Singularities of Møller-Plesset series: example "a87"

Molecule Cl-. 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
-0.9388 + 0.0539 i
0.00128 + 0.00512 i
Singularities of quadratic [6, 6, 5] approximant
2
-0.9388 - 0.0539 i
0.00128 - 0.00512 i
3
-0.9899
0.00397
4
1.773
0.0175
5
1.8855
0.0232 i
6
2.1744 + 0.869 i
0.0586 - 0.0179 i
7
2.1744 - 0.869 i
0.0586 + 0.0179 i
8
1.9924 + 2.1041 i
0.0527 - 0.0252 i
9
1.9924 - 2.1041 i
0.0527 + 0.0252 i
10
-0.9407 + 2.9172 i
0.0542 - 0.00891 i
11
-0.9407 - 2.9172 i
0.0542 + 0.00891 i
12
-3.1895
0.239 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
0.0551
0
Singularities of quadratic [6, 6, 6] approximant
2
0.0551
0
3
-0.958 + 0.0436 i
0.00178 + 0.01 i
4
-0.958 - 0.0436 i
0.00178 - 0.01 i
5
-1.0345
0.007
6
2.1765 + 0.613 i
0.0327 - 0.191 i
7
2.1765 - 0.613 i
0.0327 + 0.191 i
8
-0.8058 + 3.5872 i
0.143 - 0.0579 i
9
-0.8058 - 3.5872 i
0.143 + 0.0579 i
10
-4.2269
0.146 i
11
4.2485 + 1.7011 i
0.113 + 0.648 i
12
4.2485 - 1.7011 i
0.113 - 0.648 i
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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
-0.9744 + 0.0256 i
0.0011 - 0.027 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.9744 - 0.0256 i
0.0011 + 0.027 i
3
-1.0769
0.0124
4
1.9711 + 0.7773 i
0.038 + 0.00239 i
5
1.9711 - 0.7773 i
0.038 - 0.00239 i
6
2.5659
0.117
7
-0.7433 + 2.9268 i
0.0369 - 0.00369 i
8
-0.7433 - 2.9268 i
0.0369 + 0.00369 i
9
1.5092 + 2.7264 i
0.0399 + 0.0126 i
10
1.5092 - 2.7264 i
0.0399 - 0.0126 i
11
-5.0463
0.521 i
12
-18.9312
4.78
13
34.3601
1.3 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
-0.9744 + 0.0253 i
0.00181 - 0.0272 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.9744 - 0.0253 i
0.00181 + 0.0272 i
3
-1.0766
0.0123
4
1.8652 + 0.6623 i
0.0133 - 0.00899 i
5
1.8652 - 0.6623 i
0.0133 + 0.00899 i
6
2.2284 + 0.1828 i
0.0224 - 0.00452 i
7
2.2284 - 0.1828 i
0.0224 + 0.00452 i
8
2.0133 + 2.2621 i
0.0348 - 0.0302 i
9
2.0133 - 2.2621 i
0.0348 + 0.0302 i
10
-0.6364 + 3.0066 i
0.0458 - 0.0202 i
11
-0.6364 - 3.0066 i
0.0458 + 0.0202 i
12
-3.6386 + 1.7731 i
0.0809 + 0.227 i
13
-3.6386 - 1.7731 i
0.0809 - 0.227 i
14
-13.751
0.443 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
-0.9802 + 0.0152 i
0.0161 - 0.0537 i
Singularities of quadratic [7, 7, 7] approximant
2
-0.9802 - 0.0152 i
0.0161 + 0.0537 i
3
-1.0963
