Singularities of Møller-Plesset series: example "a38"

Molecule BH. Basis aug-cc-pVQZ. 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
1.4792 + 0.246 i
0.0351 + 0.0418 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4792 - 0.246 i
0.0351 - 0.0418 i
3
1.3152 + 0.7784 i
0.00715 - 0.00355 i
4
1.3152 - 0.7784 i
0.00715 + 0.00355 i
5
1.3682 + 0.7509 i
0.00435 + 0.00746 i
6
1.3682 - 0.7509 i
0.00435 - 0.00746 i
7
-2.0343 + 0.0358 i
0.00189 + 0.00187 i
8
-2.0343 - 0.0358 i
0.00189 - 0.00187 i
9
-3.4166
0.0214
10
4.0852
0.553
11
-12.0568
0.653 i
12
2842.6613
8.3 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
0.3117
1.25e-7
Singularities of quadratic [6, 6, 6] approximant
2
0.3117
1.25e-7 i
3
1.3571 + 0.2802 i
0.0043 + 0.00579 i
4
1.3571 - 0.2802 i
0.0043 - 0.00579 i
5
1.347 + 0.6345 i
0.00201 + 0.00264 i
6
1.347 - 0.6345 i
0.00201 - 0.00264 i
7
1.2963 + 0.7464 i
0.00312 - 0.000908 i
8
1.2963 - 0.7464 i
0.00312 + 0.000908 i
9
-2.046
0.00278
10
-2.1349
0.00306 i
11
-3.9782
0.282
12
6.8139
0.421
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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
1.3403
0.00869
Singularities of quadratic [7, 6, 6] approximant
2
0.7509 + 1.26 i
0.000301 + 0.000151 i
3
0.7509 - 1.26 i
0.000301 - 0.000151 i
4
0.7507 + 1.282 i
0.000158 - 0.000303 i
5
0.7507 - 1.282 i
0.000158 + 0.000303 i
6
1.4416 + 0.5718 i
0.00304 + 0.00613 i
7
1.4416 - 0.5718 i
0.00304 - 0.00613 i
8
1.899
0.457 i
9
-2.0796
0.00125
10
-2.313
0.00154 i
11
1.6087 + 3.981 i
0.00283 - 0.0166 i
12
1.6087 - 3.981 i
0.00283 + 0.0166 i
13
-7.842
0.0545
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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
-0.4363 + 0.e-5 i
3.44e-8 + 3.44e-8 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.4363 - 0.e-5 i
3.44e-8 - 3.44e-8 i
3
0.9417 + 0.0008 i
0.000044 - 0.0000438 i
4
0.9417 - 0.0008 i
0.000044 + 0.0000438 i
5
1.4007
0.0119
6
-0.5477 + 1.7257 i
0.000157 - 0.0000204 i
7
-0.5477 - 1.7257 i
0.000157 + 0.0000204 i
8
-0.5898 + 1.7378 i
0.0000108 + 0.00016 i
9
-0.5898 - 1.7378 i
0.0000108 - 0.00016 i
10
1.753 + 0.7754 i
0.0184 + 0.0153 i
11
1.753 - 0.7754 i
0.0184 - 0.0153 i
12
-2.0694
0.000459
13
-2.8194
0.00141 i
14
86.723
0.76 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
-0.4465 + 0.9108 i
4.66e-6 + 6.54e-6 i
Singularities of quadratic [7, 7, 7] approximant
2
-0.4465 - 0.9108 i
4.66e-6 - 6.54e-6 i
3
-0.4465 + 0.9114 i
6.55e-6 - 4.67e-6 i
4
-0.4465 - 0.9114 i
6.55e-6 + 4.67e-6 i
5
1.0278 + 0.0015 i
0.0000901 - 0.0000893 i
