0.064 + 0.0572 i
8
-2.9863 - 2.4893 i
0.064 - 0.0572 i
9
5.3341 + 18.011 i
0.198 - 0.227 i
10
5.3341 - 18.011 i
0.198 + 0.227 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
1.1899 + 0.45 i
0.0843 + 0.175 i
Singularities of quadratic [5, 5, 5] approximant
2
1.1899 - 0.45 i
0.0843 - 0.175 i
3
1.3683 + 0.6412 i
0.179 + 0.00106 i
4
1.3683 - 0.6412 i
0.179 - 0.00106 i
5
1.6392 + 0.6696 i
0.303 - 0.379 i
6
1.6392 - 0.6696 i
0.303 + 0.379 i
7
1.9415
0.435
8
-3.2089 + 2.5267 i
0.092 + 0.083 i
9
-3.2089 - 2.5267 i
0.092 - 0.083 i
10
-21.7813
0.11
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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
1.1911 + 0.4348 i
0.122 + 0.104 i
Singularities of quadratic [6, 5, 5] approximant
2
1.1911 - 0.4348 i
0.122 - 0.104 i
3
1.2771 + 0.6296 i
0.137 - 0.0853 i
4
1.2771 - 0.6296 i
0.137 + 0.0853 i
5
1.4481 + 0.582 i
0.396 + 0.218 i
6
1.4481 - 0.582 i
0.396 - 0.218 i
7
2.3125
0.414
8
-3.1672 + 2.5206 i
0.0876 + 0.0748 i
9
-3.1672 - 2.5206 i
0.0876 - 0.0748 i
10
-18.2277
0.134
11
33.5154
0.259 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
1.2051 + 0.4502 i
0.157 + 0.22 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2051 - 0.4502 i
0.157 - 0.22 i
3
1.312 + 0.5831 i
0.289 - 0.11 i
4
1.312 - 0.5831 i
0.289 + 0.11 i
5
1.4929 + 0.5375 i
1.44 + 0.249 i
6
1.4929 - 0.5375 i
1.44 - 0.249 i
7
2.3856
0.431
8
-3.1994 + 2.5018 i
0.084 + 0.0883 i
9
-3.1994 - 2.5018 i
0.084 - 0.0883 i
10
-10.8049 + 24.8143 i
0.162 + 0.0435 i
11
-10.8049 - 24.8143 i
0.162 - 0.0435 i
12
30.6162
0.225 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
-0.779
0.0000749
Singularities of quadratic [6, 6, 6] approximant
2
-0.779
0.0000749 i
3
1.2021 + 0.4834 i
0.172 - 0.261 i
4
1.2021 - 0.4834 i
0.172 + 0.261 i
5
1.4136 + 0.4964 i
0.359 + 0.0796 i
6
1.4136 - 0.4964 i
0.359 - 0.0796 i
7
1.6744 + 0.5068 i
5.21 + 0.507 i
8
1.6744 - 0.5068 i
5.21 - 0.507 i
9
2.0649
0.39
10
-3.1992 + 2.5779 i
0.11 + 0.0687 i
11
-3.1992 - 2.5779 i
0.11 - 0.0687 i
12
-16.6362
0.111
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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
1.1889 + 0.49 i
0.138 - 0.142 i
Singularities of quadratic [7, 6, 6] approximant
2
1.1889 - 0.49 i
0.138 + 0.142 i
3
1.5433 + 0.4146 i
0.326 + 0.00532 i
4
1.5433 - 0.4146 i
0.326 - 0.00532 i
5
1.8092
0.311
6
1.8667 + 0.5392 i
1.28 + 0.757 i
7
1.8667 - 0.5392 i
1.28 - 0.757 i
8
-3.9129
0.0747
9
-3.8595 + 2.519 i
0.795 + 2.73 i
10
-3.8595 - 2.519 i
0.795 - 2.73 i
11
-5.2322
0.053 i
12
-8.8283 + 2.0454 i
0.0459 + 0.033 i
13
-8.8283 - 2.0454 i
