Singularities of Møller-Plesset series: example "a45"

Molecule C2. Basis 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
-0.954 + 0.3294 i
0.554 + 0.56 i
Singularities of quadratic [6, 6, 5] approximant
2
-0.954 - 0.3294 i
0.554 - 0.56 i
3
1.2172 + 0.3488 i
0.195 - 0.154 i
4
1.2172 - 0.3488 i
0.195 + 0.154 i
5
-1.6222
1.42
6
2.3307
1.17
7
1.3788 + 2.1767 i
0.012 - 0.326 i
8
1.3788 - 2.1767 i
0.012 + 0.326 i
9
-2.8981
1.58 i
10
1.581 + 3.4057 i
0.361 + 0.107 i
11
1.581 - 3.4057 i
0.361 - 0.107 i
12
62.3914
1.91 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
-0.9591 + 0.3285 i
0.695 + 0.626 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.9591 - 0.3285 i
0.695 - 0.626 i
3
1.2166 + 0.3354 i
0.127 - 0.214 i
4
1.2166 - 0.3354 i
0.127 + 0.214 i
5
1.1167 + 1.0374 i
0.0617 - 0.0472 i
6
1.1167 - 1.0374 i
0.0617 + 0.0472 i
7
1.1665 + 0.9898 i
0.0485 + 0.059 i
8
1.1665 - 0.9898 i
0.0485 - 0.059 i
9
-1.5281 + 0.3455 i
0.86 - 0.493 i
10
-1.5281 - 0.3455 i
0.86 + 0.493 i
11
-2.1428
0.666
12
3.7492
152.
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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
-0.9562 + 0.3284 i
0.604 + 0.604 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.9562 - 0.3284 i
0.604 - 0.604 i
3
1.2684
0.276
4
1.2969 + 0.2219 i
0.0502 - 0.441 i
5
1.2969 - 0.2219 i
0.0502 + 0.441 i
6
1.2753 + 0.3482 i
0.878 + 1.01 i
7
1.2753 - 0.3482 i
0.878 - 1.01 i
8
-1.8068 + 0.2518 i
1.56 - 1.26 i
9
-1.8068 - 0.2518 i
1.56 + 1.26 i
10
2.3937
0.715 i
11
-5.0215
0.837
12
2.9629 + 4.1011 i
0.411 + 1.15 i
13
2.9629 - 4.1011 i
0.411 - 1.15 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
-0.956 + 0.3284 i
0.598 + 0.602 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.956 - 0.3284 i
0.598 - 0.602 i
3
1.2051 + 0.327 i
0.0953 - 0.274 i
4
1.2051 - 0.327 i
0.0953 + 0.274 i
5
1.4982 + 0.3994 i
0.246 + 0.0779 i
6
1.4982 - 0.3994 i
0.246 - 0.0779 i
7
1.7851
0.5
8
-1.7995 + 0.2582 i
1.54 - 1.17 i
9
-1.7995 - 0.2582 i
1.54 + 1.17 i
10
2.3162
0.338 i
11
-4.6111
0.667
12
1.6999 + 5.3312 i
0.213 - 0.798 i
13
1.6999 - 5.3312 i
0.213 + 0.798 i
14
-40.2633
1.47 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
0.5942
0.000436
Singularities of quadratic [7, 7, 7] approximant
2
0.5942
0.000436 i
3
-0.9562 + 0.3283 i
0.606 + 0.611 i
4
-0.9562 - 0.3283 i
0.606 - 0.611 i
5
1.1953 + 0.374 i
0.157 - 0.0276 i
6
