Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 1.8r_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
0.9568
0.00204
Singularities of quadratic [5, 5, 4] approximant
2
0.958
0.00204 i
3
1.326 + 0.4266 i
0.0204 + 0.101 i
4
1.326 - 0.4266 i
0.0204 - 0.101 i
5
-2.7235 + 0.2419 i
0.125 + 0.0302 i
6
-2.7235 - 0.2419 i
0.125 - 0.0302 i
7
3.0285
1.29
8
-4.5166
0.11
9
7.2155
0.472 i
10
-18.0001
0.207 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
1.0039
0.00398
Singularities of quadratic [5, 5, 5] approximant
2
1.0072
0.004 i
3
1.3214 + 0.4241 i
0.0228 + 0.0972 i
4
1.3214 - 0.4241 i
0.0228 - 0.0972 i
5
-2.9455 + 0.3856 i
0.254 - 0.357 i
6
-2.9455 - 0.3856 i
0.254 + 0.357 i
7
3.2732 + 1.0771 i
0.131 - 0.699 i
8
3.2732 - 1.0771 i
0.131 + 0.699 i
9
-6.1624
0.202
10
11.939
1.97
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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
1.3672
0.0607
Singularities of quadratic [6, 5, 5] approximant
2
1.3334 + 0.4431 i
0.0156 - 0.144 i
3
1.3334 - 0.4431 i
0.0156 + 0.144 i
4
1.4244
0.0719 i
5
2.4475 + 1.2658 i
0.175 + 0.206 i
6
2.4475 - 1.2658 i
0.175 - 0.206 i
7
-3.0914 + 0.5362 i
0.408 + 0.213 i
8
-3.0914 - 0.5362 i
0.408 - 0.213 i
9
4.7882
0.262
10
-10.4992
68.7
11
-11.6902
2.74 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
1.2955
0.0359
Singularities of quadratic [6, 6, 5] approximant
2
1.3295
0.039 i
3
1.3293 + 0.44 i
0.00849 - 0.128 i
4
1.3293 - 0.44 i
0.00849 + 0.128 i
5
2.7119 + 1.3442 i
0.107 + 0.301 i
6
2.7119 - 1.3442 i
0.107 - 0.301 i
7
-3.1103 + 0.5609 i
0.385 + 0.126 i
8
-3.1103 - 0.5609 i
0.385 - 0.126 i
9
-7.2251 + 4.6815 i
0.291 + 0.212 i
10
-7.2251 - 4.6815 i
0.291 - 0.212 i
11
10.5616
0.445
12
52.7312
112. 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
-1.2044 + 0.e-4 i
0.00045 + 0.00045 i
Singularities of quadratic [6, 6, 6] approximant
2
-1.2044 - 0.e-4 i
0.00045 - 0.00045 i
3
1.3344 + 0.4383 i
0.013 + 0.155 i
4
1.3344 - 0.4383 i
0.013 - 0.155 i
5
1.4516
0.14
6
1.5749
0.216 i
7
2.2698 + 1.2789 i
0.129 + 0.147 i
8
2.2698 - 1.2789 i
0.129 - 0.147 i
9
-2.8954 + 0.3587 i
0.207 - 0.158 i
10
-2.8954 - 0.3587 i
0.207 + 0.158 i
11
3.705
0.266
12
-7.4259
0.293
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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
1.3269 + 0.4253 i
0.0639 + 0.0889 i
Singularities of quadratic [7, 6, 6] approximant
2
1.3269 - 0.4253 i
0.0639 - 0.0889 i
3
1.5198 + 0.8033 i
0.0483 + 0.0344 i
4
1.5198 - 0.8033 i
0.0483 - 0.0344 i
5
1.5882 + 0.9294 i
0.0515 - 0.0357 i
6
1.5882 - 0.9294 i
0.0515 + 0.0357 i
7
1.9861
0.623
8
-2.9236 + 1.1453 i