0.0459 - 0.033 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
1.1919 + 0.4753 i
0.0151 - 0.213 i
Singularities of quadratic [7, 7, 6] approximant
2
1.1919 - 0.4753 i
0.0151 + 0.213 i
3
1.4315 + 0.4202 i
0.827 - 1.41 i
4
1.4315 - 0.4202 i
0.827 + 1.41 i
5
1.4114 + 0.5328 i
0.18 + 0.228 i
6
1.4114 - 0.5328 i
0.18 - 0.228 i
7
-1.8107 + 0.0006 i
0.000713 + 0.000713 i
8
-1.8107 - 0.0006 i
0.000713 - 0.000713 i
9
3.2171 + 1.6403 i
0.147 - 0.252 i
10
3.2171 - 1.6403 i
0.147 + 0.252 i
11
-3.1669 + 2.2514 i
0.00851 + 0.0694 i
12
-3.1669 - 2.2514 i
0.00851 - 0.0694 i
13
3.3057 + 6.5986 i
0.0553 - 0.138 i
14
3.3057 - 6.5986 i
0.0553 + 0.138 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
1.1896 + 0.4897 i
0.139 - 0.147 i
Singularities of quadratic [7, 7, 7] approximant
2
1.1896 - 0.4897 i
0.139 + 0.147 i
3
1.5273 + 0.4229 i
0.33 + 0.0257 i
4
1.5273 - 0.4229 i
0.33 - 0.0257 i
5
1.8298 + 0.4956 i
0.976 + 1.47 i
6
1.8298 - 0.4956 i
0.976 - 1.47 i
7
1.8964
0.327
8
-3.2777 + 1.9889 i
0.0528 - 0.0833 i
9
-3.2777 - 1.9889 i
0.0528 + 0.0833 i
10
-4.3056 + 2.705 i
0.0813 + 0.0355 i
11
-4.3056 - 2.705 i
0.0813 - 0.0355 i
12
-3.2059 + 4.0298 i
0.0415 + 0.138 i
13
-3.2059 - 4.0298 i
0.0415 - 0.138 i
14
-15.1868
0.183
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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
1.1898 + 0.4847 i
0.102 - 0.178 i
Singularities of quadratic [8, 7, 7] approximant
2
1.1898 - 0.4847 i
0.102 + 0.178 i
3
1.52 + 0.4471 i
0.288 + 0.23 i
4
1.52 - 0.4471 i
0.288 - 0.23 i
5
1.5552 + 0.476 i
0.562 - 0.245 i
6
1.5552 - 0.476 i
0.562 + 0.245 i
7
-1.6386 + 0.0001 i
0.000381 + 0.000381 i
8
-1.6386 - 0.0001 i
0.000381 - 0.000381 i
9
2.637
0.703
10
-3.2072 + 2.1015 i
0.0214 - 0.0613 i
11
-3.2072 - 2.1015 i
0.0214 + 0.0613 i
12
-1.4926 + 5.9735 i
0.0723 - 0.00675 i
13
-1.4926 - 5.9735 i
0.0723 + 0.00675 i
14
-6.7325 + 11.736 i
0.0123 - 0.125 i
15
-6.7325 - 11.736 i
0.0123 + 0.125 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
-1.2826 + 0.e-5 i
0.0000939 + 0.0000939 i
Singularities of quadratic [8, 8, 7] approximant
2
-1.2826 - 0.e-5 i
0.0000939 - 0.0000939 i
3
1.1903 + 0.4828 i
0.0876 - 0.19 i
4
1.1903 - 0.4828 i
0.0876 + 0.19 i
5
1.5043 + 0.4249 i
0.327 + 0.615 i
6
1.5043 - 0.4249 i
0.327 - 0.615 i
7
1.4982 + 0.5039 i
0.359 + 0.23 i
8
1.4982 - 0.5039 i
0.359 - 0.23 i
9
3.1349
1.45
10
-3.2093
0.0583
11
-3.2545
0.0608 i
12
-3.3113 + 2.2802 i
0.000852 + 0.112 i
13
-3.3113 - 2.2802 i
0.000852 - 0.112 i
14
7.2429
0.333 i
15
1.1153 + 8.629 i
0.126 - 0.0573 i
16
1.1153 - 8.629 i
0.126 + 0.0573 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
