Singularities of Møller-Plesset series: example "a88"

Molecule Ne. Basis aug-cc-pVDZ. 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
0.3042 + 0.e-5 i
4.16e-7 - 4.16e-7 i
Singularities of quadratic [6, 6, 5] approximant
2
0.3042 - 0.e-5 i
4.16e-7 + 4.16e-7 i
3
-0.8214 + 0.0296 i
0.000967 + 0.00131 i
4
-0.8214 - 0.0296 i
0.000967 - 0.00131 i
5
-0.8811
0.00203
6
1.3072 + 2.8509 i
0.00688 + 0.0439 i
7
1.3072 - 2.8509 i
0.00688 - 0.0439 i
8
-3.4019
21. i
9
-2.0582 + 2.7664 i
0.058 + 0.104 i
10
-2.0582 - 2.7664 i
0.058 - 0.104 i
11
3.1277 + 2.7404 i
0.0749 - 0.0663 i
12
3.1277 - 2.7404 i
0.0749 + 0.0663 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
-0.8317 + 0.0028 i
0.0567 - 0.000758 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.8317 - 0.0028 i
0.0567 + 0.000758 i
3
-0.9203 + 0.0525 i
0.00213 + 0.00674 i
4
-0.9203 - 0.0525 i
0.00213 - 0.00674 i
5
-0.9534
0.00556
6
3.0625 + 0.6706 i
0.0664 - 0.729 i
7
3.0625 - 0.6706 i
0.0664 + 0.729 i
8
-3.7494
0.952 i
9
4.3954
0.725
10
-0.7078 + 4.549 i
0.0728 + 0.643 i
11
-0.7078 - 4.549 i
0.0728 - 0.643 i
12
-29.654
0.616
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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
-0.8283 + 0.0115 i
0.00555 + 0.00472 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.8283 - 0.0115 i
0.00555 - 0.00472 i
3
-0.9232 + 0.0419 i
0.000576 + 0.00923 i
4
-0.9232 - 0.0419 i
0.000576 - 0.00923 i
5
-0.9666
0.00755
6
3.0404 + 0.5651 i
0.397 + 0.555 i
7
3.0404 - 0.5651 i
0.397 - 0.555 i
8
4.3981
0.65
9
-0.3677 + 4.4135 i
0.229 + 0.361 i
10
-0.3677 - 4.4135 i
0.229 - 0.361 i
11
-5.028 + 0.5766 i
0.229 - 0.224 i
12
-5.028 - 0.5766 i
0.229 + 0.224 i
13
15.6351
8.71 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
-0.7805
0.000274
Singularities of quadratic [7, 7, 6] approximant
2
-0.791 + 0.0659 i
0.000284 - 0.0000789 i
3
-0.791 - 0.0659 i
0.000284 + 0.0000789 i
4
-0.7963 + 0.0527 i
0.0000316 + 0.00024 i
5
-0.7963 - 0.0527 i
0.0000316 - 0.00024 i
6
2.6224
0.34
7
2.7231
0.745 i
8
-2.7829
41.2 i
9
-1.5653 + 3.1093 i
0.0954 + 0.0497 i
10
-1.5653 - 3.1093 i
0.0954 - 0.0497 i
11
1.5654 + 3.5217 i
0.0426 + 0.0998 i
12
1.5654 - 3.5217 i
0.0426 - 0.0998 i
13
3.9151
2.07
14
11.2879
0.77 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
-0.8088
0.00191
Singularities of quadratic [7, 7, 7] approximant
2
-0.859 + 0.0645 i
0.000872 - 0.00107 i
3
-0.859 - 0.0645 i
0.000872 + 0.00107 i
4
-0.8767 + 0.0797 i
0.00118 + 0.0013 i
5
-0.8767 - 0.0797 i
0.00118 - 0.0013 i
6
1.0909