6
1.0278 - 0.0015 i
0.0000901 + 0.0000893 i
7
1.3828
0.00879
8
-1.6631 + 0.0394 i
0.0000457 + 0.0000433 i
9
-1.6631 - 0.0394 i
0.0000457 - 0.0000433 i
10
1.7077 + 0.7641 i
0.0192 + 0.0105 i
11
1.7077 - 0.7641 i
0.0192 - 0.0105 i
12
-2.2931
0.000411
13
-6.1169
0.37 i
14
6.9607
0.283 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
-0.4679 + 0.9546 i
5.48e-6 + 0.0000107 i
Singularities of quadratic [8, 7, 7] approximant
2
-0.4679 - 0.9546 i
5.48e-6 - 0.0000107 i
3
-0.4678 + 0.9554 i
0.0000107 - 5.49e-6 i
4
-0.4678 - 0.9554 i
0.0000107 + 5.49e-6 i
5
1.1419 + 0.0055 i
0.0003 - 0.000291 i
6
1.1419 - 0.0055 i
0.0003 + 0.000291 i
7
1.3803
0.0071
8
-1.5596 + 0.0214 i
0.0000334 + 0.0000326 i
9
-1.5596 - 0.0214 i
0.0000334 - 0.0000326 i
10
1.7375 + 0.7479 i
0.0244 + 0.0152 i
11
1.7375 - 0.7479 i
0.0244 - 0.0152 i
12
-2.2483
0.000431
13
-4.7021
0.0289 i
14
5.62
0.862 i
15
15.3937
3.15
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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
-0.6259 + 0.6326 i
6.24e-7 - 1.56e-6 i
Singularities of quadratic [8, 8, 7] approximant
2
-0.6259 - 0.6326 i
6.24e-7 + 1.56e-6 i
3
-0.6261 + 0.6326 i
1.56e-6 + 6.24e-7 i
4
-0.6261 - 0.6326 i
1.56e-6 - 6.24e-7 i
5
1.3872
0.0278
6
1.5284
0.151 i
7
1.6715 + 0.5258 i
0.0164 - 0.0636 i
8
1.6715 - 0.5258 i
0.0164 + 0.0636 i
9
-0.7555 + 1.5851 i
0.0000297 + 0.0000798 i
10
-0.7555 - 1.5851 i
0.0000297 - 0.0000798 i
11
-0.719 + 1.6179 i
0.0000841 - 0.0000378 i
12
-0.719 - 1.6179 i
0.0000841 + 0.0000378 i
13
-1.9807
0.000224
14
2.2385
2.05
15
-2.9465
0.00127 i
16
34.0565
0.349 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
-0.4891 + 0.7661 i
5.5e-6 + 9.22e-7 i
Singularities of quadratic [8, 8, 8] approximant
2
-0.4891 - 0.7661 i
5.5e-6 - 9.22e-7 i
3
-0.4891 + 0.7663 i
9.22e-7 - 5.5e-6 i
4
-0.4891 - 0.7663 i
9.22e-7 + 5.5e-6 i
5
1.3813
0.0134
6
1.5117 + 0.6831 i
0.00427 - 0.00568 i
7
1.5117 - 0.6831 i
0.00427 + 0.00568 i
8
0.9563 + 1.4376 i
0.0000199 + 0.00056 i
9
0.9563 - 1.4376 i
0.0000199 - 0.00056 i
10
1.0099 + 1.4674 i
0.000622 - 0.0000285 i
11
1.0099 - 1.4674 i
0.000622 + 0.0000285 i
12
-1.9034
0.000961
13
-1.9823
0.00126 i
14
2.9848
0.299 i
15
-3.2128
0.0152
16
-39.0583
0.19 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
0.6547
5.31e-7
Singularities of quadratic [9, 8, 8] approximant
2
0.6547
5.31e-7 i
3
1.1016
0.000203
4
1.1156
0.000233 i
5
-0.6321 + 0.9356 i
1.71e-6 - 1.2e-6 i
6
-0.6321 - 0.9356 i
1.71e-6 + 1.2e-6 i
7
-0.6359 + 0.9407 i
1.18e-6 + 1.75e-6 i
8
-0.6359 - 0.9407 i
1.18e-6 - 1.75e-6 i