0.0439 - 0.0208 i
9
-2.9236 - 1.1453 i
0.0439 + 0.0208 i
10
-3.4221 + 2.0121 i
0.0315 + 0.0334 i
11
-3.4221 - 2.0121 i
0.0315 - 0.0334 i
12
6.2878
22.1 i
13
-16.9368
0.226
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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
1.3289 + 0.4715 i
0.0777 - 0.0876 i
Singularities of quadratic [7, 7, 6] approximant
2
1.3289 - 0.4715 i
0.0777 + 0.0876 i
3
1.4834 + 0.0348 i
0.0384 - 0.0309 i
4
1.4834 - 0.0348 i
0.0384 + 0.0309 i
5
-1.8257
0.00382
6
-1.8319
0.00383 i
7
1.9951
0.756
8
2.0405 + 0.4113 i
1.52 + 0.932 i
9
2.0405 - 0.4113 i
1.52 - 0.932 i
10
-3.1797 + 0.7535 i
0.121 - 0.231 i
11
-3.1797 - 0.7535 i
0.121 + 0.231 i
12
-4.5201
0.462
13
-11.3576
0.193 i
14
13.4377
0.286 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
1.3287 + 0.4714 i
0.077 - 0.0869 i
Singularities of quadratic [7, 7, 7] approximant
2
1.3287 - 0.4714 i
0.077 + 0.0869 i
3
1.4742 + 0.032 i
0.0361 - 0.0295 i
4
1.4742 - 0.032 i
0.0361 + 0.0295 i
5
-1.8017
0.00338
6
-1.8072
0.00339 i
7
2.0103
0.886
8
2.0467 + 0.4274 i
1.64 + 0.734 i
9
2.0467 - 0.4274 i
1.64 - 0.734 i
10
-3.1822 + 0.7802 i
0.101 - 0.208 i
11
-3.1822 - 0.7802 i
0.101 + 0.208 i
12
-4.5288
0.556
13
-10.5615
0.191 i
14
14.2209
0.283 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
1.3445 + 0.4734 i
0.142 - 0.146 i
Singularities of quadratic [8, 7, 7] approximant
2
1.3445 - 0.4734 i
0.142 + 0.146 i
3
1.5272 + 0.3767 i
0.231 + 0.153 i
4
1.5272 - 0.3767 i
0.231 - 0.153 i
5
1.5942 + 0.3868 i
0.551 - 0.391 i
6
1.5942 - 0.3868 i
0.551 + 0.391 i
7
-2.1786 + 0.0082 i
0.0421 + 0.0425 i
8
-2.1786 - 0.0082 i
0.0421 - 0.0425 i
9
2.4941
0.614
10
-2.9062 + 0.4455 i
0.117 - 0.331 i
11
-2.9062 - 0.4455 i
0.117 + 0.331 i
12
-5.478
0.21
13
5.5898
1.17 i
14
-22.8742
0.437 i
15
24.136
8.2
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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
1.3421 + 0.4726 i
0.126 - 0.137 i
Singularities of quadratic [8, 8, 7] approximant
2
1.3421 - 0.4726 i
0.126 + 0.137 i
3
1.5532 + 0.3584 i
0.232 + 0.0989 i
4
1.5532 - 0.3584 i
0.232 - 0.0989 i
5
1.6181 + 0.3722 i
0.341 - 0.502 i
6
1.6181 - 0.3722 i
0.341 + 0.502 i
7
-2.2538 + 0.0234 i
0.0223 + 0.0227 i
8
-2.2538 - 0.0234 i
0.0223 - 0.0227 i
9
2.4166
0.602
10
-2.8127 + 0.4055 i
0.121 - 0.123 i
11
-2.8127 - 0.4055 i
0.121 + 0.123 i
12
-6.3714
0.207
13
6.9747
0.511 i
14
-13.0899
34.2 i
15
-6.0169 + 15.0734 i
0.361 + 0.128 i
16
-6.0169 - 15.0734 i
0.361 - 0.128 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
1.3385 + 0.473 i
0.11 - 0.113 i
Singularities of quadratic [8, 8, 8] approximant