0.0165
4
-2.0886
0.111 i
5
2.0171 + 0.7546 i
0.0631 - 0.00983 i
6
2.0171 - 0.7546 i
0.0631 + 0.00983 i
7
-2.4722
0.063
8
3.1264 + 0.4983 i
0.241 + 0.275 i
9
3.1264 - 0.4983 i
0.241 - 0.275 i
10
-2.2293 + 3.061 i
0.00459 + 0.0526 i
11
-2.2293 - 3.061 i
0.00459 - 0.0526 i
12
1.088 + 3.8881 i
0.198 + 0.25 i
13
1.088 - 3.8881 i
0.198 - 0.25 i
14
-11.4139
0.0892 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
-0.9634
0.0258
Singularities of quadratic [8, 7, 7] approximant
2
-1.0611
0.00525 i
3
-1.0693
0.00493
4
-1.1053 + 0.0866 i
0.00715 - 0.0173 i
5
-1.1053 - 0.0866 i
0.00715 + 0.0173 i
6
1.9796 + 0.7645 i
0.0432 - 0.00222 i
7
1.9796 - 0.7645 i
0.0432 + 0.00222 i
8
2.6806
0.149
9
-0.7771 + 3.2273 i
0.0674 - 0.00181 i
10
-0.7771 - 3.2273 i
0.0674 + 0.00181 i
11
1.748 + 2.9132 i
0.0677 + 0.00474 i
12
1.748 - 2.9132 i
0.0677 - 0.00474 i
13
5.2535
0.596 i
14
-4.8763 + 2.3908 i
0.0821 + 0.249 i
15
-4.8763 - 2.3908 i
0.0821 - 0.249 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
-0.982
0.0741
Singularities of quadratic [8, 8, 7] approximant
2
-0.9851
0.175 i
3
-1.1109
0.0208
4
-1.655
0.0511 i
5
-1.8069
0.566
6
1.9904 + 0.703 i
0.0463 - 0.0241 i
7
1.9904 - 0.703 i
0.0463 + 0.0241 i
8
2.5385 + 0.2986 i
0.115 + 0.0329 i
9
2.5385 - 0.2986 i
0.115 - 0.0329 i
10
-2.6029 + 1.9315 i
0.0194 - 0.0489 i
11
-2.6029 - 1.9315 i
0.0194 + 0.0489 i
12
-0.1956 + 3.6936 i
0.0171 + 0.485 i
13
-0.1956 - 3.6936 i
0.0171 - 0.485 i
14
3.7877 + 2.522 i
0.212 - 0.296 i
15
3.7877 - 2.522 i
0.212 + 0.296 i
16
-6.3625
0.0805 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
-0.9766
0.0558
Singularities of quadratic [8, 8, 8] approximant
2
-0.9911
34.3 i
3
-1.1146
0.0211
4
1.314
0.000268
5
1.3143
0.000268 i
6
-1.4221
0.0977 i
7
-1.4819
0.153
8
1.9867 + 0.5992 i
0.0103 + 0.036 i
9
1.9867 - 0.5992 i
0.0103 - 0.036 i
10
2.5124 + 1.1462 i
0.0591 + 0.0582 i
11
2.5124 - 1.1462 i
0.0591 - 0.0582 i
12
3.7183
0.549
13
-0.1234 + 3.8197 i
0.159 - 0.412 i
14
-0.1234 - 3.8197 i
0.159 + 0.412 i
15
-3.8222 + 3.0384 i
0.00982 - 0.106 i
16
-3.8222 - 3.0384 i
0.00982 + 0.106 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
-0.9783
0.0728
Singularities of quadratic [9, 8, 8] approximant
2
-0.9901
20.3 i
3
-1.1143
0.0223
4
-1.6169
0.0484 i
5
-1.7645
0.587
6
2.1075 + 0.6943 i
0.192 - 0.0394 i
7
2.1075 - 0.6943 i
0.192 + 0.0394 i
8
2.3469
0.542