9
-1.1256 + 0.3818 i
1.3e-6 + 1.97e-7 i
10
-1.1256 - 0.3818 i
1.3e-6 - 1.97e-7 i
11
-1.1231 + 0.3979 i
1.63e-7 - 1.32e-6 i
12
-1.1231 - 0.3979 i
1.63e-7 + 1.32e-6 i
13
1.4654
0.0628
14
1.664 + 0.8015 i
0.00927 + 0.00531 i
15
1.664 - 0.8015 i
0.00927 - 0.00531 i
16
-2.3196 + 0.8239 i
0.000126 + 0.000266 i
17
-2.3196 - 0.8239 i
0.000126 - 0.000266 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
-0.4266
1.73e-9
Singularities of quadratic [9, 9, 8] approximant
2
-0.4266
1.73e-9 i
3
-0.501 + 0.8689 i
7.5e-7 - 7.53e-7 i
4
-0.501 - 0.8689 i
7.5e-7 + 7.53e-7 i
5
-0.5009 + 0.8707 i
7.57e-7 + 7.54e-7 i
6
-0.5009 - 0.8707 i
7.57e-7 - 7.54e-7 i
7
0.9471 + 0.4792 i
4.7e-6 - 0.0000314 i
8
0.9471 - 0.4792 i
4.7e-6 + 0.0000314 i
9
0.9495 + 0.4834 i
0.0000316 + 5.38e-6 i
10
0.9495 - 0.4834 i
0.0000316 - 5.38e-6 i
11
1.4532
0.0775
12
-1.6777
0.0000262
13
1.5413 + 0.8612 i
0.00304 + 0.00183 i
14
1.5413 - 0.8612 i
0.00304 - 0.00183 i
15
-2.1242
0.0000726 i
16
-2.5923 + 1.4771 i
0.000691 - 0.0000948 i
17
-2.5923 - 1.4771 i
0.000691 + 0.0000948 i
18
93.0772
7.34 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
0.4918 + 0.4134 i
1.8e-8 + 5.57e-8 i
Singularities of quadratic [9, 9, 9] approximant
2
0.4918 - 0.4134 i
1.8e-8 - 5.57e-8 i
3
0.4918 + 0.4134 i
5.57e-8 - 1.8e-8 i
4
0.4918 - 0.4134 i
5.57e-8 + 1.8e-8 i
5
-0.8191 + 0.0883 i
1.3e-8 + 1.45e-8 i
6
-0.8191 - 0.0883 i
1.3e-8 - 1.45e-8 i
7
-0.8198 + 0.09 i
1.47e-8 - 1.31e-8 i
8
-0.8198 - 0.09 i
1.47e-8 + 1.31e-8 i
9
-0.4642 + 0.9427 i
4.24e-7 - 2.84e-7 i
10
-0.4642 - 0.9427 i
4.24e-7 + 2.84e-7 i
11
-0.4687 + 0.9455 i
2.8e-7 + 4.33e-7 i
12
-0.4687 - 0.9455 i
2.8e-7 - 4.33e-7 i
13
1.2802
0.00121
14
1.6512
0.0985 i
15
-1.7551
0.0000175
16
1.7868 + 1.2215 i
0.00425 + 0.00245 i
17
1.7868 - 1.2215 i
0.00425 - 0.00245 i
18
9.4451
0.168
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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
0.1334 + 0.204 i
0
Singularities of quadratic [10, 9, 9] approximant
2
0.1334 - 0.204 i
0
3
0.1334 + 0.204 i
0
4
0.1334 - 0.204 i
0
5
-0.465
2.25e-10
6
-0.465
2.25e-10 i
7
0.5521
6.6e-9
8
0.5521
6.6e-9 i
9
-0.534 + 0.8373 i
3.88e-8 + 1.48e-7 i
10
-0.534 - 0.8373 i
3.88e-8 - 1.48e-7 i
11
-0.5394 + 0.8389 i
1.51e-7 - 3.63e-8 i
12
-0.5394 - 0.8389 i
1.51e-7 + 3.63e-8 i
13
1.2681
0.000818
14
-1.6414
9.52e-6
15
1.9004
4.72 i
16
2.6197
0.432
17
-1.1174 + 2.5824 i
0.0000312 + 0.000193 i
18
-1.1174 - 2.5824 i
0.0000312 - 0.000193 i
19
41.1942
0.0979 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
0.2387 + 0.8387 i
