Singularities of Møller-Plesset series: example "a30"

Molecule BH. Basis aug-cc-pVTZ. Structure "mpn_Rfci"

Content


Examplesa1a2a8a16a22a30a38a44a45a51a62a69a75a83a84a85a86a87a88a90a91
MoleculeArBHBHBHBHBHBHBO+C2CN+N2HFHFHClHClF-Cl-Cl-NeOH-SH-
Basisaug-cc-pVDZcc-pVDZcc-pVTZcc-pVQZaug-cc-pVDZaug-cc-pVTZaug-cc-pVQZcc-pVDZcc-pVDZcc-pVDZcc-pVDZcc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-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 [6, 6, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4297 + 0.022 i
0.101 - 0.137 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4297 - 0.022 i
0.101 + 0.137 i
3
1.6579 + 0.4269 i
0.176 + 0.157 i
4
1.6579 - 0.4269 i
0.176 - 0.157 i
5
2.4747
8.67
6
-2.9675
0.00524
7
-2.7124 + 1.6161 i
0.000715 + 0.0049 i
8
-2.7124 - 1.6161 i
0.000715 - 0.0049 i
9
-2.7035 + 2.1193 i
0.00663 - 0.00088 i
10
-2.7035 - 2.1193 i
0.00663 + 0.00088 i
11
18.0867
4.45 i
12
-57.7998
1.46 i
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Table 2. 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
0.2544 + 0.e-5 i
6.27e-8 - 6.27e-8 i
Singularities of quadratic [6, 6, 6] approximant
2
0.2544 - 0.e-5 i
6.27e-8 + 6.27e-8 i
3
1.4488
0.139
4
1.5142
0.765 i
5
1.6549 + 0.4684 i
0.0684 + 0.111 i
6
1.6549 - 0.4684 i
0.0684 - 0.111 i
7
2.5653
5.24e4
8
-2.8514 + 0.814 i
0.004 + 0.00279 i
9
-2.8514 - 0.814 i
0.004 - 0.00279 i
10
-3.2502 + 1.5582 i
0.00425 - 0.0069 i
11
-3.2502 - 1.5582 i
0.00425 + 0.0069 i
12
-6.5728
0.235
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Table 3. 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
-0.4278 + 0.e-5 i
3.68e-7 + 3.68e-7 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.4278 - 0.e-5 i
3.68e-7 - 3.68e-7 i
3
1.3852
0.0349
4
1.4994
0.0931 i
5
1.5775 + 0.4526 i
0.0601 + 0.0246 i
6
1.5775 - 0.4526 i
0.0601 - 0.0246 i
7
-3.0933
0.0158
8
-2.2854 + 2.8671 i
0.00722 - 0.00361 i
9
-2.2854 - 2.8671 i
0.00722 + 0.00361 i
10
3.9442 + 1.1436 i
0.183 - 0.199 i
11
3.9442 - 1.1436 i
0.183 + 0.199 i
12
-3.7911 + 2.7039 i
0.000483 + 0.00862 i
13
-3.7911 - 2.7039 i
0.000483 - 0.00862 i
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Table 4. 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
-0.2539 + 0.4889 i
2.44e-7 + 4.e-8 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.2539 - 0.4889 i
2.44e-7 - 4.e-8 i
3
-0.2539 + 0.4889 i
4.e-8 - 2.44e-7 i
4
-0.2539 - 0.4889 i
4.e-8 + 2.44e-7 i
5
1.0336 + 0.0022 i
0.000139 - 0.000137 i
6
1.0336 - 0.0022 i
0.000139 + 0.000137 i
