Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 2.1r_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
1.1269 + 0.4455 i
0.0685 - 0.0825 i
Singularities of quadratic [5, 5, 4] approximant
2
1.1269 - 0.4455 i
0.0685 + 0.0825 i
3
1.3343
0.0847
4
1.4928
0.176 i
5
-2.3217 + 0.5291 i
0.0342 + 0.312 i
6
-2.3217 - 0.5291 i
0.0342 - 0.312 i
7
3.4141
1.22
8
-6.7496
0.212
9
6.9715
0.971 i
10
-210.8127
1.6 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
1.1263 + 0.4452 i
0.0673 - 0.0827 i
Singularities of quadratic [5, 5, 5] approximant
2
1.1263 - 0.4452 i
0.0673 + 0.0827 i
3
1.3305
0.0863
4
1.5016
0.191 i
5
-2.3248 + 0.5419 i
0.0646 + 0.302 i
6
-2.3248 - 0.5419 i
0.0646 - 0.302 i
7
3.9659
3.66
8
4.7506
21.6 i
9
-6.7253
0.241
10
30.3837
10.2
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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
1.13 + 0.4409 i
0.0623 - 0.0986 i
Singularities of quadratic [6, 5, 5] approximant
2
1.13 - 0.4409 i
0.0623 + 0.0986 i
3
1.3676
0.114
4
-1.5668 + 0.0116 i
0.00606 + 0.00607 i
5
-1.5668 - 0.0116 i
0.00606 - 0.00607 i
6
1.6027
0.36 i
7
-2.1515 + 0.4141 i
0.0646 - 0.0594 i
8
-2.1515 - 0.4141 i
0.0646 + 0.0594 i
9
3.4356 + 1.8938 i
0.149 - 0.397 i
10
3.4356 - 1.8938 i
0.149 + 0.397 i
11
-10.6727
0.274
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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
1.1455 + 0.4239 i
0.00247 - 0.172 i
Singularities of quadratic [6, 6, 5] approximant
2
1.1455 - 0.4239 i
0.00247 + 0.172 i
3
1.5278
0.323
4
1.4286 + 0.6336 i
0.145 + 0.0473 i
5
1.4286 - 0.6336 i
0.145 - 0.0473 i
6
1.6451 + 0.8217 i
0.157 - 0.136 i
7
1.6451 - 0.8217 i
0.157 + 0.136 i
8
-2.342 + 0.6114 i
0.202 + 0.2 i
9
-2.342 - 0.6114 i
0.202 - 0.2 i
10
-5.2926
0.266
11
-22.5666
0.332 i
12
26.2049
0.376 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
0.2711 + 0.e-5 i
3.46e-7 - 3.46e-7 i
Singularities of quadratic [6, 6, 6] approximant
2
0.2711 - 0.e-5 i
3.46e-7 + 3.46e-7 i
3
0.8559 + 0.5337 i
0.00186 + 0.000454 i
4
0.8559 - 0.5337 i
0.00186 - 0.000454 i
5
0.8683 + 0.5487 i
0.000445 - 0.00196 i
6
0.8683 - 0.5487 i
0.000445 + 0.00196 i
7
1.0324 + 0.45 i
0.00573 - 0.00871 i
8
1.0324 - 0.45 i
0.00573 + 0.00871 i
9
1.7935
0.628
10
-2.3201 + 0.5823 i
0.1 + 0.22 i
11
-2.3201 - 0.5823 i
0.1 - 0.22 i
12
-8.035
0.642
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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
1.1609 + 0.4394 i
0.117 - 0.258 i
Singularities of quadratic [7, 6, 6] approximant
2
1.1609 - 0.4394 i
0.117 + 0.258 i