2.43e-7 - 1.73e-7 i
Singularities of quadratic [10, 10, 9] approximant
2
0.2387 - 0.8387 i
2.43e-7 + 1.73e-7 i
3
0.2388 + 0.8392 i
1.73e-7 + 2.43e-7 i
4
0.2388 - 0.8392 i
1.73e-7 - 2.43e-7 i
5
-0.9444 + 0.2536 i
9.54e-8 + 6.51e-8 i
6
-0.9444 - 0.2536 i
9.54e-8 - 6.51e-8 i
7
-0.9464 + 0.2599 i
6.56e-8 - 9.71e-8 i
8
-0.9464 - 0.2599 i
6.56e-8 + 9.71e-8 i
9
-0.4658 + 1.2797 i
2.25e-6 - 8.62e-7 i
10
-0.4658 - 1.2797 i
2.25e-6 + 8.62e-7 i
11
-0.5211 + 1.2686 i
4.56e-7 + 2.29e-6 i
12
-0.5211 - 1.2686 i
4.56e-7 - 2.29e-6 i
13
1.4252 + 0.2351 i
0.00323 - 0.00517 i
14
1.4252 - 0.2351 i
0.00323 + 0.00517 i
15
1.3827 + 0.5031 i
0.00175 - 0.000753 i
16
1.3827 - 0.5031 i
0.00175 + 0.000753 i
17
-1.7597 + 0.8378 i
0.0000175 + 0.0000143 i
18
-1.7597 - 0.8378 i
0.0000175 - 0.0000143 i
19
7.1795
0.306
20
12.7727
0.0968 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
-0.9025
3.76e-8
Singularities of quadratic [10, 10, 10] approximant
2
-0.9071
3.76e-8 i
3
0.2396 + 0.8965 i
3.3e-7 - 4.42e-8 i
4
0.2396 - 0.8965 i
3.3e-7 + 4.42e-8 i
5
0.2401 + 0.8979 i
4.27e-8 + 3.32e-7 i
6
0.2401 - 0.8979 i
4.27e-8 - 3.32e-7 i
7
-1.0425 + 0.6993 i
4.56e-7 - 1.97e-7 i
8
-1.0425 - 0.6993 i
4.56e-7 + 1.97e-7 i
9
-1.1187 + 0.6796 i
8.67e-8 + 5.39e-7 i
10
-1.1187 - 0.6796 i
8.67e-8 - 5.39e-7 i
11
-0.2547 + 1.35 i
1.29e-6 - 1.76e-6 i
12
-0.2547 - 1.35 i
1.29e-6 + 1.76e-6 i
13
-1.3895
1.02e-6
14
-0.2448 + 1.4307 i
2.31e-6 + 1.76e-6 i
15
-0.2448 - 1.4307 i
2.31e-6 - 1.76e-6 i
16
1.4617 + 0.2114 i
0.00695 - 0.00977 i
17
1.4617 - 0.2114 i
0.00695 + 0.00977 i
18
1.4033 + 0.5434 i
0.00212 + 0.000413 i
19
1.4033 - 0.5434 i
0.00212 - 0.000413 i
20
2.9771
2.6
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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
0.1608 + 0.8308 i
3.11e-7 + 6.58e-7 i
Singularities of quadratic [11, 10, 10] approximant
2
0.1608 - 0.8308 i
3.11e-7 - 6.58e-7 i
3
0.1608 + 0.8309 i
6.58e-7 - 3.11e-7 i
4
0.1608 - 0.8309 i
6.58e-7 + 3.11e-7 i
5
-0.9393 + 0.2366 i
2.32e-7 + 2.71e-7 i
6
-0.9393 - 0.2366 i
2.32e-7 - 2.71e-7 i
7
-0.9404 + 0.2389 i
2.73e-7 - 2.33e-7 i
8
-0.9404 - 0.2389 i
2.73e-7 + 2.33e-7 i
9
-0.6095 + 1.1829 i
3.93e-6 - 3.09e-6 i
10
-0.6095 - 1.1829 i
3.93e-6 + 3.09e-6 i
11
-0.5912 + 1.1973 i
3.4e-6 + 3.91e-6 i
12
-0.5912 - 1.1973 i
3.4e-6 - 3.91e-6 i
13
1.073 + 0.8224 i
0.000511 + 0.000243 i
14
1.073 - 0.8224 i
0.000511 - 0.000243 i
15
1.0729 + 0.8343 i
0.000314 - 0.000486 i
16
1.0729 - 0.8343 i
0.000314 + 0.000486 i
17
1.3787
0.0105
18
1.6236 + 0.8191 i
0.00981 + 0.00392 i
19
1.6236 - 0.8191 i