7
1.4468
0.0193
8
1.8305 + 0.697 i
0.0404 + 0.0382 i
9
1.8305 - 0.697 i
0.0404 - 0.0382 i
10
-2.3396 + 0.6743 i
0.000511 + 0.000222 i
11
-2.3396 - 0.6743 i
0.000511 - 0.000222 i
12
-3.6688
0.00131
13
-6.5053
0.0178 i
14
14.9597
4.58 i
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Table 5. 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
-0.6159 + 0.e-5 i
2.25e-7 + 2.25e-7 i
Singularities of quadratic [7, 7, 7] approximant
2
-0.6159 - 0.e-5 i
2.25e-7 - 2.25e-7 i
3
1.4167
0.0233
4
-0.1364 + 1.5203 i
0.0000567 - 0.0000396 i
5
-0.1364 - 1.5203 i
0.0000567 + 0.0000396 i
6
-0.1372 + 1.5298 i
0.0000395 + 0.0000577 i
7
-0.1372 - 1.5298 i
0.0000395 - 0.0000577 i
8
1.5602 + 0.634 i
0.006 - 0.0148 i
9
1.5602 - 0.634 i
0.006 + 0.0148 i
10
2.2502
0.168 i
11
-2.4368 + 0.7254 i
0.000599 + 0.0000455 i
12
-2.4368 - 0.7254 i
0.000599 - 0.0000455 i
13
-4.5002
0.00475
14
9.9755
1.57
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Table 6. 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
-0.6273 + 0.e-5 i
2.86e-7 + 2.86e-7 i
Singularities of quadratic [8, 7, 7] approximant
2
-0.6273 - 0.e-5 i
2.86e-7 - 2.86e-7 i
3
1.4176
0.0237
4
-0.045 + 1.5312 i
0.0000464 - 0.0000671 i
5
-0.045 - 1.5312 i
0.0000464 + 0.0000671 i
6
-0.0417 + 1.5399 i
0.0000679 + 0.0000472 i
7
-0.0417 - 1.5399 i
0.0000679 - 0.0000472 i
8
1.5612 + 0.6323 i
0.00582 - 0.0152 i
9
1.5612 - 0.6323 i
0.00582 + 0.0152 i
10
2.2205
0.173 i
11
-2.5566 + 0.7565 i
0.000884 - 0.0000102 i
12
-2.5566 - 0.7565 i
0.000884 + 0.0000102 i
13
7.1154
71.4
14
-8.011 + 2.832 i
0.0584 + 0.0762 i
15
-8.011 - 2.832 i
0.0584 - 0.0762 i
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Table 7. 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
0.1674
0
Singularities of quadratic [8, 8, 7] approximant
2
0.1674
0
3
-0.6678
6.3e-7
4
-0.6678
6.3e-7 i
5
1.4139
0.0188
6
1.5706 + 0.731 i
0.0103 - 0.00376 i
7
1.5706 - 0.731 i
0.0103 + 0.00376 i
8
0.8027 + 1.8393 i
0.000814 - 0.0000936 i
9
0.8027 - 1.8393 i
0.000814 + 0.0000936 i
10
0.903 + 1.9347 i
0.0000916 + 0.00099 i
11
0.903 - 1.9347 i
0.0000916 - 0.00099 i
12
-2.8947
0.00439
13
-2.6815 + 3.7051 i
0.0134 + 0.00405 i
14
-2.6815 - 3.7051 i
0.0134 - 0.00405 i
15
-4.9868
0.0219 i
16
11.6828
0.398 i
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Table 8. 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
-0.1085 + 0.6476 i
1.09e-7 - 2.15e-7 i
Singularities of quadratic [8, 8, 8] approximant
2
-0.1085 - 0.6476 i
1.09e-7 + 2.15e-7 i
3