3
1.3408 + 0.4258 i
0.28 + 0.176 i
4
1.3408 - 0.4258 i
0.28 - 0.176 i
5
1.4806 + 0.332 i
1.99 - 1.12 i
6
1.4806 - 0.332 i
1.99 + 1.12 i
7
2.3977
0.437
8
-2.3332 + 0.6282 i
0.187 + 0.168 i
9
-2.3332 - 0.6282 i
0.187 - 0.168 i
10
-5.3071
0.559
11
5.8256
1.95 i
12
-7.5102
1.39 i
13
157.2949
8.81
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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
1.1482 + 0.4452 i
0.11 - 0.138 i
Singularities of quadratic [7, 7, 6] approximant
2
1.1482 - 0.4452 i
0.11 + 0.138 i
3
1.5172 + 0.4149 i
0.3 + 0.022 i
4
1.5172 - 0.4149 i
0.3 - 0.022 i
5
1.6453
0.276
6
1.8379 + 0.546 i
0.994 + 0.0134 i
7
1.8379 - 0.546 i
0.994 - 0.0134 i
8
-2.3063 + 0.5693 i
0.0124 + 0.278 i
9
-2.3063 - 0.5693 i
0.0124 - 0.278 i
10
-2.7067
21.8
11
-3.1885
0.119 i
12
-3.8018
0.088
13
12.0457
0.317 i
14
-18.5762
0.245 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
1.1491 + 0.4429 i
0.0961 - 0.159 i
Singularities of quadratic [7, 7, 7] approximant
2
1.1491 - 0.4429 i
0.0961 + 0.159 i
3
1.4776 + 0.3946 i
0.261 + 0.0971 i
4
1.4776 - 0.3946 i
0.261 - 0.0971 i
5
1.5156 + 0.3202 i
0.151 + 0.499 i
6
1.5156 - 0.3202 i
0.151 - 0.499 i
7
-2.3228 + 0.6385 i
0.177 + 0.145 i
8
-2.3228 - 0.6385 i
0.177 - 0.145 i
9
2.5952 + 0.9399 i
0.287 + 0.306 i
10
2.5952 - 0.9399 i
0.287 - 0.306 i
11
-3.8851 + 0.1434 i
0.287 - 1.15 i
12
-3.8851 - 0.1434 i
0.287 + 1.15 i
13
4.9518
0.343
14
-8.9156
0.586
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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
1.1474 + 0.4458 i
0.11 - 0.131 i
Singularities of quadratic [8, 7, 7] approximant
2
1.1474 - 0.4458 i
0.11 + 0.131 i
3
1.5963
0.242
4
1.5505 + 0.4118 i
0.301 - 0.00262 i
5
1.5505 - 0.4118 i
0.301 + 0.00262 i
6
1.8406 + 0.6382 i
0.742 - 0.306 i
7
1.8406 - 0.6382 i
0.742 + 0.306 i
8
-2.2967 + 0.593 i
0.0492 + 0.211 i
9
-2.2967 - 0.593 i
0.0492 - 0.211 i
10
-3.5238 + 1.1916 i
0.0794 - 0.0543 i
11
-3.5238 - 1.1916 i
0.0794 + 0.0543 i
12
-3.7608
0.133
13
-13.877
0.141 i
14
6.5689 + 17.5764 i
0.0295 + 0.238 i
15
6.5689 - 17.5764 i
0.0295 - 0.238 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
0.7035
0.000374
Singularities of quadratic [8, 8, 7] approximant
2
0.7035
0.000374 i
3
1.1492 + 0.4466 i
0.127 - 0.136 i
4
1.1492 - 0.4466 i
0.127 + 0.136 i
5
1.5394
0.208
6
1.5478 + 0.4067 i
0.281 + 0.00118 i
7
1.5478 - 0.4067 i
0.281 - 0.00118 i
8
1.8769 + 0.6652 i
0.554 - 0.165 i
9
1.8769 - 0.6652 i
0.554 + 0.165 i
10
-2.3114 + 0.6113 i
0.126 + 0.208 i
11
-2.3114 - 0.6113 i
0.126 - 0.208 i
12