0.00981 - 0.00392 i
20
-2.1991 + 0.7057 i
0.0000103 - 0.000196 i
21
-2.1991 - 0.7057 i
0.0000103 + 0.000196 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
-0.466
0
Singularities of quadratic [11, 11, 10] approximant
2
-0.466
0
3
-0.8218
8.58e-9
4
-0.8241
8.63e-9 i
5
0.1693 + 0.9188 i
1.53e-7 + 1.78e-7 i
6
0.1693 - 0.9188 i
1.53e-7 - 1.78e-7 i
7
0.1714 + 0.9186 i
1.79e-7 - 1.54e-7 i
8
0.1714 - 0.9186 i
1.79e-7 + 1.54e-7 i
9
-0.937 + 0.8381 i
1.11e-7 + 3.69e-7 i
10
-0.937 - 0.8381 i
1.11e-7 - 3.69e-7 i
11
-0.9957 + 0.9141 i
5.18e-7 - 1.35e-7 i
12
-0.9957 - 0.9141 i
5.18e-7 + 1.35e-7 i
13
-1.3817
7.91e-7
14
1.472
0.242
15
1.4014 + 0.6042 i
0.00178 + 0.00138 i
16
1.4014 - 0.6042 i
0.00178 - 0.00138 i
17
-0.0263 + 1.6302 i
5.77e-6 + 3.18e-6 i
18
-0.0263 - 1.6302 i
5.77e-6 - 3.18e-6 i
19
0.2748 + 1.7523 i
2.58e-6 + 0.0000164 i
20
0.2748 - 1.7523 i
2.58e-6 - 0.0000164 i
21
2.2685
0.0649 i
22
-8.7043
0.0585 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
-0.8005 + 0.2573 i
2.02e-8 - 2.64e-9 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.8005 - 0.2573 i
2.02e-8 + 2.64e-9 i
3
-0.8006 + 0.2586 i
2.74e-9 + 2.02e-8 i
4
-0.8006 - 0.2586 i
2.74e-9 - 2.02e-8 i
5
0.0037 + 0.9123 i
4.19e-8 - 2.63e-8 i
6
0.0037 - 0.9123 i
4.19e-8 + 2.63e-8 i
7
0.0019 + 0.9149 i
2.61e-8 + 4.22e-8 i
8
0.0019 - 0.9149 i
2.61e-8 - 4.22e-8 i
9
0.9949
5.4e-6
10
0.9983
5.55e-6 i
11
-0.5732 + 0.8862 i
2.03e-8 + 1.01e-7 i
12
-0.5732 - 0.8862 i
2.03e-8 - 1.01e-7 i
13
-0.5853 + 0.8907 i
1.06e-7 - 1.83e-8 i
14
-0.5853 - 0.8907 i
1.06e-7 + 1.83e-8 i
15
0.4771 + 1.0546 i
4.5e-8 + 9.32e-7 i
16
0.4771 - 1.0546 i
4.5e-8 - 9.32e-7 i
17
0.4785 + 1.0805 i
1.e-6 + 8.02e-8 i
18
0.4785 - 1.0805 i
1.e-6 - 8.02e-8 i
19
1.3258
0.0017
20
1.4424 + 0.6368 i
0.00113 + 0.0014 i
21
1.4424 - 0.6368 i
0.00113 - 0.0014 i
22
-1.7871
0.0000336
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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
-0.1163 + 0.8333 i
2.51e-8 + 6.78e-9 i
Singularities of quadratic [12, 11, 11] approximant
2
-0.1163 - 0.8333 i
2.51e-8 - 6.78e-9 i
3
-0.1169 + 0.834 i
6.84e-9 - 2.51e-8 i
4
-0.1169 - 0.834 i
6.84e-9 + 2.51e-8 i
5
-0.8305 + 0.2678 i
1.51e-8 + 2.03e-8 i
6
-0.8305 - 0.2678 i
1.51e-8 - 2.03e-8 i
7
-0.8327 + 0.268 i
2.05e-8 - 1.51e-8 i
8
-0.8327 - 0.268 i
2.05e-8 + 1.51e-8 i
9
0.3662 + 0.9301 i
1.35e-7 - 4.62e-7 i
10
0.3662 - 0.9301 i
1.35e-7 + 4.62e-7 i
11
0.3697 + 0.93 i
4.72e-7 + 1.35e-7 i
12
0.3697 - 0.93 i
4.72e-7 - 1.35e-7 i
13
-0.4583 + 0.9693 i
1.37e-9 - 1.4e-7 i
14
-0.4583 - 0.9693 i