-0.1085 + 0.6476 i
2.15e-7 + 1.09e-7 i
4
-0.1085 - 0.6476 i
2.15e-7 - 1.09e-7 i
5
-1.0572 + 0.4279 i
6.99e-7 - 1.16e-6 i
6
-1.0572 - 0.4279 i
6.99e-7 + 1.16e-6 i
7
-1.0629 + 0.4191 i
1.14e-6 + 6.98e-7 i
8
-1.0629 - 0.4191 i
1.14e-6 - 6.98e-7 i
9
1.4214
0.0316
10
1.5569 + 0.5709 i
0.00504 + 0.0208 i
11
1.5569 - 0.5709 i
0.00504 - 0.0208 i
12
1.8458
1.34 i
13
-1.7293 + 0.6455 i
0.0000238 - 0.0000129 i
14
-1.7293 - 0.6455 i
0.0000238 + 0.0000129 i
15
-2.036
0.0000297
16
4.9725
0.758
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Table 9. 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
-0.1036 + 0.69 i
1.62e-7 - 3.e-7 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.1036 - 0.69 i
1.62e-7 + 3.e-7 i
3
-0.1036 + 0.6901 i
3.e-7 + 1.62e-7 i
4
-0.1036 - 0.6901 i
3.e-7 - 1.62e-7 i
5
-0.8547 + 0.427 i
2.49e-8 - 6.63e-7 i
6
-0.8547 - 0.427 i
2.49e-8 + 6.63e-7 i
7
-0.8558 + 0.4266 i
6.63e-7 + 2.62e-8 i
8
-0.8558 - 0.4266 i
6.63e-7 - 2.62e-8 i
9
1.4232
0.0343
10
1.5581 + 0.5622 i
0.00728 + 0.0214 i
11
1.5581 - 0.5622 i
0.00728 - 0.0214 i
12
1.8046
3.66 i
13
-1.9453 + 0.728 i
0.0000737 - 0.0000352 i
14
-1.9453 - 0.728 i
0.0000737 + 0.0000352 i
15
-2.7579
0.000227
16
4.5572
0.626
17
-46.3729
0.179 i
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Table 10. 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
-0.0572 + 0.6864 i
1.94e-7 - 5.62e-9 i
Singularities of quadratic [9, 9, 8] approximant
2
-0.0572 - 0.6864 i
1.94e-7 + 5.62e-9 i
3
-0.0572 + 0.6864 i
5.61e-9 + 1.94e-7 i
4
-0.0572 - 0.6864 i
5.61e-9 - 1.94e-7 i
5
-0.7467 + 0.3531 i
1.26e-8 - 2.01e-7 i
6
-0.7467 - 0.3531 i
1.26e-8 + 2.01e-7 i
7
-0.7469 + 0.3529 i
2.01e-7 + 1.27e-8 i
8
-0.7469 - 0.3529 i
2.01e-7 - 1.27e-8 i
9
1.4405
0.0549
10
1.5293 + 0.5604 i
0.00907 + 0.013 i
11
1.5293 - 0.5604 i
0.00907 - 0.013 i
12
1.8201
1.58 i
13
-2.1835 + 0.9826 i
0.0000748 - 0.000178 i
14
-2.1835 - 0.9826 i
0.0000748 + 0.000178 i
15
-3.0645 + 4.0175 i
0.000215 + 0.00444 i
16
-3.0645 - 4.0175 i
0.000215 - 0.00444 i
17
4.4049 + 5.3288 i
0.0593 + 0.00741 i
18
4.4049 - 5.3288 i
0.0593 - 0.00741 i
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Table 11. 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
0.2904
4.63e-10
Singularities of quadratic [9, 9, 9] approximant
2
0.2904
4.63e-10 i
3
-0.0998 + 0.7068 i
3.89e-8 + 2.42e-7 i
4
-0.0998 - 0.7068 i
3.89e-8 - 2.42e-7 i
5
-0.0998 + 0.7068 i
2.42e-7 - 3.89e-8 i
6
-0.0998 - 0.7068 i
2.42e-7 + 3.89e-8 i
7
-0.8206 + 0.4201 i
7.34e-8 + 3.7e-7 i
8