9
2.334 + 0.4345 i
0.115 + 0.187 i
10
2.334 - 0.4345 i
0.115 - 0.187 i
11
-2.5454 + 1.6699 i
0.0108 - 0.0429 i
12
-2.5454 - 1.6699 i
0.0108 + 0.0429 i
13
0.5902 + 3.9005 i
0.167 - 0.257 i
14
0.5902 - 3.9005 i
0.167 + 0.257 i
15
-2.41 + 4.3047 i
0.195 - 0.0418 i
16
-2.41 - 4.3047 i
0.195 + 0.0418 i
17
-4.9872
0.104 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
-0.98
0.105
Singularities of quadratic [9, 9, 8] approximant
2
-0.9898
560. i
3
-1.1154
0.0245
4
-1.4086 + 0.5158 i
0.0104 - 0.000354 i
5
-1.4086 - 0.5158 i
0.0104 + 0.000354 i
6
-1.419 + 0.4977 i
0.0000463 - 0.01 i
7
-1.419 - 0.4977 i
0.0000463 + 0.01 i
8
2.0966 + 0.6457 i
0.115 - 0.217 i
9
2.0966 - 0.6457 i
0.115 + 0.217 i
10
2.3906 + 0.5883 i
0.233 + 0.109 i
11
2.3906 - 0.5883 i
0.233 - 0.109 i
12
2.5635
6.1
13
0.2358 + 3.7747 i
0.339 + 0.0595 i
14
0.2358 - 3.7747 i
0.339 - 0.0595 i
15
-4.2188
0.0769 i
16
-4.1689 + 3.8235 i
0.137 - 0.0484 i
17
-4.1689 - 3.8235 i
0.137 + 0.0484 i
18
85.8018
2.24 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
-0.9828
0.146
Singularities of quadratic [9, 9, 9] approximant
2
-0.9868
0.86 i
3
-1.1139
0.0253
4
-1.2622 + 0.2821 i
0.014 - 0.00146 i
5
-1.2622 - 0.2821 i
0.014 + 0.00146 i
6
-1.2753 + 0.2851 i
0.000182 + 0.0135 i
7
-1.2753 - 0.2851 i
0.000182 - 0.0135 i
8
2.0134 + 0.0334 i
0.0235 - 0.0185 i
9
2.0134 - 0.0334 i
0.0235 + 0.0185 i
10
2.0229 + 0.6732 i
0.0398 - 0.0455 i
11
2.0229 - 0.6732 i
0.0398 + 0.0455 i
12
3.0329 + 1.0391 i
0.0741 + 0.21 i
13
3.0329 - 1.0391 i
0.0741 - 0.21 i
14
-0.0421 + 3.9817 i
0.021 - 1.06 i
15
-0.0421 - 3.9817 i
0.021 + 1.06 i
16
-4.4594 + 3.0043 i
0.032 - 0.0934 i
17
-4.4594 - 3.0043 i
0.032 + 0.0934 i
18
7.4668
2.62
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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
-0.4485
4.32e-7
Singularities of quadratic [10, 9, 9] approximant
2
-0.4485
4.32e-7 i
3
-0.9787
0.0556
4
-0.9871
0.437 i
5
-1.1103
0.0198
6
-1.5435 + 0.3961 i
0.0331 + 0.0129 i
7
-1.5435 - 0.3961 i
0.0331 - 0.0129 i
8
-1.5612 + 0.3515 i
0.0106 - 0.0249 i
9
-1.5612 - 0.3515 i
0.0106 + 0.0249 i
10
2.0913 + 0.5984 i
0.104 + 0.17 i
11
2.0913 - 0.5984 i
0.104 - 0.17 i
12
2.3575 + 0.7454 i
0.221 - 0.016 i
13
2.3575 - 0.7454 i
0.221 + 0.016 i
14
2.6434
4.98
15
0.1559 + 3.8179 i
0.32 + 0.205 i
16
0.1559 - 3.8179 i
0.32 - 0.205 i
17
-4.0877
0.11 i
18