2
1.3385 - 0.473 i
0.11 + 0.113 i
3
1.6094 + 0.2952 i
0.217 - 0.0585 i
4
1.6094 - 0.2952 i
0.217 + 0.0585 i
5
1.7671
0.225
6
1.8038 + 0.4129 i
3.63 - 5.27 i
7
1.8038 - 0.4129 i
3.63 + 5.27 i
8
-2.2117 + 0.003 i
0.262 + 0.3 i
9
-2.2117 - 0.003 i
0.262 - 0.3 i
10
-2.8904 + 0.4187 i
0.223 - 0.306 i
11
-2.8904 - 0.4187 i
0.223 + 0.306 i
12
3.1263
0.785 i
13
4.2571 + 1.2608 i
0.803 + 0.446 i
14
4.2571 - 1.2608 i
0.803 - 0.446 i
15
-5.2366
0.163
16
36.0696
3.16
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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
1.3377 + 0.4735 i
0.108 - 0.107 i
Singularities of quadratic [9, 8, 8] approximant
2
1.3377 - 0.4735 i
0.108 + 0.107 i
3
1.6175 + 0.2763 i
0.197 - 0.0843 i
4
1.6175 - 0.2763 i
0.197 + 0.0843 i
5
1.6811
0.172
6
1.8269 + 0.4573 i
8.55 + 3.49 i
7
1.8269 - 0.4573 i
8.55 - 3.49 i
8
-2.2031
0.102
9
-2.2176
0.109 i
10
-2.8991 + 0.4149 i
0.271 - 0.347 i
11
-2.8991 - 0.4149 i
0.271 + 0.347 i
12
3.0495
0.729 i
13
4.3306 + 1.32 i
0.558 + 0.495 i
14
4.3306 - 1.32 i
0.558 - 0.495 i
15
-5.1258
0.153
16
18.2038 + 30.0113 i
0.263 + 0.621 i
17
18.2038 - 30.0113 i
0.263 - 0.621 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
1.3429 + 0.4693 i
0.109 - 0.163 i
Singularities of quadratic [9, 9, 8] approximant
2
1.3429 - 0.4693 i
0.109 + 0.163 i
3
1.5739 + 0.3787 i
0.0948 + 0.249 i
4
1.5739 - 0.3787 i
0.0948 - 0.249 i
5
1.5743 + 0.4019 i
0.249 - 0.00642 i
6
1.5743 - 0.4019 i
0.249 + 0.00642 i
7
-2.0887 + 0.0213 i
0.00266 + 0.00265 i
8
-2.0887 - 0.0213 i
0.00266 - 0.00265 i
9
2.5156
0.72
10
-2.6137 + 0.5876 i
0.0124 - 0.0191 i
11
-2.6137 - 0.5876 i
0.0124 + 0.0191 i
12
-3.5354 + 0.4288 i
0.0276 - 0.0414 i
13
-3.5354 - 0.4288 i
0.0276 + 0.0414 i
14
-4.4536
0.0259
15
-8.1174
0.0807 i
16
8.473
0.287 i
17
-3.4146 + 8.3854 i
0.097 + 0.0607 i
18
-3.4146 - 8.3854 i
0.097 - 0.0607 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
1.3439 + 0.4677 i
0.0996 - 0.181 i
Singularities of quadratic [9, 9, 9] approximant
2
1.3439 - 0.4677 i
0.0996 + 0.181 i
3
1.5508 + 0.4274 i
0.28 + 0.125 i
4
1.5508 - 0.4274 i
0.28 - 0.125 i
5
1.5663 + 0.3848 i
0.0508 + 0.505 i
6
1.5663 - 0.3848 i
0.0508 - 0.505 i
7
-2.1895 + 0.0185 i
0.0143 + 0.0138 i
8
-2.1895 - 0.0185 i
0.0143 - 0.0138 i
9
-0.2441 + 2.2952 i
0.00111 + 0.0033 i
10
-0.2441 - 2.2952 i
0.00111 - 0.0033 i
11
-0.2452 + 2.2965 i
0.0033 - 0.00111 i
12
-0.2452 - 2.2965 i
0.0033 + 0.00111 i
13
2.6102
0.81
14
-2.8828 + 0.4709 i
0.033 - 0.224 i
15
-2.8828 - 0.4709 i
0.033 + 0.224 i
16
-5.4702
0.238
17
6.6178
0.453 i
18
-91.8501