-0.8206 - 0.4201 i
7.34e-8 - 3.7e-7 i
9
-0.8216 + 0.4197 i
3.7e-7 - 7.26e-8 i
10
-0.8216 - 0.4197 i
3.7e-7 + 7.26e-8 i
11
1.4077
0.0221
12
1.5798 + 0.5686 i
0.00113 + 0.0296 i
13
1.5798 - 0.5686 i
0.00113 - 0.0296 i
14
1.8407
1.93 i
15
-1.9665 + 0.7729 i
0.0000668 - 0.000053 i
16
-1.9665 - 0.7729 i
0.0000668 + 0.000053 i
17
-2.967
0.000344
18
4.3754
0.541
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Table 12. 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
-0.0505 + 0.9211 i
1.27e-7 + 7.6e-8 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.0505 - 0.9211 i
1.27e-7 - 7.6e-8 i
3
-0.0511 + 0.9234 i
7.77e-8 - 1.27e-7 i
4
-0.0511 - 0.9234 i
7.77e-8 + 1.27e-7 i
5
-0.4985 + 0.8071 i
3.47e-8 - 6.74e-8 i
6
-0.4985 - 0.8071 i
3.47e-8 + 6.74e-8 i
7
-0.5035 + 0.8064 i
6.72e-8 + 3.53e-8 i
8
-0.5035 - 0.8064 i
6.72e-8 - 3.53e-8 i
9
-1.2513 + 0.248 i
2.08e-7 + 3.17e-7 i
10
-1.2513 - 0.248 i
2.08e-7 - 3.17e-7 i
11
1.3084 + 0.2478 i
0.0000347 + 0.00106 i
12
1.3084 - 0.2478 i
0.0000347 - 0.00106 i
13
1.3379 + 0.3934 i
0.000353 + 0.00113 i
14
1.3379 - 0.3934 i
0.000353 - 0.00113 i
15
-1.4759 + 0.0205 i
1.48e-7 + 1.23e-7 i
16
-1.4759 - 0.0205 i
1.48e-7 - 1.23e-7 i
17
-1.145 + 1.8434 i
0.0000206 - 0.0000143 i
18
-1.145 - 1.8434 i
0.0000206 + 0.0000143 i
19
11.9989
0.156
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Table 13. 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
-0.4539 + 0.5762 i
1.94e-9 - 7.08e-9 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.4539 - 0.5762 i
1.94e-9 + 7.08e-9 i
3
-0.4537 + 0.5765 i
7.09e-9 + 1.93e-9 i
4
-0.4537 - 0.5765 i
7.09e-9 - 1.93e-9 i
5
-0.7491 + 0.1846 i
2.6e-9 + 5.15e-9 i
6
-0.7491 - 0.1846 i
2.6e-9 - 5.15e-9 i
7
-0.7501 + 0.1845 i
5.17e-9 - 2.59e-9 i
8
-0.7501 - 0.1845 i
5.17e-9 + 2.59e-9 i
9
-0.0174 + 0.831 i
4.5e-8 + 4.91e-8 i
10
-0.0174 - 0.831 i
4.5e-8 - 4.91e-8 i
11
-0.0172 + 0.8317 i
4.94e-8 - 4.51e-8 i
12
-0.0172 - 0.8317 i
4.94e-8 + 4.51e-8 i
13
1.254 + 0.2117 i
0.000287 + 0.000383 i
14
1.254 - 0.2117 i
0.000287 - 0.000383 i
15
1.3451 + 0.3132 i
0.00108 + 0.000305 i
16
1.3451 - 0.3132 i
0.00108 - 0.000305 i
17
-2.3386 + 1.6715 i
0.000163 - 0.000156 i
18
-2.3386 - 1.6715 i
0.000163 + 0.000156 i
19
3.382
0.565
20
19.704
2.22 i
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Table 14. 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
-0.3427 + 0.7428 i
4.7e-9 + 3.51e-8 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.3427 - 0.7428 i
4.7e-9 - 3.51e-8 i
3
-0.3426 + 0.7436 i
