Singularities of Møller-Plesset series: example "a22"

Molecule BH. 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
1.6046
0.187
Singularities of quadratic [6, 6, 5] approximant
2
1.5661 + 0.4779 i
0.107 + 0.0412 i
3
1.5661 - 0.4779 i
0.107 - 0.0412 i
4
1.9195
2.95 i
5
-2.7304
0.00121
6
-3.1753
0.00104 i
7
-3.4951 + 1.1585 i
0.00252 - 0.000814 i
8
-3.4951 - 1.1585 i
0.00252 + 0.000814 i
9
4.3579
0.645
10
-6.9267
0.014
11
8.0308
3.27 i
12
-11.0333
9.61 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
1.5889
0.201
Singularities of quadratic [6, 6, 6] approximant
2
1.5591 + 0.4646 i
0.121 + 0.0123 i
3
1.5591 - 0.4646 i
0.121 - 0.0123 i
4
1.8089
141. i
5
-2.5621 + 0.0434 i
0.000349 + 0.000397 i
6
-2.5621 - 0.0434 i
0.000349 - 0.000397 i
7
-3.0001
0.00105
8
3.7136
1.6
9
1.8588 + 4.7733 i
0.0144 - 0.0111 i
10
1.8588 - 4.7733 i
0.0144 + 0.0111 i
11
0.7549 + 5.1224 i
0.00645 + 0.0096 i
12
0.7549 - 5.1224 i
0.00645 - 0.0096 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
1.5891
0.201
Singularities of quadratic [7, 6, 6] approximant
2
1.559 + 0.4646 i
0.121 + 0.012 i
3
1.559 - 0.4646 i
0.121 - 0.012 i
4
1.809
133. i
5
-2.5497 + 0.0415 i
0.000339 + 0.000382 i
6
-2.5497 - 0.0415 i
0.000339 - 0.000382 i
7
-2.9967
0.00105
8
3.724
1.56
9
1.8547 + 4.7067 i
0.0136 - 0.0116 i
10
1.8547 - 4.7067 i
0.0136 + 0.0116 i
11
0.7965 + 5.0787 i
0.00674 + 0.00931 i
12
0.7965 - 5.0787 i
0.00674 - 0.00931 i
13
589.5998
0.0232 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
1.6019
0.217
Singularities of quadratic [7, 7, 6] approximant
2
1.5561 + 0.4684 i
0.109 + 0.00956 i
3
1.5561 - 0.4684 i
0.109 - 0.00956 i
4
1.8581
6.2 i
5
-2.0094 + 0.0049 i
0.0000832 + 0.0000837 i
6
-2.0094 - 0.0049 i
0.0000832 - 0.0000837 i
7
-2.9293
0.0011
8
0.2655 + 3.0244 i
0.00212 - 0.000269 i
9
0.2655 - 3.0244 i
0.00212 + 0.000269 i
10
0.3517 + 3.04 i
0.00029 + 0.00224 i
11
0.3517 - 3.04 i
0.00029 - 0.00224 i
12
4.414
0.703
13
14.0665
0.214 i
14
-76.1998
0.0656 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
1.0442
0.0011
Singularities of quadratic [7, 7, 7] approximant
2
1.0444
0.0011 i
3
1.5441
0.139
4
1.5626 + 0.4529 i
0.158 + 0.00438 i
5
1.5626 - 0.4529 i
0.158 - 0.00438 i
6
1.7041
1.9 i
7
-2.3652 + 0.0217 i
0.000205 + 0.000213 i
8
-2.3652 - 0.0217 i
0.000205 - 0.000213 i
9
-2.958
0.00103
10
3.2916
11.3
11
2.4216 + 3.9714 i
0.0037 - 0.0305 i
12
2.4216 - 3.9714 i
0.0037 + 0.0305 i
13
1.7653 + 4.8465 i