1.1953 - 0.374 i
0.157 + 0.0276 i
7
1.5073
0.35
8
1.7332
90.5 i
9
-1.8483
2.4
10
-2.034
26.6 i
11
-2.6076 + 3.2423 i
0.273 - 0.551 i
12
-2.6076 - 3.2423 i
0.273 + 0.551 i
13
5.5093 + 3.4186 i
0.452 + 0.751 i
14
5.5093 - 3.4186 i
0.452 - 0.751 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
-0.6711 + 0.e-5 i
0.0735 + 0.0735 i
Singularities of quadratic [8, 7, 7] approximant
2
-0.6711 - 0.e-5 i
0.0735 - 0.0735 i
3
-0.9563 + 0.3283 i
0.606 + 0.61 i
4
-0.9563 - 0.3283 i
0.606 - 0.61 i
5
1.2717 + 0.2857 i
1.85 - 0.851 i
6
1.2717 - 0.2857 i
1.85 + 0.851 i
7
1.3355
0.632
8
1.3098 + 0.3299 i
1.78 - 0.843 i
9
1.3098 - 0.3299 i
1.78 + 0.843 i
10
-1.7969 + 0.2627 i
1.46 - 1.24 i
11
-1.7969 - 0.2627 i
1.46 + 1.24 i
12
2.2946
0.674 i
13
-4.8187
0.812
14
3.0587 + 4.1627 i
0.361 + 1.15 i
15
3.0587 - 4.1627 i
0.361 - 1.15 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
-0.9548 + 0.3279 i
0.541 + 0.588 i
Singularities of quadratic [8, 8, 7] approximant
2
-0.9548 - 0.3279 i
0.541 - 0.588 i
3
1.0676
0.0147
4
1.0724
0.015 i
5
1.1696 + 0.3334 i
0.0421 - 0.0897 i
6
1.1696 - 0.3334 i
0.0421 + 0.0897 i
7
-1.5059 + 0.2591 i
1.51 - 0.34 i
8
-1.5059 - 0.2591 i
1.51 + 0.34 i
9
-1.6537
3.85
10
1.5225 + 0.9687 i
0.00323 + 0.0929 i
11
1.5225 - 0.9687 i
0.00323 - 0.0929 i
12
1.5656 + 1.2437 i
0.101 + 0.0229 i
13
1.5656 - 1.2437 i
0.101 - 0.0229 i
14
-3.4272
0.544 i
15
-1.3245 + 5.7143 i
0.452 - 0.0383 i
16
-1.3245 - 5.7143 i
0.452 + 0.0383 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
-0.9556 + 0.328 i
0.58 + 0.605 i
Singularities of quadratic [8, 8, 8] approximant
2
-0.9556 - 0.328 i
0.58 - 0.605 i
3
1.1963 + 0.3361 i
0.126 - 0.177 i
4
1.1963 - 0.3361 i
0.126 + 0.177 i
5
1.511 + 0.1019 i
0.293 + 0.357 i
6
1.511 - 0.1019 i
0.293 - 0.357 i
7
-1.6142
1.59
8
-1.6964 + 0.5221 i
0.597 - 1.24 i
9
-1.6964 - 0.5221 i
0.597 + 1.24 i
10
-2.1368 + 0.3384 i
0.608 - 0.294 i
11
-2.1368 - 0.3384 i
0.608 + 0.294 i
12
2.1934
0.382
13
1.6546 + 2.0438 i
0.251 + 0.135 i
14
1.6546 - 2.0438 i
0.251 - 0.135 i
15
1.5604 + 2.7325 i
0.2 - 0.249 i
16
1.5604 - 2.7325 i
0.2 + 0.249 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
-0.9551 + 0.328 i
0.559 + 0.594 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.9551 - 0.328 i
0.559 - 0.594 i
3
1.1914 + 0.3419 i
0.122 - 0.125 i
4
1.1914 - 0.3419 i
0.122 + 0.125 i
5
1.3392 + 0.0374 i
0.354 - 0.0633 i
6