0.000588
7
1.0909
0.000588 i
8
3.0836 + 0.8228 i
0.284 - 0.39 i
9
3.0836 - 0.8228 i
0.284 + 0.39 i
10
-3.3404
2.49 i
11
-1.1928 + 4.1233 i
0.291 - 0.234 i
12
-1.1928 - 4.1233 i
0.291 + 0.234 i
13
5.6337 + 3.0902 i
0.731 - 0.929 i
14
5.6337 - 3.0902 i
0.731 + 0.929 i
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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
-0.3296
1.94e-7
Singularities of quadratic [8, 7, 7] approximant
2
-0.3296
1.94e-7 i
3
-0.8071 + 0.0314 i
0.000454 + 0.000664 i
4
-0.8071 - 0.0314 i
0.000454 - 0.000664 i
5
-0.8473
0.000868
6
-2.5098
1.76 i
7
2.6064
0.0523
8
2.9485 + 0.5354 i
0.112 - 0.062 i
9
2.9485 - 0.5354 i
0.112 + 0.062 i
10
-1.4446 + 2.7126 i
0.0345 + 0.036 i
11
-1.4446 - 2.7126 i
0.0345 - 0.036 i
12
1.31 + 3.2078 i
0.0171 + 0.0461 i
13
1.31 - 3.2078 i
0.0171 - 0.0461 i
14
-5.9889 + 9.7473 i
0.11 - 0.402 i
15
-5.9889 - 9.7473 i
0.11 + 0.402 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
0.0223
0
Singularities of quadratic [8, 8, 7] approximant
2
0.0223
0
3
-0.2509
1.22e-8
4
-0.2509
1.22e-8 i
5
-0.8049 + 0.0322 i
0.000399 + 0.00059 i
6
-0.8049 - 0.0322 i
0.000399 - 0.00059 i
7
-0.8423
0.000749
8
2.4639 + 0.0538 i
0.0649 - 0.0607 i
9
2.4639 - 0.0538 i
0.0649 + 0.0607 i
10
-2.6575
5.96 i
11
-1.4143 + 3.0158 i
0.0738 + 0.0255 i
12
-1.4143 - 3.0158 i
0.0738 - 0.0255 i
13
1.683 + 3.3431 i
0.0658 + 0.0765 i
14
1.683 - 3.3431 i
0.0658 - 0.0765 i
15
5.9061 + 0.4725 i
0.127 - 0.134 i
16
5.9061 - 0.4725 i
0.127 + 0.134 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
-0.6456
0.0000206
Singularities of quadratic [8, 8, 8] approximant
2
-0.6458
0.0000206 i
3
-0.7932 + 0.0378 i
0.000223 + 0.000291 i
4
-0.7932 - 0.0378 i
0.000223 - 0.000291 i
5
-0.8167
0.00034
6
0.244 + 0.8384 i
0.000052 + 3.09e-6 i
7
0.244 - 0.8384 i
0.000052 - 3.09e-6 i
8
0.244 + 0.8384 i
3.09e-6 - 0.000052 i
9
0.244 - 0.8384 i
3.09e-6 + 0.000052 i
10
3.083 + 0.7281 i
0.781 - 0.594 i
11
3.083 - 0.7281 i
0.781 + 0.594 i
12
-3.2637
3.42 i
13
3.9032
0.582
14
-0.6833 + 4.0978 i
0.00417 - 0.263 i
15
-0.6833 - 4.0978 i
0.00417 + 0.263 i
16
826.1809
0.198 i
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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
-0.8038 + 0.0309 i
0.000359 + 0.0006 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.8038 - 0.0309 i
0.000359 - 0.0006 i
3
-0.8376
0.00069
4
-1.2039
13.6 i
5
-1.2216
0.119
6
0.7302 + 1.029 i
0.0000589 - 0.0000306 i
7
0.7302 - 1.029 i
0.0000589 + 0.0000306 i
8
0.7298 + 1.0311 i
0.0000307 + 0.000059 i