0.3476
5.06e-7
Singularities of quadratic [8, 8, 8] approximant
2
0.3476
5.06e-7 i
3
1.19 + 0.4828 i
0.086 - 0.186 i
4
1.19 - 0.4828 i
0.086 + 0.186 i
5
1.5031 + 0.4314 i
0.314 + 0.598 i
6
1.5031 - 0.4314 i
0.314 - 0.598 i
7
1.5013 + 0.5043 i
0.379 + 0.231 i
8
1.5013 - 0.5043 i
0.379 - 0.231 i
9
-2.5923 + 0.0079 i
0.00576 + 0.00572 i
10
-2.5923 - 0.0079 i
0.00576 - 0.00572 i
11
3.027
1.15
12
-3.2174 + 2.2554 i
0.00954 + 0.0797 i
13
-3.2174 - 2.2554 i
0.00954 - 0.0797 i
14
0.49 + 7.7755 i
0.108 - 0.061 i
15
0.49 - 7.7755 i
0.108 + 0.061 i
16
9.781
0.215 i
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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
1.1887 + 0.4844 i
0.0977 - 0.17 i
Singularities of quadratic [9, 8, 8] approximant
2
1.1887 - 0.4844 i
0.0977 + 0.17 i
3
1.5392 + 0.4692 i
0.578 + 0.0654 i
4
1.5392 - 0.4692 i
0.578 - 0.0654 i
5
1.5576 + 0.5829 i
0.535 + 0.902 i
6
1.5576 - 0.5829 i
0.535 - 0.902 i
7
1.7676
0.47
8
2.1818
24.7 i
9
-2.8194 + 0.016 i
0.0092 + 0.00899 i
10
-2.8194 - 0.016 i
0.0092 - 0.00899 i
11
3.0055 + 1.6957 i
0.0726 - 0.28 i
12
3.0055 - 1.6957 i
0.0726 + 0.28 i
13
-3.2297 + 2.3074 i
0.0242 + 0.0831 i
14
-3.2297 - 2.3074 i
0.0242 - 0.0831 i
15
8.9337
0.876
16
1.9808 + 18.3695 i
0.327 - 0.0517 i
17
1.9808 - 18.3695 i
0.327 + 0.0517 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
1.1902 + 0.4857 i
0.118 - 0.177 i
Singularities of quadratic [9, 9, 8] approximant
2
1.1902 - 0.4857 i
0.118 + 0.177 i
3
1.5625 + 0.3872 i
0.401 + 0.342 i
4
1.5625 - 0.3872 i
0.401 - 0.342 i
5
1.5427 + 0.48 i
0.406 + 0.111 i
6
1.5427 - 0.48 i
0.406 - 0.111 i
7
1.337 + 0.9777 i
0.0436 + 0.102 i
8
1.337 - 0.9777 i
0.0436 - 0.102 i
9
1.3451 + 0.9775 i
0.0982 - 0.0404 i
10
1.3451 - 0.9775 i
0.0982 + 0.0404 i
11
-2.7797 + 0.012 i
0.0109 + 0.0107 i
12
-2.7797 - 0.012 i
0.0109 - 0.0107 i
13
3.0643
1.48
14
-3.2435 + 2.2992 i
0.02 + 0.0911 i
15
-3.2435 - 2.2992 i
0.02 - 0.0911 i
16
7.2259
0.322 i
17
1.2947 + 8.5182 i
0.135 - 0.0612 i
18
1.2947 - 8.5182 i
0.135 + 0.0612 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
-1.1092 + 0.e-5 i
0.0000186 + 0.0000186 i
Singularities of quadratic [9, 9, 9] approximant
2
-1.1092 - 0.e-5 i
0.0000186 - 0.0000186 i
3
1.1886 + 0.4839 i
0.0904 - 0.172 i
4
1.1886 - 0.4839 i
0.0904 + 0.172 i
5
1.5085 + 0.451 i
0.482 + 0.201 i
6
1.5085 - 0.451 i
0.482 - 0.201 i
7
1.5748 + 0.5471 i
0.911 + 1.09 i
8
1.5748 - 0.5471 i
0.911 - 1.09 i
9
2.0531
0.604
10
-2.9075
0.0261
11
-2.9371
0.0269 i
12
2.8202 + 2.4036 i
0.128 - 0.0713 i
13
2.8202 - 2.4036 i
0.128 + 0.0713 i
14
4.024