1.3392 - 0.0374 i
0.354 + 0.0633 i
7
-1.612 + 0.3015 i
1.47 - 0.397 i
8
-1.612 - 0.3015 i
1.47 + 0.397 i
9
-2.1536
0.848
10
1.61 + 1.9136 i
0.0898 + 0.223 i
11
1.61 - 1.9136 i
0.0898 - 0.223 i
12
-2.8834
0.485 i
13
2.924 + 2.1206 i
0.375 - 0.0846 i
14
2.924 - 2.1206 i
0.375 + 0.0846 i
15
3.7213
7.66
16
-4.3472 + 3.2144 i
0.653 - 0.101 i
17
-4.3472 - 3.2144 i
0.653 + 0.101 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
-0.9556 + 0.3282 i
0.587 + 0.599 i
Singularities of quadratic [9, 9, 8] approximant
2
-0.9556 - 0.3282 i
0.587 - 0.599 i
3
1.1909 + 0.3402 i
0.117 - 0.134 i
4
1.1909 - 0.3402 i
0.117 + 0.134 i
5
1.3696 + 0.0435 i
0.419 - 0.0223 i
6
1.3696 - 0.0435 i
0.419 + 0.0223 i
7
-1.5412
1.58
8
-1.4894 + 0.5514 i
0.868 - 0.466 i
9
-1.4894 - 0.5514 i
0.868 + 0.466 i
10
-1.6193 + 0.5273 i
0.777 + 0.752 i
11
-1.6193 - 0.5273 i
0.777 - 0.752 i
12
1.6852 + 1.6536 i
0.166 + 0.118 i
13
1.6852 - 1.6536 i
0.166 - 0.118 i
14
2.1137 + 1.1815 i
0.0884 - 0.27 i
15
2.1137 - 1.1815 i
0.0884 + 0.27 i
16
-5.1148
0.413 i
17
0.8143 + 6.3424 i
0.372 - 0.196 i
18
0.8143 - 6.3424 i
0.372 + 0.196 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
0.8811
0.00253
Singularities of quadratic [9, 9, 9] approximant
2
0.8811
0.00253 i
3
-0.9553 + 0.328 i
0.569 + 0.598 i
4
-0.9553 - 0.328 i
0.569 - 0.598 i
5
1.189 + 0.3294 i
0.0579 - 0.166 i
6
1.189 - 0.3294 i
0.0579 + 0.166 i
7
-1.7529 + 0.3979 i
1.89 - 1.39 i
8
-1.7529 - 0.3979 i
1.89 + 1.39 i
9
1.7653 + 0.3797 i
0.102 + 0.177 i
10
1.7653 - 0.3797 i
0.102 - 0.177 i
11
-1.8787
1.32
12
1.9433
0.261
13
-2.1415
0.555 i
14
-2.3648
0.478
15
1.7531 + 2.0637 i
0.192 + 0.112 i
16
1.7531 - 2.0637 i
0.192 - 0.112 i
17
1.4341 + 2.987 i
0.198 - 0.177 i
18
1.4341 - 2.987 i
0.198 + 0.177 i
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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
0.3762
1.11e-6
Singularities of quadratic [10, 9, 9] approximant
2
0.3762
1.11e-6 i
3
-0.9553 + 0.3282 i
0.571 + 0.589 i
4
-0.9553 - 0.3282 i
0.571 - 0.589 i
5
1.1872 + 0.3267 i
0.0331 - 0.167 i
6
1.1872 - 0.3267 i
0.0331 + 0.167 i
7
-1.4224
2.32
8
-1.4613
5.03 i
9
-1.6201 + 0.3969 i
0.917 - 0.743 i
10
-1.6201 - 0.3969 i
0.917 + 0.743 i
11
1.7765 + 0.6103 i
0.0148 + 0.146 i
12
1.7765 - 0.6103 i
0.0148 - 0.146 i
13
1.3558 + 1.944 i
0.0542 + 0.00986 i
14
1.3558 - 1.944 i
0.0542 - 0.00986 i
15
-2.5972
0.532
16
1.1126 + 2.3683 i