3.51e-8 - 4.71e-9 i
4
-0.3426 - 0.7436 i
3.51e-8 + 4.71e-9 i
5
0.0856 + 0.9185 i
1.95e-7 - 9.24e-9 i
6
0.0856 - 0.9185 i
1.95e-7 + 9.24e-9 i
7
0.087 + 0.9184 i
1.03e-8 + 1.96e-7 i
8
0.087 - 0.9184 i
1.03e-8 - 1.96e-7 i
9
-1.0382 + 0.3901 i
1.84e-7 + 7.37e-9 i
10
-1.0382 - 0.3901 i
1.84e-7 - 7.37e-9 i
11
-1.0444 + 0.4135 i
1.07e-9 + 1.93e-7 i
12
-1.0444 - 0.4135 i
1.07e-9 - 1.93e-7 i
13
1.3528 + 0.2502 i
0.00043 - 0.00195 i
14
1.3528 - 0.2502 i
0.00043 + 0.00195 i
15
1.3651 + 0.435 i
0.000519 - 0.0016 i
16
1.3651 - 0.435 i
0.000519 + 0.0016 i
17
-1.6308 + 1.3208 i
0.0000166 - 0.0000187 i
18
-1.6308 - 1.3208 i
0.0000166 + 0.0000187 i
19
4.7439
1.59
20
-5.2008
0.106
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Table 15. 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
0.0283
0
Singularities of quadratic [11, 10, 10] approximant
2
0.0283
0
3
-0.3549 + 0.7407 i
7.32e-9 + 2.02e-8 i
4
-0.3549 - 0.7407 i
7.32e-9 - 2.02e-8 i
5
-0.3552 + 0.7418 i
2.02e-8 - 7.31e-9 i
6
-0.3552 - 0.7418 i
2.02e-8 + 7.31e-9 i
7
0.0731 + 0.9268 i
1.32e-7 - 4.84e-8 i
8
0.0731 - 0.9268 i
1.32e-7 + 4.84e-8 i
9
0.0751 + 0.9275 i
4.94e-8 + 1.33e-7 i
10
0.0751 - 0.9275 i
4.94e-8 - 1.33e-7 i
11
-1.0067 + 0.3618 i
8.98e-8 + 3.4e-9 i
12
-1.0067 - 0.3618 i
8.98e-8 - 3.4e-9 i
13
-1.0182 + 0.3815 i
9.57e-8 i
14
-1.0182 - 0.3815 i
-9.57e-8 i
15
1.3693 + 0.2535 i
0.000657 - 0.00253 i
16
1.3693 - 0.2535 i
0.000657 + 0.00253 i
17
1.3607 + 0.4401 i
0.000453 - 0.00161 i
18
1.3607 - 0.4401 i
0.000453 + 0.00161 i
19
-1.5381 + 1.5761 i
9.44e-6 + 0.0000237 i
20
-1.5381 - 1.5761 i
9.44e-6 - 0.0000237 i
21
14.2055
0.155
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Table 16. 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
-0.8654 + 0.1615 i
3.92e-8 + 5.06e-8 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.8654 - 0.1615 i
3.92e-8 - 5.06e-8 i
3
-0.8663 + 0.1625 i
5.09e-8 - 3.93e-8 i
4
-0.8663 - 0.1625 i
5.09e-8 + 3.93e-8 i
5
-0.4731 + 0.7593 i
9.99e-8 - 7.08e-8 i
6
-0.4731 - 0.7593 i
9.99e-8 + 7.08e-8 i
7
-0.4722 + 0.7605 i
7.1e-8 + 9.98e-8 i
8
-0.4722 - 0.7605 i
7.1e-8 - 9.98e-8 i
9
-0.063 + 0.993 i
4.13e-7 - 8.85e-8 i
10
-0.063 - 0.993 i
4.13e-7 + 8.85e-8 i
11
-0.066 + 0.9953 i
8.3e-8 + 4.13e-7 i
12
-0.066 - 0.9953 i
8.3e-8 - 4.13e-7 i
13
1.3754 + 0.5234 i
0.00198 - 0.000523 i
14
1.3754 - 0.5234 i
0.00198 + 0.000523 i
15
1.5194 + 0.2476 i
0.0201 - 0.00555 i
16
1.5194 - 0.2476 i
0.0201 + 0.00555 i
17
0.618 + 1.8043 i
0.0000661 + 0.0000298 i
18