-3.3243 + 0.0343 i
0.0533 + 0.0678 i
13
-3.3243 - 0.0343 i
0.0533 - 0.0678 i
14
-4.2962
0.101
15
13.7103
0.324 i
16
-21.7352
0.285 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
1.1444 + 0.4448 i
0.0921 - 0.118 i
Singularities of quadratic [8, 8, 8] approximant
2
1.1444 - 0.4448 i
0.0921 + 0.118 i
3
1.4104
0.106
4
1.4812
0.156 i
5
1.4508 + 0.5222 i
0.704 - 0.429 i
6
1.4508 - 0.5222 i
0.704 + 0.429 i
7
1.4836 + 0.5902 i
0.411 - 0.676 i
8
1.4836 - 0.5902 i
0.411 + 0.676 i
9
-2.3121 + 0.6247 i
0.139 + 0.174 i
10
-2.3121 - 0.6247 i
0.139 - 0.174 i
11
3.2758 + 0.7524 i
0.17 + 1.1 i
12
3.2758 - 0.7524 i
0.17 - 1.1 i
13
-3.7291 + 0.3137 i
0.0436 + 0.24 i
14
-3.7291 - 0.3137 i
0.0436 - 0.24 i
15
-5.9912
0.17
16
10.4346
1.23
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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
1.1467 + 0.4431 i
0.091 - 0.142 i
Singularities of quadratic [9, 8, 8] approximant
2
1.1467 - 0.4431 i
0.091 + 0.142 i
3
1.5881 + 0.5018 i
0.608 + 0.0143 i
4
1.5881 - 0.5018 i
0.608 - 0.0143 i
5
1.6848 + 0.42 i
0.429 - 0.215 i
6
1.6848 - 0.42 i
0.429 + 0.215 i
7
1.9022 + 0.2002 i
0.383 + 0.101 i
8
1.9022 - 0.2002 i
0.383 - 0.101 i
9
-2.3139 + 0.6356 i
0.162 + 0.146 i
10
-2.3139 - 0.6356 i
0.162 - 0.146 i
11
-3.0816 + 0.0803 i
0.44 - 0.828 i
12
-3.0816 - 0.0803 i
0.44 + 0.828 i
13
3.3556 + 0.8851 i
0.426 + 0.57 i
14
3.3556 - 0.8851 i
0.426 - 0.57 i
15
-6.8948
0.557
16
11.2336
0.53
17
-14.8857
0.943 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
0.3805
2.49e-7
Singularities of quadratic [9, 9, 8] approximant
2
0.3805
2.49e-7 i
3
1.1457 + 0.4423 i
0.0778 - 0.137 i
4
1.1457 - 0.4423 i
0.0778 + 0.137 i
5
1.5009 + 0.4066 i
0.356 + 0.0903 i
6
1.5009 - 0.4066 i
0.356 - 0.0903 i
7
1.6312 + 0.4499 i
3.41 - 6.07 i
8
1.6312 - 0.4499 i
3.41 + 6.07 i
9
2.1002
0.49
10
-2.3029 + 0.6244 i
0.104 + 0.154 i
11
-2.3029 - 0.6244 i
0.104 - 0.154 i
12
-1.7562 + 2.3108 i
0.0127 - 0.00815 i
13
-1.7562 - 2.3108 i
0.0127 + 0.00815 i
14
-1.7872 + 2.3273 i
0.00825 + 0.0128 i
15
-1.7872 - 2.3273 i
0.00825 - 0.0128 i
16
-5.0745
0.478
17
12.2236
0.273 i
18
-12.405
0.223 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
1.1462 + 0.4438 i
0.0942 - 0.133 i
Singularities of quadratic [9, 9, 9] approximant
2
1.1462 - 0.4438 i
0.0942 + 0.133 i
3
1.4367 + 0.0181 i
0.11 - 0.0829 i
4
1.4367 - 0.0181 i
0.11 + 0.0829 i
5
1.4876 + 0.4872 i
0.438 + 0.101 i
6
1.4876 - 0.4872 i
0.438 - 0.101 i
7
1.5934 + 0.4958 i
637. + 216. i
8
1.5934 - 0.4958 i
637. - 216. i
9
2.3159
0.531
10
-2.3124 + 0.6314 i