9
0.7298 - 1.0311 i
0.0000307 - 0.000059 i
10
2.3688 + 0.1958 i
0.00372 - 0.00132 i
11
2.3688 - 0.1958 i
0.00372 + 0.00132 i
12
-2.665
1.92 i
13
1.8793 + 1.9581 i
0.000225 + 0.00619 i
14
1.8793 - 1.9581 i
0.000225 - 0.00619 i
15
-0.7496 + 2.7236 i
0.0169 - 0.00262 i
16
-0.7496 - 2.7236 i
0.0169 + 0.00262 i
17
-9.2057
2.21
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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
-0.3019
1.25e-8
Singularities of quadratic [9, 9, 8] approximant
2
-0.3019
1.25e-8 i
3
-0.7855 + 0.0327 i
0.000101 + 0.000264 i
4
-0.7855 - 0.0327 i
0.000101 - 0.000264 i
5
-0.7958
0.000219
6
-1.437
0.137 i
7
1.0862 + 1.1927 i
0.000289 + 0.000197 i
8
1.0862 - 1.1927 i
0.000289 - 0.000197 i
9
1.0867 + 1.2133 i
0.000204 - 0.000291 i
10
1.0867 - 1.2133 i
0.000204 + 0.000291 i
11
-1.6304
0.312
12
-1.9136
0.145 i
13
2.0582 + 1.7055 i
0.0105 - 0.000383 i
14
2.0582 - 1.7055 i
0.0105 + 0.000383 i
15
-0.7764 + 2.6849 i
0.0154 - 0.00766 i
16
-0.7764 - 2.6849 i
0.0154 + 0.00766 i
17
3.0635 + 2.963 i
0.169 - 0.0303 i
18
3.0635 - 2.963 i
0.169 + 0.0303 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
0.701
5.5e-6
Singularities of quadratic [9, 9, 9] approximant
2
0.701
5.5e-6 i
3
-0.7868
0.000411
4
-0.8005 + 0.072 i
0.000332 - 0.000152 i
5
-0.8005 - 0.072 i
0.000332 + 0.000152 i
6
-0.8086 + 0.0626 i
0.0000894 + 0.000317 i
7
-0.8086 - 0.0626 i
0.0000894 - 0.000317 i
8
0.0776 + 1.0675 i
2.99e-6 - 0.000164 i
9
0.0776 - 1.0675 i
2.99e-6 + 0.000164 i
10
0.0775 + 1.0677 i
0.000164 + 2.98e-6 i
11
0.0775 - 1.0677 i
0.000164 - 2.98e-6 i
12
3.0469
0.211
13
3.0595 + 0.7901 i
0.278 + 0.185 i
14
3.0595 - 0.7901 i
0.278 - 0.185 i
15
-0.0881 + 3.9136 i
0.107 + 0.0909 i
16
-0.0881 - 3.9136 i
0.107 - 0.0909 i
17
-3.9287
0.689 i
18
-6.0012
0.503
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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
-0.8076
0.00175
Singularities of quadratic [10, 9, 9] approximant
2
-0.894 + 0.0482 i
0.000768 - 0.00172 i
3
-0.894 - 0.0482 i
0.000768 + 0.00172 i
4
-0.9097 + 0.0794 i
0.00328 + 0.00121 i
5
-0.9097 - 0.0794 i
0.00328 - 0.00121 i
6
0.1066 + 0.9187 i
9.89e-6 + 6.67e-6 i
7
0.1066 - 0.9187 i
9.89e-6 - 6.67e-6 i
8
0.1067 + 0.9187 i
6.67e-6 - 9.89e-6 i
9
0.1067 - 0.9187 i
6.67e-6 + 9.89e-6 i
10
0.957 + 0.0001 i
3.32e-6 - 3.32e-6 i
11
0.957 - 0.0001 i
3.32e-6 + 3.32e-6 i
12
1.8909 + 0.0686 i
0.000433 - 0.000296 i
13
1.8909 - 0.0686 i
0.000433 + 0.000296 i
14
1.9313 + 2.0808 i
0.000149 + 0.00771 i
15
1.9313 - 2.0808 i