0.251 i
15
-3.2958 + 2.3201 i
0.0125 + 0.116 i
16
-3.2958 - 2.3201 i
0.0125 - 0.116 i
17
5.8589 + 5.5733 i
0.064 - 0.217 i
18
5.8589 - 5.5733 i
0.064 + 0.217 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
-0.8792 + 0.e-5 i
8.61e-6 + 8.61e-6 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.8792 - 0.e-5 i
8.61e-6 - 8.61e-6 i
3
1.1888 + 0.4842 i
0.0945 - 0.172 i
4
1.1888 - 0.4842 i
0.0945 + 0.172 i
5
1.5223 + 0.4532 i
0.487 + 0.168 i
6
1.5223 - 0.4532 i
0.487 - 0.168 i
7
1.5772 + 0.5549 i
0.947 + 1.01 i
8
1.5772 - 0.5549 i
0.947 - 1.01 i
9
1.9825
0.596
10
-2.88 + 0.0131 i
0.018 + 0.0177 i
11
-2.88 - 0.0131 i
0.018 - 0.0177 i
12
2.758 + 2.0794 i
0.0948 - 0.152 i
13
2.758 - 2.0794 i
0.0948 + 0.152 i
14
3.8245
0.174 i
15
-3.2551 + 2.3193 i
0.0241 + 0.0946 i
16
-3.2551 - 2.3193 i
0.0241 - 0.0946 i
17
5.2195
0.177
18
4.6579 + 21.7183 i
0.331 - 0.00762 i
19
4.6579 - 21.7183 i
0.331 + 0.00762 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
-0.6579 + 0.7546 i
3.32e-6 - 6.37e-6 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.6579 - 0.7546 i
3.32e-6 + 6.37e-6 i
3
-0.6579 + 0.7546 i
6.37e-6 + 3.32e-6 i
4
-0.6579 - 0.7546 i
6.37e-6 - 3.32e-6 i
5
1.189 + 0.4861 i
0.122 - 0.162 i
6
1.189 - 0.4861 i
0.122 + 0.162 i
7
1.4503
0.0683
8
1.4661
0.0746 i
9
1.4922 + 0.5851 i
0.459 + 0.328 i
10
1.4922 - 0.5851 i
0.459 - 0.328 i
11
1.5436 + 0.546 i
4.13 - 0.427 i
12
1.5436 - 0.546 i
4.13 + 0.427 i
13
-2.6987
0.00715
14
-2.7275
0.00744 i
15
3.53 + 1.3963 i
0.199 - 0.419 i
16
3.53 - 1.3963 i
0.199 + 0.419 i
17
-3.281 + 2.2512 i
0.017 - 0.0955 i
18
-3.281 - 2.2512 i
0.017 + 0.0955 i
19
3.2128 + 7.351 i
0.0697 - 0.133 i
20
3.2128 - 7.351 i
0.0697 + 0.133 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
-0.6255 + 0.6888 i
3.65e-6 + 2.38e-6 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.6255 - 0.6888 i
3.65e-6 - 2.38e-6 i
3
-0.6255 + 0.6888 i
2.38e-6 - 3.65e-6 i
4
-0.6255 - 0.6888 i
2.38e-6 + 3.65e-6 i
5
1.1892 + 0.4859 i
0.12 - 0.166 i
6
1.1892 - 0.4859 i
0.12 + 0.166 i
7
1.4853
0.0967
8
1.5127
0.114 i
9
1.5005 + 0.59 i
0.45 + 0.363 i
10
1.5005 - 0.59 i
0.45 - 0.363 i
11
1.552 + 0.5413 i
2.46 - 0.771 i
12
1.552 - 0.5413 i
2.46 + 0.771 i
13
-2.7162
0.00787
14
-2.7455
0.0082 i
15
3.4713 + 1.4688 i
0.183 - 0.371 i
16
3.4713 - 1.4688 i
0.183 + 0.371 i
17
-3.2821 + 2.2571 i
0.0149 - 0.0975 i
18
-3.2821 - 2.2571 i
0.0149 + 0.0975 i
19
3.3327 + 7.3495 i
0.0721 - 0.135 i
20
3.3327 - 7.3495 i
0.0721 + 0.135 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
-0.6231 + 0.6669 i
2.12e-6 + 1.74e-6 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.6231 - 0.6669 i