-3.6361 + 5.5228 i
0.279 - 0.148 i
19
-3.6361 - 5.5228 i
0.279 + 0.148 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
0.2987
8.61e-10
Singularities of quadratic [10, 10, 9] approximant
2
0.2987
8.61e-10 i
3
-0.9561 + 0.0056 i
0.0035 + 0.00264 i
4
-0.9561 - 0.0056 i
0.0035 - 0.00264 i
5
-1.0107
0.0093
6
-1.0594
0.00809 i
7
-1.1592
0.38
8
-1.6284
0.0645 i
9
-1.7131
0.256
10
1.9876 + 0.5785 i
0.0202 + 0.0297 i
11
1.9876 - 0.5785 i
0.0202 - 0.0297 i
12
2.3003 + 1.252 i
0.0323 + 0.0268 i
13
2.3003 - 1.252 i
0.0323 - 0.0268 i
14
-0.299 + 3.4942 i
0.035 - 0.0746 i
15
-0.299 - 3.4942 i
0.035 + 0.0746 i
16
3.5107 + 2.2278 i
0.147 + 0.022 i
17
3.5107 - 2.2278 i
0.147 - 0.022 i
18
-4.9085
0.254 i
19
-0.7409 + 6.3379 i
1.05 - 1.91 i
20
-0.7409 - 6.3379 i
1.05 + 1.91 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
-0.992
0.0469
Singularities of quadratic [10, 10, 10] approximant
2
-1.0101
0.0117 i
3
-1.0616 + 0.2098 i
0.00141 - 0.0000581 i
4
-1.0616 - 0.2098 i
0.00141 + 0.0000581 i
5
-1.0642 + 0.2165 i
0.0000794 + 0.00143 i
6
-1.0642 - 0.2165 i
0.0000794 - 0.00143 i
7
-1.1627
198.
8
0.0481 + 1.273 i
0.0000861 - 6.56e-6 i
9
0.0481 - 1.273 i
0.0000861 + 6.56e-6 i
10
0.0481 + 1.273 i
6.57e-6 + 0.0000861 i
11
0.0481 - 1.273 i
6.57e-6 - 0.0000861 i
12
2.0061 + 0.5833 i
0.0266 + 0.0397 i
13
2.0061 - 0.5833 i
0.0266 - 0.0397 i
14
2.4149 + 1.1261 i
0.0551 + 0.0362 i
15
2.4149 - 1.1261 i
0.0551 - 0.0362 i
16
3.8029
0.47
17
-0.2566 + 4.0189 i
0.7 + 0.065 i
18
-0.2566 - 4.0189 i
0.7 - 0.065 i
19
-3.4998 + 2.8652 i
0.0112 - 0.0741 i
20
-3.4998 - 2.8652 i
0.0112 + 0.0741 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
0.4051 + 0.8511 i
0.0000142 - 2.82e-6 i
Singularities of quadratic [11, 10, 10] approximant
2
0.4051 - 0.8511 i
0.0000142 + 2.82e-6 i
3
0.4051 + 0.8511 i
2.82e-6 + 0.0000142 i
4
0.4051 - 0.8511 i
2.82e-6 - 0.0000142 i
5
-0.979 + 0.0065 i
0.0452 - 0.0014 i
6
-0.979 - 0.0065 i
0.0452 + 0.0014 i
7
-1.0841
0.0122
8
-1.2839 + 0.0962 i
0.0125 + 0.0864 i
9
-1.2839 - 0.0962 i
0.0125 - 0.0864 i
10
-1.2875 + 0.0346 i
0.0149 - 0.0265 i
11
-1.2875 - 0.0346 i
0.0149 + 0.0265 i
12
2.1244 + 0.6826 i
0.348 + 0.0279 i
13
2.1244 - 0.6826 i
0.348 - 0.0279 i
14
2.3094 + 0.5435 i
0.224 + 0.163 i
15
2.3094 - 0.5435 i
0.224 - 0.163 i
16
2.5948
20.4
17
0.0145 + 3.7091 i
0.105 + 0.22 i
18
0.0145 - 3.7091 i
0.105 - 0.22 i
19