0.0151 - 0.069 i
17
1.1126 - 2.3683 i
0.0151 + 0.069 i
18
2.433 + 1.6646 i
0.0073 + 0.145 i
19
2.433 - 1.6646 i
0.0073 - 0.145 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
0.2316
1.38e-8
Singularities of quadratic [10, 10, 9] approximant
2
0.2316
1.38e-8 i
3
-0.9552 + 0.3283 i
0.569 + 0.582 i
4
-0.9552 - 0.3283 i
0.569 - 0.582 i
5
1.1864 + 0.3262 i
0.0283 - 0.164 i
6
1.1864 - 0.3262 i
0.0283 + 0.164 i
7
-1.2637
5.02
8
-1.2677
15.6 i
9
-1.6186 + 0.3689 i
0.968 - 0.622 i
10
-1.6186 - 0.3689 i
0.968 + 0.622 i
11
1.7759 + 0.6728 i
0.0024 - 0.134 i
12
1.7759 - 0.6728 i
0.0024 + 0.134 i
13
1.1599 + 1.8931 i
0.0363 + 0.00348 i
14
1.1599 - 1.8931 i
0.0363 - 0.00348 i
15
1.0183 + 2.15 i
0.00369 - 0.0438 i
16
1.0183 - 2.15 i
0.00369 + 0.0438 i
17
2.0445 + 1.7309 i
0.00121 + 0.0915 i
18
2.0445 - 1.7309 i
0.00121 - 0.0915 i
19
-2.693
0.516
20
-2614.5101
13.6 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
0.0764
0
Singularities of quadratic [10, 10, 10] approximant
2
0.0764
0
3
-0.9553 + 0.3282 i
0.572 + 0.586 i
4
-0.9553 - 0.3282 i
0.572 - 0.586 i
5
1.1858 + 0.3254 i
0.0218 - 0.162 i
6
1.1858 - 0.3254 i
0.0218 + 0.162 i
7
-1.3991
2.4
8
-1.4255
5.02 i
9
-1.622 + 0.3946 i
0.88 - 0.748 i
10
-1.622 - 0.3946 i
0.88 + 0.748 i
11
1.4174 + 1.2807 i
0.026 + 0.0157 i
12
1.4174 - 1.2807 i
0.026 - 0.0157 i
13
1.7274 + 0.8267 i
0.0273 - 0.0836 i
14
1.7274 - 0.8267 i
0.0273 + 0.0836 i
15
1.312 + 1.4725 i
0.0172 - 0.0265 i
16
1.312 - 1.4725 i
0.0172 + 0.0265 i
17
1.5043 + 2.1574 i
0.094 + 0.0347 i
18
1.5043 - 2.1574 i
0.094 - 0.0347 i
19
-2.6559
0.545
20
9.1254
2.1
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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
0.1002
0
Singularities of quadratic [11, 10, 10] approximant
2
0.1002
0
3
-0.9553 + 0.3282 i
0.572 + 0.585 i
4
-0.9553 - 0.3282 i
0.572 - 0.585 i
5
1.1857 + 0.3253 i
0.0211 - 0.162 i
6
1.1857 - 0.3253 i
0.0211 + 0.162 i
7
-1.3852
2.56
8
-1.4087
5.9 i
9
-1.6201 + 0.3913 i
0.896 - 0.727 i
10
-1.6201 - 0.3913 i
0.896 + 0.727 i
11
1.6743 + 0.8361 i
0.0161 - 0.0743 i
12
1.6743 - 0.8361 i
0.0161 + 0.0743 i
13
1.4815 + 1.199 i
0.0339 + 0.0155 i
14
1.4815 - 1.199 i
0.0339 - 0.0155 i
15
1.403 + 1.5166 i
0.0217 - 0.0353 i
16
1.403 - 1.5166 i
0.0217 + 0.0353 i
17
-2.6472
0.539
18
1.473 + 2.2181 i
0.0872 + 0.0695 i
19
1.473 - 2.2181 i
0.0872 - 0.0695 i
20
4.8016
3.03
21
16.4751