0.146 + 0.158 i
11
-2.3124 - 0.6314 i
0.146 - 0.158 i
12
-3.8185 + 0.1217 i
0.552 + 1.64 i
13
-3.8185 - 0.1217 i
0.552 - 1.64 i
14
-4.6547 + 2.6204 i
0.0796 - 0.136 i
15
-4.6547 - 2.6204 i
0.0796 + 0.136 i
16
6.8234
0.527 i
17
-6.9057
0.136
18
-46.1253
0.259 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
1.1461 + 0.4433 i
0.0893 - 0.135 i
Singularities of quadratic [10, 9, 9] approximant
2
1.1461 - 0.4433 i
0.0893 + 0.135 i
3
1.3135 + 0.0017 i
0.0429 - 0.0412 i
4
1.3135 - 0.0017 i
0.0429 + 0.0412 i
5
1.5144 + 0.4446 i
0.401 + 0.116 i
6
1.5144 - 0.4446 i
0.401 - 0.116 i
7
1.5951 + 0.4658 i
1.5 - 2.46 i
8
1.5951 - 0.4658 i
1.5 + 2.46 i
9
2.2022
0.61
10
-2.3134 + 0.6356 i
0.16 + 0.146 i
11
-2.3134 - 0.6356 i
0.16 - 0.146 i
12
-3.1068 + 0.0778 i
0.468 - 0.879 i
13
-3.1068 - 0.0778 i
0.468 + 0.879 i
14
3.5764 + 2.0586 i
0.151 - 0.272 i
15
3.5764 - 2.0586 i
0.151 + 0.272 i
16
4.9944
0.181 i
17
7.3816
0.172
18
-7.4753
0.886
19
-12.3021
1.83 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
1.1457 + 0.4436 i
0.09 - 0.129 i
Singularities of quadratic [10, 10, 9] approximant
2
1.1457 - 0.4436 i
0.09 + 0.129 i
3
1.256 + 0.0022 i
0.0322 - 0.0309 i
4
1.256 - 0.0022 i
0.0322 + 0.0309 i
5
1.4803 + 0.4515 i
0.41 + 0.116 i
6
1.4803 - 0.4515 i
0.41 - 0.116 i
7
1.6008 + 0.4668 i
14.2 - 10.8 i
8
1.6008 - 0.4668 i
14.2 + 10.8 i
9
2.1959
0.515
10
-2.3068 + 0.6381 i
0.144 + 0.128 i
11
-2.3068 - 0.6381 i
0.144 - 0.128 i
12
-2.5828 + 0.0017 i
0.137 + 0.126 i
13
-2.5828 - 0.0017 i
0.137 - 0.126 i
14
-1.9734 + 4.2376 i
0.0137 + 0.0525 i
15
-1.9734 - 4.2376 i
0.0137 - 0.0525 i
16
-1.7753 + 4.4995 i
0.0518 - 0.0142 i
17
-1.7753 - 4.4995 i
0.0518 + 0.0142 i
18
-5.4294
0.614
19
10.3363
0.28 i
20
-11.1244
0.233 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
1.1462 + 0.4434 i
0.0912 - 0.136 i
Singularities of quadratic [10, 10, 10] approximant
2
1.1462 - 0.4434 i
0.0912 + 0.136 i
3
1.5299 + 0.0259 i
0.158 - 0.105 i
4
1.5299 - 0.0259 i
0.158 + 0.105 i
5
1.5113 + 0.4876 i
0.471 + 0.0893 i
6
1.5113 - 0.4876 i
0.471 - 0.0893 i
7
1.5934 + 0.5056 i
5.84 + 29.8 i
8
1.5934 - 0.5056 i
5.84 - 29.8 i
9
-1.7867
0.00368
10
-1.7871
0.00369 i
11
-2.2945 + 0.6369 i
0.103 + 0.107 i
12
-2.2945 - 0.6369 i
0.103 - 0.107 i
13
2.4108
0.591
14
-2.0034 + 2.0751 i
0.0118 + 0.012 i
15
-2.0034 - 2.0751 i
0.0118 - 0.012 i
16
-1.9907 + 2.0942 i
0.0119 - 0.0119 i
17
-1.9907 - 2.0942 i
0.0119 + 0.0119 i
18
-5.029
0.243
19
6.6546
0.511 i
20
-330.8325
0.199 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
1.1463 + 0.4433 i