0.000149 - 0.00771 i
16
-0.762 + 2.8927 i
0.0226 - 0.00199 i
17
-0.762 - 2.8927 i
0.0226 + 0.00199 i
18
-3.8471 + 0.8508 i
2.63 - 5.75 i
19
-3.8471 - 0.8508 i
2.63 + 5.75 i
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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
-0.8121
0.00261
Singularities of quadratic [10, 10, 9] approximant
2
-0.8518
0.00528 i
3
0.2803 + 0.8637 i
2.2e-6 + 2.6e-6 i
4
0.2803 - 0.8637 i
2.2e-6 - 2.6e-6 i
5
0.2805 + 0.8638 i
2.6e-6 - 2.2e-6 i
6
0.2805 - 0.8638 i
2.6e-6 + 2.2e-6 i
7
-0.9151
0.0125
8
-1.1527
0.0442 i
9
-1.2106
0.193
10
1.1821 + 0.525 i
0.0000165 - 3.86e-6 i
11
1.1821 - 0.525 i
0.0000165 + 3.86e-6 i
12
1.1879 + 0.5322 i
3.8e-6 + 0.0000168 i
13
1.1879 - 0.5322 i
3.8e-6 - 0.0000168 i
14
1.6263 + 1.7224 i
0.00031 + 0.0015 i
15
1.6263 - 1.7224 i
0.00031 - 0.0015 i
16
-0.6492 + 2.4689 i
0.00716 + 0.00234 i
17
-0.6492 - 2.4689 i
0.00716 - 0.00234 i
18
-2.7438 + 1.4911 i
0.0141 - 0.943 i
19
-2.7438 - 1.4911 i
0.0141 + 0.943 i
20
-45.3993
1.08 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
0.2382
0
Singularities of quadratic [10, 10, 10] approximant
2
0.2382
0
3
-0.5407 + 0.e-5 i
9.69e-7 + 9.69e-7 i
4
-0.5407 - 0.e-5 i
9.69e-7 - 9.69e-7 i
5
0.8067 + 0.e-4 i
6.72e-7 - 6.71e-7 i
6
0.8067 - 0.e-4 i
6.72e-7 + 6.71e-7 i
7
-0.8126 + 0.025 i
0.000537 + 0.0012 i
8
-0.8126 - 0.025 i
0.000537 - 0.0012 i
9
-0.8581
0.00129
10
0.0306 + 0.9428 i
3.25e-6 + 0.0000108 i
11
0.0306 - 0.9428 i
3.25e-6 - 0.0000108 i
12
0.0304 + 0.9428 i
0.0000108 - 3.24e-6 i
13
0.0304 - 0.9428 i
0.0000108 + 3.24e-6 i
14
2.4257 + 0.2869 i
0.0072 + 0.000105 i
15
2.4257 - 0.2869 i
0.0072 - 0.000105 i
16
-3.0489
7.07 i
17
2.0546 + 3.2647 i
0.0467 + 0.00629 i
18
2.0546 - 3.2647 i
0.0467 - 0.00629 i
19
-1.8742 + 3.8419 i
0.278 + 0.45 i
20
-1.8742 - 3.8419 i
0.278 - 0.45 i
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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
-0.8251 + 0.0035 i
0.0137 - 0.0107 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.8251 - 0.0035 i
0.0137 + 0.0107 i
3
0.4977 + 0.6886 i
4.47e-7 - 4.98e-7 i
4
0.4977 - 0.6886 i
4.47e-7 + 4.98e-7 i
5
0.4976 + 0.6887 i
4.98e-7 + 4.47e-7 i
6
0.4976 - 0.6887 i
4.98e-7 - 4.47e-7 i
7
-0.8906
0.00413
8
1.2674 + 0.0035 i
6.06e-6 - 5.94e-6 i
9
1.2674 - 0.0035 i
6.06e-6 + 5.94e-6 i
10
0.6057 + 1.4136 i
6.98e-6 + 0.0000443 i
11
0.6057 - 1.4136 i
6.98e-6 - 0.0000443 i
12
0.6093 + 1.5009 i
0.0000542 - 8.47e-6 i
13
0.6093 - 1.5009 i
0.0000542 + 8.47e-6 i
14
-1.6329
0.237 i
15
-1.9693