0.251 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
1.3427 + 0.4681 i
0.0957 - 0.168 i
Singularities of quadratic [10, 9, 9] approximant
2
1.3427 - 0.4681 i
0.0957 + 0.168 i
3
1.5663 + 0.3876 i
0.136 + 0.35 i
4
1.5663 - 0.3876 i
0.136 - 0.35 i
5
1.5695 + 0.4216 i
0.322 + 0.0551 i
6
1.5695 - 0.4216 i
0.322 - 0.0551 i
7
-0.6274 + 1.5235 i
0.0000757 + 0.000274 i
8
-0.6274 - 1.5235 i
0.0000757 - 0.000274 i
9
-0.6274 + 1.5236 i
0.000274 - 0.0000757 i
10
-0.6274 - 1.5236 i
0.000274 + 0.0000757 i
11
-2.1919 + 0.0372 i
0.00531 + 0.00486 i
12
-2.1919 - 0.0372 i
0.00531 - 0.00486 i
13
2.5207
0.701
14
-2.7957 + 0.5187 i
0.00144 + 0.0721 i
15
-2.7957 - 0.5187 i
0.00144 - 0.0721 i
16
6.0599
0.913 i
17
-7.731 + 2.8384 i
0.417 + 0.0864 i
18
-7.731 - 2.8384 i
0.417 - 0.0864 i
19
23.3721
2.26
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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
1.3427 + 0.4681 i
0.0957 - 0.168 i
Singularities of quadratic [10, 10, 9] approximant
2
1.3427 - 0.4681 i
0.0957 + 0.168 i
3
1.5663 + 0.3877 i
0.137 + 0.35 i
4
1.5663 - 0.3877 i
0.137 - 0.35 i
5
1.5695 + 0.4217 i
0.322 + 0.0549 i
6
1.5695 - 0.4217 i
0.322 - 0.0549 i
7
-0.6269 + 1.5239 i
0.0000754 + 0.000273 i
8
-0.6269 - 1.5239 i
0.0000754 - 0.000273 i
9
-0.6269 + 1.524 i
0.000273 - 0.0000754 i
10
-0.6269 - 1.524 i
0.000273 + 0.0000754 i
11
-2.1918 + 0.0373 i
0.00529 + 0.00484 i
12
-2.1918 - 0.0373 i
0.00529 - 0.00484 i
13
2.5204
0.701
14
-2.7952 + 0.5192 i
0.00157 + 0.0716 i
15
-2.7952 - 0.5192 i
0.00157 - 0.0716 i
16
6.0476
0.925 i
17
-7.7017 + 2.8647 i
0.406 + 0.0839 i
18
-7.7017 - 2.8647 i
0.406 - 0.0839 i
19
22.8908
2.14
20
261832.5183
121. 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
-0.0755 + 1.3826 i
2.92e-6 - 0.000063 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.0755 - 1.3826 i
2.92e-6 + 0.000063 i
3
-0.0756 + 1.3826 i
0.000063 + 2.92e-6 i
4
-0.0756 - 1.3826 i
0.000063 - 2.92e-6 i
5
1.3459 + 0.4717 i
0.166 - 0.167 i
6
1.3459 - 0.4717 i
0.166 + 0.167 i
7
1.5517 + 0.3898 i
0.239 + 0.0454 i
8
1.5517 - 0.3898 i
0.239 - 0.0454 i
9
1.5863 + 0.3208 i
0.195 + 0.308 i
10
1.5863 - 0.3208 i
0.195 - 0.308 i
11
-2.1698
0.00452
12
-2.3227
0.005 i
13
-2.6131
0.0178
14
2.7271
1.59
15
-3.5603 + 0.8389 i
0.0628 + 0.0105 i
16
-3.5603 - 0.8389 i
0.0628 - 0.0105 i
17
2.7039 + 3.4502 i
0.0403 - 0.015 i
18
2.7039 - 3.4502 i
0.0403 + 0.015 i
19
2.6108 + 4.5427 i
0.00077 - 0.0417 i
20
2.6108 - 4.5427 i
0.00077 + 0.0417 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
-0.4099 + 1.0662 i
8.34e-6 - 6.47e-6 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.4099 - 1.0662 i