1.01 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
-0.5038 + 0.e-5 i
0.0000785 + 0.0000785 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.5038 - 0.e-5 i
0.0000785 - 0.0000785 i
3
0.5057
0.0000106
4
0.5057
0.0000106 i
5
-0.9552 + 0.3283 i
0.57 + 0.576 i
6
-0.9552 - 0.3283 i
0.57 - 0.576 i
7
-1.2279 + 0.0028 i
9.88 - 5.05 i
8
-1.2279 - 0.0028 i
9.88 + 5.05 i
9
1.1865 + 0.3264 i
0.0303 - 0.163 i
10
1.1865 - 0.3264 i
0.0303 + 0.163 i
11
-1.6277 + 0.3635 i
0.967 - 0.644 i
12
-1.6277 - 0.3635 i
0.967 + 0.644 i
13
1.7617 + 0.654 i
0.0104 + 0.137 i
14
1.7617 - 0.654 i
0.0104 - 0.137 i
15
1.2131 + 1.9385 i
0.0455 + 0.0028 i
16
1.2131 - 1.9385 i
0.0455 - 0.0028 i
17
1.0259 + 2.201 i
0.00488 - 0.0551 i
18
1.0259 - 2.201 i
0.00488 + 0.0551 i
19
2.1704 + 1.6125 i
0.0281 + 0.111 i
20
2.1704 - 1.6125 i
0.0281 - 0.111 i
21
-2.7793
0.519
22
-674.4473
7.41 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
-0.2981 + 0.8299 i
0.00177 - 0.00151 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.2981 - 0.8299 i
0.00177 + 0.00151 i
3
-0.2981 + 0.8299 i
0.00151 + 0.00177 i
4
-0.2981 - 0.8299 i
0.00151 - 0.00177 i
5
-0.9554 + 0.3281 i
0.573 + 0.594 i
6
-0.9554 - 0.3281 i
0.573 - 0.594 i
7
1.0234
0.0219
8
1.0242
0.022 i
9
1.1926 + 0.3316 i
0.0879 - 0.173 i
10
1.1926 - 0.3316 i
0.0879 + 0.173 i
11
-1.6044
1.62
12
1.6977 + 0.1316 i
0.0737 + 0.148 i
13
1.6977 - 0.1316 i
0.0737 - 0.148 i
14
1.7122
0.144
15
-1.6643 + 0.4607 i
0.84 - 1.11 i
16
-1.6643 - 0.4607 i
0.84 + 1.11 i
17
-1.8921
0.844 i
18
-2.3352
0.496
19
1.8456 + 2.0794 i
0.341 + 0.129 i
20
1.8456 - 2.0794 i
0.341 - 0.129 i
21
1.6171 + 2.9149 i
0.227 - 0.327 i
22
1.6171 - 2.9149 i
0.227 + 0.327 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
-0.9554 + 0.3281 i
0.574 + 0.596 i
Singularities of quadratic [12, 11, 11] approximant
2
-0.9554 - 0.3281 i
0.574 - 0.596 i
3
-0.3029 + 0.9982 i
0.000995 + 0.00304 i
4
-0.3029 - 0.9982 i
0.000995 - 0.00304 i
5
-0.3029 + 0.9982 i
0.00305 - 0.000996 i
6
-0.3029 - 0.9982 i
0.00305 + 0.000996 i
7
1.1655 + 0.3023 i
0.0902 + 0.0543 i
8
1.1655 - 0.3023 i
0.0902 - 0.0543 i
9
1.1587 + 0.3549 i
0.0137 - 0.0479 i
10
1.1587 - 0.3549 i
0.0137 + 0.0479 i
11
1.1626 + 0.3857 i
0.0528 + 0.0108 i
12
1.1626 - 0.3857 i
0.0528 - 0.0108 i
13
-1.8332 + 0.5516 i
0.616 + 2.77 i
14
-1.8332 - 0.5516 i
0.616 - 2.77 i
15
-1.9314
0.731
16
-2.0263
0.752 i