0.891
16
-0.2816 + 2.1284 i
0.00115 - 0.000289 i
17
-0.2816 - 2.1284 i
0.00115 + 0.000289 i
18
1.9684 + 1.0055 i
0.000906 + 0.000543 i
19
1.9684 - 1.0055 i
0.000906 - 0.000543 i
20
-5.2584 + 1.3237 i
0.0783 - 0.0498 i
21
-5.2584 - 1.3237 i
0.0783 + 0.0498 i
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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
-0.8071 + 0.0158 i
0.000132 - 0.00139 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.8071 - 0.0158 i
0.000132 + 0.00139 i
3
-0.8114
0.000994
4
-0.8572
0.00627 i
5
-0.9023
0.00683
6
0.5176 + 0.8446 i
1.5e-6 + 1.7e-6 i
7
0.5176 - 0.8446 i
1.5e-6 - 1.7e-6 i
8
0.5184 + 0.8455 i
1.69e-6 - 1.51e-6 i
9
0.5184 - 0.8455 i
1.69e-6 + 1.51e-6 i
10
0.8894 + 0.8451 i
6.2e-6 + 3.88e-6 i
11
0.8894 - 0.8451 i
6.2e-6 - 3.88e-6 i
12
0.8957 + 0.8568 i
4.16e-6 - 6.27e-6 i
13
0.8957 - 0.8568 i
4.16e-6 + 6.27e-6 i
14
-1.5363
0.427 i
15
-1.8092
35.5
16
1.5392 + 1.4736 i
0.000384 + 0.000379 i
17
1.5392 - 1.4736 i
0.000384 - 0.000379 i
18
-0.5638 + 2.2254 i
0.00288 + 0.00175 i
19
-0.5638 - 2.2254 i
0.00288 - 0.00175 i
20
-2.1872 + 1.7792 i
0.115 + 0.0851 i
21
-2.1872 - 1.7792 i
0.115 - 0.0851 i
22
-12.4083
0.154 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
0.4531
3.e-9
Singularities of quadratic [11, 11, 11] approximant
2
0.4531
3.e-9 i
3
-0.8245 + 0.0067 i
0.00318 - 0.0102 i
4
-0.8245 - 0.0067 i
0.00318 + 0.0102 i
5
-0.8885
0.00381
6
0.4549 + 0.7967 i
1.02e-6 + 1.11e-6 i
7
0.4549 - 0.7967 i
1.02e-6 - 1.11e-6 i
8
0.455 + 0.797 i
1.11e-6 - 1.02e-6 i
9
0.455 - 0.797 i
1.11e-6 + 1.02e-6 i
10
1.0975 + 0.7984 i
0.0000163 - 0.0000104 i
11
1.0975 - 0.7984 i
0.0000163 + 0.0000104 i
12
1.1176 + 0.7913 i
0.0000113 + 0.0000168 i
13
1.1176 - 0.7913 i
0.0000113 - 0.0000168 i
14
-1.8837
0.239 i
15
-0.6073 + 1.9718 i
0.00079 + 0.00131 i
16
-0.6073 - 1.9718 i
0.00079 - 0.00131 i
17
1.4541 + 1.6303 i
0.0000664 + 0.000643 i
18
1.4541 - 1.6303 i
0.0000664 - 0.000643 i
19
-1.251 + 2.0841 i
0.00498 - 0.00111 i
20
-1.251 - 2.0841 i
0.00498 + 0.00111 i
21
-2.2299 + 1.113 i
0.0589 + 0.0291 i
22
-2.2299 - 1.113 i
0.0589 - 0.0291 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
-0.4684 + 0.6224 i
4.77e-6 + 1.67e-6 i
Singularities of quadratic [12, 11, 11] approximant
2
-0.4684 - 0.6224 i
4.77e-6 - 1.67e-6 i
3
-0.4684 + 0.6225 i
1.67e-6 - 4.77e-6 i
4
-0.4684 - 0.6225 i
1.67e-6 + 4.77e-6 i
5
-0.8199
0.0069
6
-0.8327
0.081 i
7
-0.8948
0.00493
8
0.4494 + 0.9386 i
2.87e-6 - 5.73e-6 i
9
0.4494 - 0.9386 i
2.87e-6 + 5.73e-6 i
10