0.618 - 1.8043 i
0.0000661 - 0.0000298 i
19
0.368 + 1.8769 i
0.0000438 - 0.0000228 i
20
0.368 - 1.8769 i
0.0000438 + 0.0000228 i
21
-2.4905
0.000475
22
-6.4821
0.0147 i
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Table 17. 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
-0.7353
6.02e-10
Singularities of quadratic [11, 11, 11] approximant
2
-0.7361
6.01e-10 i
3
-0.46 + 0.757 i
1.01e-8 - 7.35e-9 i
4
-0.46 - 0.757 i
1.01e-8 + 7.35e-9 i
5
-0.4556 + 0.7608 i
7.56e-9 + 1.01e-8 i
6
-0.4556 - 0.7608 i
7.56e-9 - 1.01e-8 i
7
-0.0479 + 0.9828 i
6.35e-8 - 3.57e-8 i
8
-0.0479 - 0.9828 i
6.35e-8 + 3.57e-8 i
9
-0.0562 + 0.9891 i
3.2e-8 + 6.44e-8 i
10
-0.0562 - 0.9891 i
3.2e-8 - 6.44e-8 i
11
-0.9872 + 0.2184 i
8.52e-9 + 4.97e-9 i
12
-0.9872 - 0.2184 i
8.52e-9 - 4.97e-9 i
13
-1.0264 + 0.1929 i
7.89e-9 - 7.44e-9 i
14
-1.0264 - 0.1929 i
7.89e-9 + 7.44e-9 i
15
1.3634 + 0.5083 i
0.00104 - 0.00137 i
16
1.3634 - 0.5083 i
0.00104 + 0.00137 i
17
1.6286 + 0.1791 i
0.208 + 0.1 i
18
1.6286 - 0.1791 i
0.208 - 0.1 i
19
0.8234 + 1.6764 i
0.0000393 - 0.0000161 i
20
0.8234 - 1.6764 i
0.0000393 + 0.0000161 i
21
0.3448 + 2.1328 i
0.0000295 + 5.93e-6 i
22
0.3448 - 2.1328 i
0.0000295 - 5.93e-6 i
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Table 18. Singularities with their weights for the quadratic approximant [12, 11, 11]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.3742 + 0.e-5 i
0
Singularities of quadratic [12, 11, 11] approximant
2
0.3742 - 0.e-5 i
0
3
-0.8607 + 0.163 i
5.e-10 + 5.e-9 i
4
-0.8607 - 0.163 i
5.e-10 - 5.e-9 i
5
-0.8655 + 0.1575 i
5.01e-9 - 3.42e-10 i
6
-0.8655 - 0.1575 i
5.01e-9 + 3.42e-10 i
7
-0.4728 + 0.7646 i
6.21e-9 - 8.98e-9 i
8
-0.4728 - 0.7646 i
6.21e-9 + 8.98e-9 i
9
-0.4812 + 0.7631 i
8.91e-9 + 6.46e-9 i
10
-0.4812 - 0.7631 i
8.91e-9 - 6.46e-9 i
11
-0.0648 + 0.9977 i
3.96e-8 + 2.41e-8 i
12
-0.0648 - 0.9977 i
3.96e-8 - 2.41e-8 i
13
-0.0739 + 1.0164 i
2.82e-8 - 3.85e-8 i
14
-0.0739 - 1.0164 i
2.82e-8 + 3.85e-8 i
15
1.3362 + 0.4845 i
0.000113 - 0.000837 i
16
1.3362 - 0.4845 i
0.000113 + 0.000837 i
17
1.5977 + 0.127 i
0.731 + 0.425 i
18
1.5977 - 0.127 i
0.731 - 0.425 i
19
0.0672 + 1.6865 i
1.53e-6 + 2.32e-6 i
20
0.0672 - 1.6865 i
1.53e-6 - 2.32e-6 i
21
0.4688 + 1.6413 i
3.7e-6 + 6.05e-6 i
22
0.4688 - 1.6413 i
3.7e-6 - 6.05e-6 i
23
-5.4507
0.00931
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Table 19. Singularities with their weights for the quadratic approximant [12, 12, 11]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.0273 + 0.6909 i