-6.3164
0.0957 i
20
-5.2953 + 5.4035 i
0.182 - 0.104 i
21
-5.2953 - 5.4035 i
0.182 + 0.104 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
0.3582 + 0.8345 i
0.0000123 + 3.68e-6 i
Singularities of quadratic [11, 11, 10] approximant
2
0.3582 - 0.8345 i
0.0000123 - 3.68e-6 i
3
0.3582 + 0.8345 i
3.68e-6 - 0.0000123 i
4
0.3582 - 0.8345 i
3.68e-6 + 0.0000123 i
5
-0.9792 + 0.0067 i
0.0476 - 0.00328 i
6
-0.9792 - 0.0067 i
0.0476 + 0.00328 i
7
-1.0832
0.0123
8
-1.2475
0.0218 i
9
-1.2807 + 0.0851 i
0.00284 + 0.0948 i
10
-1.2807 - 0.0851 i
0.00284 - 0.0948 i
11
-1.3235
0.0385
12
2.0979 + 0.5926 i
0.163 + 0.175 i
13
2.0979 - 0.5926 i
0.163 - 0.175 i
14
2.3296 + 0.7678 i
0.183 - 0.0452 i
15
2.3296 - 0.7678 i
0.183 + 0.0452 i
16
2.7296
80.1
17
-0.0332 + 3.7289 i
0.0555 + 0.248 i
18
-0.0332 - 3.7289 i
0.0555 - 0.248 i
19
-6.4385
0.104 i
20
-5.0541 + 5.894 i
0.195 - 0.144 i
21
-5.0541 - 5.894 i
0.195 + 0.144 i
22
307.7987
4.46 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
0.3663 + 0.8412 i
0.0000115 + 2.37e-6 i
Singularities of quadratic [11, 11, 11] approximant
2
0.3663 - 0.8412 i
0.0000115 - 2.37e-6 i
3
0.3663 + 0.8412 i
2.37e-6 - 0.0000115 i
4
0.3663 - 0.8412 i
2.37e-6 + 0.0000115 i
5
-0.9779 + 0.0066 i
0.0362 + 0.00226 i
6
-0.9779 - 0.0066 i
0.0362 - 0.00226 i
7
-1.0796
0.0109
8
-1.2238
0.0253 i
9
-1.3078 + 0.0652 i
0.0235 + 0.0448 i
10
-1.3078 - 0.0652 i
0.0235 - 0.0448 i
11
-1.3944
0.173
12
2.1037 + 0.5905 i
0.205 + 0.18 i
13
2.1037 - 0.5905 i
0.205 - 0.18 i
14
2.3159 + 0.7683 i
0.176 - 0.0582 i
15
2.3159 - 0.7683 i
0.176 + 0.0582 i
16
2.7449
475.
17
-0.0489 + 3.6789 i
0.0314 + 0.2 i
18
-0.0489 - 3.6789 i
0.0314 - 0.2 i
19
-4.6926
0.158 i
20
-3.4364 + 5.2153 i
0.025 - 0.392 i
21
-3.4364 - 5.2153 i
0.025 + 0.392 i
22
-13.5802
0.604
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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
-0.5114 + 0.e-5 i
1.15e-7 + 1.15e-7 i
Singularities of quadratic [12, 11, 11] approximant
2
-0.5114 - 0.e-5 i
1.15e-7 - 1.15e-7 i
3
0.3637 + 0.8639 i
0.0000203 - 4.29e-6 i
4
0.3637 - 0.8639 i
0.0000203 + 4.29e-6 i
5
0.3637 + 0.8639 i
4.29e-6 + 0.0000203 i
6
0.3637 - 0.8639 i
4.29e-6 - 0.0000203 i
7
-0.9731 + 0.006 i
0.0142 + 0.00531 i
8
-0.9731 - 0.006 i
0.0142 - 0.00531 i
9
-1.0733
0.00855
10
-1.2168
0.0275 i
11
-1.3125
0.028
12
-1.4189
0.0292 i
13
-1.5015
2.1
14