0.4506 + 0.9385 i
5.72e-6 + 2.85e-6 i
11
0.4506 - 0.9385 i
5.72e-6 - 2.85e-6 i
12
0.8127 + 0.6985 i
5.3e-6 - 2.41e-6 i
13
0.8127 - 0.6985 i
5.3e-6 + 2.41e-6 i
14
0.8129 + 0.7 i
2.39e-6 + 5.31e-6 i
15
0.8129 - 0.7 i
2.39e-6 - 5.31e-6 i
16
-1.4306
1.11 i
17
-1.5579
0.402
18
1.7855 + 1.4639 i
0.00153 - 0.0000415 i
19
1.7855 - 1.4639 i
0.00153 + 0.0000415 i
20
-0.3824 + 2.3891 i
0.00305 - 0.00173 i
21
-0.3824 - 2.3891 i
0.00305 + 0.00173 i
22
-3.532
0.55 i
23
-6.9741
0.217
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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
-0.3481 + 0.6129 i
1.34e-6 - 1.08e-6 i
Singularities of quadratic [12, 12, 11] approximant
2
-0.3481 - 0.6129 i
1.34e-6 + 1.08e-6 i
3
-0.3481 + 0.6129 i
1.08e-6 + 1.34e-6 i
4
-0.3481 - 0.6129 i
1.08e-6 - 1.34e-6 i
5
-0.8228
0.0102
6
-0.8283
0.429 i
7
-0.8922
0.00441
8
0.4706 + 0.9491 i
3.3e-6 - 5.04e-6 i
9
0.4706 - 0.9491 i
3.3e-6 + 5.04e-6 i
10
0.4723 + 0.9485 i
5.02e-6 + 3.28e-6 i
11
0.4723 - 0.9485 i
5.02e-6 - 3.28e-6 i
12
0.8045 + 0.7174 i
4.77e-6 - 7.67e-7 i
13
0.8045 - 0.7174 i
4.77e-6 + 7.67e-7 i
14
0.8045 + 0.7194 i
7.49e-7 + 4.77e-6 i
15
0.8045 - 0.7194 i
7.49e-7 - 4.77e-6 i
16
-1.5377
0.344 i
17
-1.7419
14.3
18
1.7243 + 1.4518 i
0.00113 + 0.000128 i
19
1.7243 - 1.4518 i
0.00113 - 0.000128 i
20
-0.3973 + 2.3275 i
0.00296 - 0.000946 i
21
-0.3973 - 2.3275 i
0.00296 + 0.000946 i
22
-3.6013 + 1.6434 i
0.361 + 0.113 i
23
-3.6013 - 1.6434 i
0.361 - 0.113 i
24
-77.815
1.76 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
-0.1848
0
Singularities of quadratic [12, 12, 12] approximant
2
-0.1848
0
3
-0.8203
0.0105
4
-0.8354
0.0184 i
5
-0.4236 + 0.736 i
3.94e-7 + 6.91e-7 i
6
-0.4236 - 0.736 i
3.94e-7 - 6.91e-7 i
7
-0.4236 + 0.7361 i
6.91e-7 - 3.94e-7 i
8
-0.4236 - 0.7361 i
6.91e-7 + 3.94e-7 i
9
-0.8989
0.00665
10
0.7372 + 0.7104 i
2.8e-7 + 2.28e-7 i
11
0.7372 - 0.7104 i
2.8e-7 - 2.28e-7 i
12
0.7354 + 0.715 i
2.31e-7 - 2.78e-7 i
13
0.7354 - 0.715 i
2.31e-7 + 2.78e-7 i
14
0.4078 + 1.0196 i
8.05e-7 + 5.11e-7 i
15
0.4078 - 1.0196 i
8.05e-7 - 5.11e-7 i
16
0.4182 + 1.0197 i
4.7e-7 - 8.13e-7 i
17
0.4182 - 1.0197 i
4.7e-7 + 8.13e-7 i
18
1.4371 + 1.0731 i
0.0000426 - 7.99e-6 i
19
1.4371 - 1.0731 i
0.0000426 + 7.99e-6 i
20
-1.7712 + 0.8879 i
0.0153 - 0.000593 i
21
-1.7712 - 0.8879 i
0.0153 + 0.000593 i
22
-2.9692
0.0876 i
23
3.1165 + 0.748 i
0.00228 - 0.00414 i
24
3.1165 - 0.748 i
0.00228 + 0.00414 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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