1.37e-9 + 1.4e-7 i
15
-0.4744 + 0.974 i
1.48e-7 + 9.81e-9 i
16
-0.4744 - 0.974 i
1.48e-7 - 9.81e-9 i
17
1.4267 + 0.2037 i
0.000326 - 0.00861 i
18
1.4267 - 0.2037 i
0.000326 + 0.00861 i
19
1.4198 + 0.4981 i
0.00263 - 0.00143 i
20
1.4198 - 0.4981 i
0.00263 + 0.00143 i
21
-1.7796
0.0000154
22
2.9896
0.992
23
-3.7527
0.0132 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
0.7371
2.15e-8
Singularities of quadratic [12, 12, 11] approximant
2
0.7371
2.15e-8 i
3
-0.2679 + 0.7736 i
4.65e-10 + 2.14e-9 i
4
-0.2679 - 0.7736 i
4.65e-10 - 2.14e-9 i
5
-0.2683 + 0.7762 i
2.14e-9 - 4.63e-10 i
6
-0.2683 - 0.7762 i
2.14e-9 + 4.63e-10 i
7
-0.8516 + 0.2729 i
7.24e-9 - 1.36e-9 i
8
-0.8516 - 0.2729 i
7.24e-9 + 1.36e-9 i
9
-0.8522 + 0.2812 i
1.6e-9 + 7.31e-9 i
10
-0.8522 - 0.2812 i
1.6e-9 - 7.31e-9 i
11
0.2888 + 0.9585 i
5.23e-8 + 2.24e-8 i
12
0.2888 - 0.9585 i
5.23e-8 - 2.24e-8 i
13
0.3049 + 0.961 i
2.28e-8 - 5.84e-8 i
14
0.3049 - 0.961 i
2.28e-8 + 5.84e-8 i
15
-0.3228 + 1.0274 i
7.72e-9 + 2.51e-8 i
16
-0.3228 - 1.0274 i
7.72e-9 - 2.51e-8 i
17
-0.2923 + 1.1134 i
3.75e-8 - 2.52e-8 i
18
-0.2923 - 1.1134 i
3.75e-8 + 2.52e-8 i
19
1.3338
0.00117
20
1.3028 + 0.5453 i
0.000197 - 0.000163 i
21
1.3028 - 0.5453 i
0.000197 + 0.000163 i
22
2.5258
0.0992 i
23
-3.8842 + 1.4282 i
0.000805 + 0.00107 i
24
-3.8842 - 1.4282 i
0.000805 - 0.00107 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
-0.805 + 0.369 i
1.94e-8 - 1.36e-8 i
Singularities of quadratic [12, 12, 12] approximant
2
-0.805 - 0.369 i
1.94e-8 + 1.36e-8 i
3
-0.8067 + 0.367 i
1.35e-8 + 1.95e-8 i
4
-0.8067 - 0.367 i
1.35e-8 - 1.95e-8 i
5
-0.9175 + 0.0018 i
2.35e-8 + 2.31e-8 i
6
-0.9175 - 0.0018 i
2.35e-8 - 2.31e-8 i
7
-0.4932 + 0.7843 i
2.02e-8 + 2.35e-8 i
8
-0.4932 - 0.7843 i
2.02e-8 - 2.35e-8 i
9
-0.4967 + 0.7854 i
2.38e-8 - 2.02e-8 i
10
-0.4967 - 0.7854 i
2.38e-8 + 2.02e-8 i
11
-0.0763 + 0.968 i
3.14e-9 - 7.36e-8 i
12
-0.0763 - 0.968 i
3.14e-9 + 7.36e-8 i
13
-0.0695 + 0.9685 i
7.46e-8 + 1.74e-9 i
14
-0.0695 - 0.9685 i
7.46e-8 - 1.74e-9 i
15
0.39 + 1.0118 i
6.84e-8 - 5.6e-7 i
16
0.39 - 1.0118 i
6.84e-8 + 5.6e-7 i
17
0.3812 + 1.0215 i
5.4e-7 + 1.06e-7 i
18
0.3812 - 1.0215 i
5.4e-7 - 1.06e-7 i
19
1.2779 + 0.1411 i
0.000592 + 0.000109 i
20
1.2779 - 0.1411 i
0.000592 - 0.000109 i
21
1.3316
0.000885
22
1.4783 + 0.6038 i
0.00196 + 0.00199 i
23
1.4783 - 0.6038 i
0.00196 - 0.00199 i
24
-1.712
0.0000194
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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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