17
-2.5727 + 0.7795 i
0.371 - 0.902 i
18
-2.5727 - 0.7795 i
0.371 + 0.902 i
19
2.585 + 0.8254 i
0.809 - 0.159 i
20
2.585 - 0.8254 i
0.809 + 0.159 i
21
1.7712 + 2.2778 i
0.228 - 0.227 i
22
1.7712 - 2.2778 i
0.228 + 0.227 i
23
-20.7998
1.45
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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
-0.9554 + 0.328 i
0.572 + 0.602 i
Singularities of quadratic [12, 12, 11] approximant
2
-0.9554 - 0.328 i
0.572 - 0.602 i
3
-0.1786 + 0.9998 i
0.000679 + 0.00117 i
4
-0.1786 - 0.9998 i
0.000679 - 0.00117 i
5
-0.1787 + 0.9998 i
0.00117 - 0.000679 i
6
-0.1787 - 0.9998 i
0.00117 + 0.000679 i
7
1.034 + 0.0003 i
0.0209 - 0.0209 i
8
1.034 - 0.0003 i
0.0209 + 0.0209 i
9
1.1935 + 0.3253 i
0.0371 - 0.219 i
10
1.1935 - 0.3253 i
0.0371 + 0.219 i
11
-1.5891
1.81
12
-1.5818 + 0.5061 i
1.02 - 0.538 i
13
-1.5818 - 0.5061 i
1.02 + 0.538 i
14
1.747 + 0.4271 i
0.0268 + 0.169 i
15
1.747 - 0.4271 i
0.0268 - 0.169 i
16
-1.8127 + 0.484 i
0.864 + 0.43 i
17
-1.8127 - 0.484 i
0.864 - 0.43 i
18
1.4441 + 1.5974 i
0.0501 - 0.00732 i
19
1.4441 - 1.5974 i
0.0501 + 0.00732 i
20
2.0472 + 1.4846 i
0.0136 + 0.0759 i
21
2.0472 - 1.4846 i
0.0136 - 0.0759 i
22
1.4874 + 3.0977 i
0.00716 + 0.107 i
23
1.4874 - 3.0977 i
0.00716 - 0.107 i
24
-18.7247
0.497 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
-0.1755 + 0.9686 i
0.000511 + 0.00196 i
Singularities of quadratic [12, 12, 12] approximant
2
-0.1755 - 0.9686 i
0.000511 - 0.00196 i
3
-0.1755 + 0.9686 i
0.00196 - 0.000511 i
4
-0.1755 - 0.9686 i
0.00196 + 0.000511 i
5
-0.9554 + 0.328 i
0.573 + 0.602 i
6
-0.9554 - 0.328 i
0.573 - 0.602 i
7
1.1244 + 0.0015 i
0.0949 - 0.0993 i
8
1.1244 - 0.0015 i
0.0949 + 0.0993 i
9
1.1973 + 0.3288 i
0.0924 - 0.228 i
10
1.1973 - 0.3288 i
0.0924 + 0.228 i
11
1.5857 + 0.1657 i
0.129 + 0.262 i
12
1.5857 - 0.1657 i
0.129 - 0.262 i
13
-1.6302
1.83
14
-1.572 + 0.5253 i
1.23 - 0.481 i
15
-1.572 - 0.5253 i
1.23 + 0.481 i
16
-1.7111 + 0.5479 i
0.84 + 1.07 i
17
-1.7111 - 0.5479 i
0.84 - 1.07 i
18
2.0929
0.234
19
1.6691 + 1.8659 i
0.161 + 0.0507 i
20
1.6691 - 1.8659 i
0.161 - 0.0507 i
21
-3.3814
0.657 i
22
1.7543 + 2.9395 i
0.144 - 0.161 i
23
1.7543 - 2.9395 i
0.144 + 0.161 i
24
-7.2012
55.1
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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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