0.0906 - 0.137 i
Singularities of quadratic [11, 10, 10] approximant
2
1.1463 - 0.4433 i
0.0906 + 0.137 i
3
1.5888 + 0.034 i
0.19 - 0.113 i
4
1.5888 - 0.034 i
0.19 + 0.113 i
5
1.5253 + 0.4914 i
0.484 + 0.0673 i
6
1.5253 - 0.4914 i
0.484 - 0.0673 i
7
1.6008 + 0.514 i
12.5 + 15.1 i
8
1.6008 - 0.514 i
12.5 - 15.1 i
9
-1.0589 + 1.6323 i
0.000632 - 0.00225 i
10
-1.0589 - 1.6323 i
0.000632 + 0.00225 i
11
-1.0592 + 1.6322 i
0.00225 + 0.000632 i
12
-1.0592 - 1.6322 i
0.00225 - 0.000632 i
13
-2.3794 + 0.0149 i
0.112 + 0.0841 i
14
-2.3794 - 0.0149 i
0.112 - 0.0841 i
15
-2.3072 + 0.6518 i
0.156 + 0.0772 i
16
-2.3072 - 0.6518 i
0.156 - 0.0772 i
17
2.4957
0.618
18
-5.5291
0.273
19
5.8889
0.793 i
20
28.7725
158.
21
-31.8292
0.438 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
1.1462 + 0.4434 i
0.0907 - 0.136 i
Singularities of quadratic [11, 11, 10] approximant
2
1.1462 - 0.4434 i
0.0907 + 0.136 i
3
-0.9211 + 0.8558 i
0.000141 + 0.0000509 i
4
-0.9211 - 0.8558 i
0.000141 - 0.0000509 i
5
-0.921 + 0.8558 i
0.0000509 - 0.000141 i
6
-0.921 - 0.8558 i
0.0000509 + 0.000141 i
7
1.5348 + 0.0277 i
0.171 - 0.109 i
8
1.5348 - 0.0277 i
0.171 + 0.109 i
9
1.5112 + 0.4847 i
0.463 + 0.0823 i
10
1.5112 - 0.4847 i
0.463 - 0.0823 i
11
1.5992 + 0.505 i
19.1 + 40.6 i
12
1.5992 - 0.505 i
19.1 - 40.6 i
13
2.3716
0.573
14
-2.3241 + 0.6442 i
0.221 + 0.113 i
15
-2.3241 - 0.6442 i
0.221 - 0.113 i
16
-2.786 + 0.0801 i
0.581 - 0.28 i
17
-2.786 - 0.0801 i
0.581 + 0.28 i
18
-6.5993
0.264
19
7.2082
0.45 i
20
-11.9729
8.66 i
21
-6.1548 + 14.7738 i
0.351 + 0.143 i
22
-6.1548 - 14.7738 i
0.351 - 0.143 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
-0.7864
8.29e-6
Singularities of quadratic [11, 11, 11] approximant
2
-0.7864
8.29e-6 i
3
1.1463 + 0.4433 i
0.091 - 0.137 i
4
1.1463 - 0.4433 i
0.091 + 0.137 i
5
-1.404
0.000372
6
-1.404
0.000372 i
7
1.5556 + 0.0288 i
0.17 - 0.109 i
8
1.5556 - 0.0288 i
0.17 + 0.109 i
9
1.5178 + 0.4894 i
0.479 + 0.0811 i
10
1.5178 - 0.4894 i
0.479 - 0.0811 i
11
1.5954 + 0.5093 i
7.76 + 21.5 i
12
1.5954 - 0.5093 i
7.76 - 21.5 i
13
-2.2933 + 0.634 i
0.0943 + 0.112 i
14
-2.2933 - 0.634 i
0.0943 - 0.112 i
15
2.4473
0.607
16
-2.0437 + 1.8509 i
0.00597 + 0.0141 i
17
-2.0437 - 1.8509 i
0.00597 - 0.0141 i
18
-2.0433 + 1.8724 i
0.014 - 0.00618 i
19
-2.0433 - 1.8724 i
0.014 + 0.00618 i
20
-5.0081
0.231
21
6.4397
0.55 i
22
487.1449
0.205
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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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