8.34e-6 + 6.47e-6 i
3
-0.4099 + 1.0662 i
6.47e-6 + 8.34e-6 i
4
-0.4099 - 1.0662 i
6.47e-6 - 8.34e-6 i
5
1.3442 + 0.4689 i
0.116 - 0.178 i
6
1.3442 - 0.4689 i
0.116 + 0.178 i
7
1.5585 + 0.4117 i
0.27 + 0.0786 i
8
1.5585 - 0.4117 i
0.27 - 0.0786 i
9
1.5747 + 0.3682 i
0.104 + 0.397 i
10
1.5747 - 0.3682 i
0.104 - 0.397 i
11
-2.1564 + 0.2817 i
0.000127 + 0.000909 i
12
-2.1564 - 0.2817 i
0.000127 - 0.000909 i
13
-2.1821
0.000591
14
-2.4411
0.00146 i
15
2.559
0.794
16
-2.6175 + 0.9533 i
0.00505 - 0.00397 i
17
-2.6175 - 0.9533 i
0.00505 + 0.00397 i
18
-4.364 + 5.2235 i
0.041 - 0.0454 i
19
-4.364 - 5.2235 i
0.041 + 0.0454 i
20
7.5909
0.43 i
21
44.287
4.36
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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
-0.4435 + 0.978 i
3.68e-6 - 4.55e-7 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.4435 - 0.978 i
3.68e-6 + 4.55e-7 i
3
-0.4435 + 0.978 i
4.55e-7 + 3.68e-6 i
4
-0.4435 - 0.978 i
4.55e-7 - 3.68e-6 i
5
1.3443 + 0.4688 i
0.117 - 0.181 i
6
1.3443 - 0.4688 i
0.117 + 0.181 i
7
1.5618 + 0.4107 i
0.274 + 0.0677 i
8
1.5618 - 0.4107 i
0.274 - 0.0677 i
9
1.5738 + 0.3657 i
0.124 + 0.363 i
10
1.5738 - 0.3657 i
0.124 - 0.363 i
11
-1.6899 + 0.0041 i
0.0000243 + 0.0000247 i
12
-1.6899 - 0.0041 i
0.0000243 - 0.0000247 i
13
-1.9988 + 0.0771 i
0.000205 + 0.0000929 i
14
-1.9988 - 0.0771 i
0.000205 - 0.0000929 i
15
2.5043
0.735
16
-2.542 + 0.8338 i
0.00487 + 0.000812 i
17
-2.542 - 0.8338 i
0.00487 - 0.000812 i
18
4.9041
124. i
19
-3.9513 + 4.8918 i
0.0284 - 0.0275 i
20
-3.9513 - 4.8918 i
0.0284 + 0.0275 i
21
6.7524
0.33
22
35.1353
0.336 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
-0.2627 + 1.2064 i
1.38e-6 + 0.000021 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.2627 - 1.2064 i
1.38e-6 - 0.000021 i
3
-0.2627 + 1.2064 i
0.000021 - 1.38e-6 i
4
-0.2627 - 1.2064 i
0.000021 + 1.38e-6 i
5
1.3425 + 0.4675 i
0.0874 - 0.165 i
6
1.3425 - 0.4675 i
0.0874 + 0.165 i
7
1.5625 + 0.4026 i
0.0216 + 0.439 i
8
1.5625 - 0.4026 i
0.0216 - 0.439 i
9
1.5572 + 0.4306 i
0.296 + 0.111 i
10
1.5572 - 0.4306 i
0.296 - 0.111 i
11
0.7015 + 1.8486 i
0.000655 - 0.0011 i
12
0.7015 - 1.8486 i
0.000655 + 0.0011 i
13
0.7003 + 1.8494 i
0.00109 + 0.000656 i
14
0.7003 - 1.8494 i
0.00109 - 0.000656 i
15
-2.1751 + 0.0435 i
0.00343 + 0.00299 i
16
-2.1751 - 0.0435 i
0.00343 - 0.00299 i
17
2.632
0.808
18
-2.7801 + 0.5694 i
0.0155 + 0.0474 i
19
-2.7801 - 0.5694 i
0.0155 - 0.0474 i
20
7.029
0.344 i
21
-7.7361
90.8
22
-18.4445
0.226 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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