1.62e-10 - 1.1e-10 i
Singularities of quadratic [12, 12, 11] approximant
2
-0.0273 - 0.6909 i
1.62e-10 + 1.1e-10 i
3
-0.0271 + 0.691 i
1.1e-10 + 1.62e-10 i
4
-0.0271 - 0.691 i
1.1e-10 - 1.62e-10 i
5
-0.4891 + 0.7283 i
1.96e-9 + 1.9e-10 i
6
-0.4891 - 0.7283 i
1.96e-9 - 1.9e-10 i
7
-0.8582 + 0.196 i
9.65e-10 + 1.5e-9 i
8
-0.8582 - 0.196 i
9.65e-10 - 1.5e-9 i
9
-0.4791 + 0.7417 i
-1.99e-9 i
10
-0.4791 - 0.7417 i
1.99e-9 i
11
-0.8718 + 0.1882 i
1.62e-9 - 9.01e-10 i
12
-0.8718 - 0.1882 i
1.62e-9 + 9.01e-10 i
13
-0.0799 + 0.9297 i
3.79e-9 + 1.73e-9 i
14
-0.0799 - 0.9297 i
3.79e-9 - 1.73e-9 i
15
-0.0504 + 0.9351 i
1.01e-9 - 4.6e-9 i
16
-0.0504 - 0.9351 i
1.01e-9 + 4.6e-9 i
17
1.3175 + 0.2559 i
0.000351 - 0.000169 i
18
1.3175 - 0.2559 i
0.000351 + 0.000169 i
19
1.2223 + 0.7092 i
0.000032 - 0.0000304 i
20
1.2223 - 0.7092 i
0.000032 + 0.0000304 i
21
1.2252 + 1.122 i
0.0000291 + 0.0000194 i
22
1.2252 - 1.122 i
0.0000291 - 0.0000194 i
23
0.5437 + 1.8375 i
6.59e-6 + 4.29e-6 i
24
0.5437 - 1.8375 i
6.59e-6 - 4.29e-6 i
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Table 20. Singularities with their weights for the quadratic approximant [12, 12, 12]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.2501 + 0.703 i
0
Singularities of quadratic [12, 12, 12] approximant
2
-0.2501 - 0.703 i
0
3
-0.2485 + 0.7052 i
-1.e-10 i
4
-0.2485 - 0.7052 i
1.e-10 i
5
-0.477 + 0.6942 i
3.07e-10 i
6
-0.477 - 0.6942 i
-3.07e-10 i
7
-0.501 + 0.7178 i
3.68e-10
8
-0.501 - 0.7178 i
3.68e-10
9
-0.8571 + 0.1924 i
3.15e-10
10
-0.8571 - 0.1924 i
3.15e-10
11
-0.8606 + 0.2389 i
-3.62e-10 i
12
-0.8606 - 0.2389 i
3.62e-10 i
13
-0.0337 + 0.9375 i
2.39e-9 + 1.83e-9 i
14
-0.0337 - 0.9375 i
2.39e-9 - 1.83e-9 i
15
-0.0256 + 0.9846 i
3.2e-9 - 2.65e-9 i
16
-0.0256 - 0.9846 i
3.2e-9 + 2.65e-9 i
17
1.3404
0.00083
18
1.2544 + 0.474 i
0.0000498 + 0.00011 i
19
1.2544 - 0.474 i
0.0000498 - 0.00011 i
20
-1.4907 + 0.3006 i
9.11e-9 - 3.21e-8 i
21
-1.4907 - 0.3006 i
9.11e-9 + 3.21e-8 i
22
0.603 + 1.4707 i
1.66e-6 + 8.68e-7 i
23
0.603 - 1.4707 i
1.66e-6 - 8.68e-7 i
24
3.9474
0.102 i
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Examplesa1a2a8a16a22a30a38a44a45a51a62a69a75a83a84a85a86a87a88a90a91
MoleculeArBHBHBHBHBHBHBO+C2CN+N2HFHFHClHClF-Cl-Cl-NeOH-SH-
Basisaug-cc-pVDZcc-pVDZcc-pVTZcc-pVQZaug-cc-pVDZaug-cc-pVTZaug-cc-pVQZcc-pVDZcc-pVDZcc-pVDZcc-pVDZcc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-pVDZ

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