2.12e-6 - 1.74e-6 i
3
-0.6231 + 0.6669 i
1.74e-6 - 2.12e-6 i
4
-0.6231 - 0.6669 i
1.74e-6 + 2.12e-6 i
5
1.1891 + 0.4862 i
0.125 - 0.162 i
6
1.1891 - 0.4862 i
0.125 + 0.162 i
7
1.4104
0.055
8
1.4234
0.0591 i
9
1.4866 + 0.5851 i
0.415 + 0.328 i
10
1.4866 - 0.5851 i
0.415 - 0.328 i
11
1.539 + 0.538 i
4.13 - 0.713 i
12
1.539 - 0.538 i
4.13 + 0.713 i
13
-2.6929
0.00437
14
-2.7321
0.00458 i
15
-3.3214 + 2.2327 i
0.0453 - 0.0978 i
16
-3.3214 - 2.2327 i
0.0453 + 0.0978 i
17
3.8973 + 1.4043 i
0.42 - 0.24 i
18
3.8973 - 1.4043 i
0.42 + 0.24 i
19
2.2653 + 6.3866 i
0.0458 - 0.0863 i
20
2.2653 - 6.3866 i
0.0458 + 0.0863 i
21
152.6728
0.606
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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
-0.6507 + 0.6666 i
3.51e-6 + 3.18e-6 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.6507 - 0.6666 i
3.51e-6 - 3.18e-6 i
3
-0.6507 + 0.6666 i
3.18e-6 - 3.51e-6 i
4
-0.6507 - 0.6666 i
3.18e-6 + 3.51e-6 i
5
1.1891 + 0.4859 i
0.12 - 0.165 i
6
1.1891 - 0.4859 i
0.12 + 0.165 i
7
1.4815
0.0915
8
1.5058
0.105 i
9
1.4994 + 0.5875 i
0.464 + 0.352 i
10
1.4994 - 0.5875 i
0.464 - 0.352 i
11
1.5498 + 0.5429 i
2.82 - 0.577 i
12
1.5498 - 0.5429 i
2.82 + 0.577 i
13
-2.5081 + 0.1265 i
0.00065 - 0.00156 i
14
-2.5081 - 0.1265 i
0.00065 + 0.00156 i
15
-2.5281 + 0.1029 i
0.00136 + 0.000705 i
16
-2.5281 - 0.1029 i
0.00136 - 0.000705 i
17
3.486 + 1.4383 i
0.179 - 0.395 i
18
3.486 - 1.4383 i
0.179 + 0.395 i
19
-3.2744 + 2.2406 i
0.019 - 0.0883 i
20
-3.2744 - 2.2406 i
0.019 + 0.0883 i
21
3.3403 + 7.3058 i
0.067 - 0.139 i
22
3.3403 - 7.3058 i
0.067 + 0.139 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
0.172
0
Singularities of quadratic [11, 11, 11] approximant
2
0.172
0
3
-0.6562 + 0.6532 i
1.72e-6 + 2.58e-6 i
4
-0.6562 - 0.6532 i
1.72e-6 - 2.58e-6 i
5
-0.6562 + 0.6532 i
2.58e-6 - 1.72e-6 i
6
-0.6562 - 0.6532 i
2.58e-6 + 1.72e-6 i
7
1.1897 + 0.4867 i
0.139 - 0.164 i
8
1.1897 - 0.4867 i
0.139 + 0.164 i
9
1.3227
0.0252
10
1.3297
0.0261 i
11
1.4741 + 0.5941 i
0.339 + 0.317 i
12
1.4741 - 0.5941 i
0.339 - 0.317 i
13
1.5307 + 0.537 i
4.21 - 3.02 i
14
1.5307 - 0.537 i
4.21 + 3.02 i
15
-2.7814 + 0.0131 i
0.00972 + 0.00938 i
16
-2.7814 - 0.0131 i
0.00972 - 0.00938 i
17
3.727 + 1.3913 i
0.384 - 0.325 i
18
3.727 - 1.3913 i
0.384 + 0.325 i
19
-3.2619 + 2.3066 i
0.0192 + 0.103 i
20
-3.2619 - 2.3066 i
0.0192 - 0.103 i
21
2.5529 + 7.6916 i
0.098 - 0.0976 i
22
2.5529 - 7.6916 i
0.098 + 0.0976 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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