2.115 + 0.6638 i
0.311 - 0.169 i
15
2.115 - 0.6638 i
0.311 + 0.169 i
16
2.3355 + 0.5702 i
0.25 + 0.136 i
17
2.3355 - 0.5702 i
0.25 - 0.136 i
18
2.5868
10.9
19
0.0657 + 3.7139 i
0.156 + 0.193 i
20
0.0657 - 3.7139 i
0.156 - 0.193 i
21
-5.2074
0.108 i
22
-4.7788 + 6.0473 i
0.277 - 0.119 i
23
-4.7788 - 6.0473 i
0.277 + 0.119 i
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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
0.3224 + 0.8488 i
5.68e-6 + 0.0000192 i
Singularities of quadratic [12, 12, 11] approximant
2
0.3224 - 0.8488 i
5.68e-6 - 0.0000192 i
3
0.3224 + 0.8488 i
0.0000192 - 5.68e-6 i
4
0.3224 - 0.8488 i
0.0000192 + 5.68e-6 i
5
-0.9813 + 0.007 i
0.0735 - 0.0314 i
6
-0.9813 - 0.007 i
0.0735 + 0.0314 i
7
-1.0889
0.0156
8
1.1871 + 0.e-5 i
0.000124 - 0.000124 i
9
1.1871 - 0.e-5 i
0.000124 + 0.000124 i
10
-1.2497 + 0.0914 i
0.151 - 0.0131 i
11
-1.2497 - 0.0914 i
0.151 + 0.0131 i
12
-1.2616 + 0.0226 i
0.0107 - 0.0126 i
13
-1.2616 - 0.0226 i
0.0107 + 0.0126 i
14
2.0226 + 0.5869 i
0.0325 + 0.0517 i
15
2.0226 - 0.5869 i
0.0325 - 0.0517 i
16
2.4112 + 1.0068 i
0.0842 + 0.0265 i
17
2.4112 - 1.0068 i
0.0842 - 0.0265 i
18
3.2828
1.05
19
-0.1446 + 3.7804 i
0.0908 - 0.272 i
20
-0.1446 - 3.7804 i
0.0908 + 0.272 i
21
-5.3008 + 5.2491 i
0.101 - 0.145 i
22
-5.3008 - 5.2491 i
0.101 + 0.145 i
23
-8.8294
0.12 i
24
42.861
3.27 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
-0.0416
0
Singularities of quadratic [12, 12, 12] approximant
2
-0.0416
0
3
0.3199 + 0.8545 i
5.86e-6 - 1.06e-6 i
4
0.3199 - 0.8545 i
5.86e-6 + 1.06e-6 i
5
0.3199 + 0.8545 i
1.06e-6 + 5.86e-6 i
6
0.3199 - 0.8545 i
1.06e-6 - 5.86e-6 i
7
-0.9779 + 0.0063 i
0.0348 + 0.00294 i
8
-0.9779 - 0.0063 i
0.0348 - 0.00294 i
9
-1.0854
0.012
10
-1.2631 + 0.1076 i
0.0237 + 0.344 i
11
-1.2631 - 0.1076 i
0.0237 - 0.344 i
12
-1.268 + 0.0873 i
0.0216 - 0.0476 i
13
-1.268 - 0.0873 i
0.0216 + 0.0476 i
14
1.3634
0.000402
15
1.3636
0.000402 i
16
2.0121 + 0.5917 i
0.0278 + 0.045 i
17
2.0121 - 0.5917 i
0.0278 - 0.045 i
18
2.4735 + 1.0904 i
0.0594 + 0.0485 i
19
2.4735 - 1.0904 i
0.0594 - 0.0485 i
20
3.8375
0.475
21
-0.1495 + 3.9345 i
0.419 - 0.593 i
22
-0.1495 - 3.9345 i
0.419 + 0.593 i
23
-4.2034 + 2.9791 i
0.0247 - 0.1 i
24
-4.2034 - 2.9791 i
0.0247 + 0.1 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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