0.0173 + 0.00822 i
14
1.7653 - 4.8465 i
0.0173 - 0.00822 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
1.4593 + 0.4533 i
0.00251 - 0.0295 i
Singularities of quadratic [8, 7, 7] approximant
2
1.4593 - 0.4533 i
0.00251 + 0.0295 i
3
1.5593 + 0.4677 i
0.0295 + 0.0164 i
4
1.5593 - 0.4677 i
0.0295 - 0.0164 i
5
1.7663 + 0.5558 i
0.0602 + 0.00648 i
6
1.7663 - 0.5558 i
0.0602 - 0.00648 i
7
1.9103
0.209
8
-2.4059 + 0.0279 i
0.00019 + 0.0002 i
9
-2.4059 - 0.0279 i
0.00019 - 0.0002 i
10
-2.9405
0.000871
11
4.6556
1.06 i
12
3.3735 + 5.9527 i
0.0573 - 0.015 i
13
3.3735 - 5.9527 i
0.0573 + 0.015 i
14
-11.7808
0.0181 i
15
198.3366
1.36
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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
1.4865 + 0.4844 i
0.0196 - 0.0164 i
Singularities of quadratic [8, 8, 7] approximant
2
1.4865 - 0.4844 i
0.0196 + 0.0164 i
3
1.6618 + 0.7271 i
0.00588 - 0.00932 i
4
1.6618 - 0.7271 i
0.00588 + 0.00932 i
5
1.8267
0.294
6
1.6717 + 0.8718 i
0.00617 + 0.00741 i
7
1.6717 - 0.8718 i
0.00617 - 0.00741 i
8
-1.9439 + 0.003 i
0.0000334 + 0.0000335 i
9
-1.9439 - 0.003 i
0.0000334 - 0.0000335 i
10
-2.7564
0.000528
11
2.9677
0.332 i
12
-3.5644
0.00187 i
13
-4.2189
0.0121
14
2.3939 + 7.2678 i
0.0193 + 0.00532 i
15
2.3939 - 7.2678 i
0.0193 - 0.00532 i
16
-52.9788
0.0308 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
-0.5906 + 0.e-5 i
5.37e-8 + 5.37e-8 i
Singularities of quadratic [8, 8, 8] approximant
2
-0.5906 - 0.e-5 i
5.37e-8 - 5.37e-8 i
3
1.466 + 0.4684 i
0.0098 - 0.0197 i
4
1.466 - 0.4684 i
0.0098 + 0.0197 i
5
1.6453 + 0.5291 i
0.00232 + 0.0249 i
6
1.6453 - 0.5291 i
0.00232 - 0.0249 i
7
1.7987 + 0.7233 i
0.0145 + 0.0181 i
8
1.7987 - 0.7233 i
0.0145 - 0.0181 i
9
1.9823
0.168
10
-2.5188 + 0.0216 i
0.000753 + 0.000919 i
11
-2.5188 - 0.0216 i
0.000753 - 0.000919 i
12
-3.0555
0.00167
13
2.2386 + 6.0387 i
0.0203 + 0.00591 i
14
2.2386 - 6.0387 i
0.0203 - 0.00591 i
15
6.4656 + 0.9675 i
0.107 + 0.116 i
16
6.4656 - 0.9675 i
0.107 - 0.116 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
0.8106 + 0.6982 i
0.0000127 + 2.03e-6 i
Singularities of quadratic [9, 8, 8] approximant
2
0.8106 - 0.6982 i
0.0000127 - 2.03e-6 i
3
0.8107 + 0.6982 i
2.03e-6 - 0.0000127 i
4
0.8107 - 0.6982 i
2.03e-6 + 0.0000127 i
5
-1.3665 + 0.e-4 i
2.16e-6 + 2.16e-6 i
6
-1.3665 - 0.e-4 i
2.16e-6 - 2.16e-6 i
7
1.4175 + 0.4519 i
0.00278 - 0.00572 i
8
1.4175 - 0.4519 i
0.00278 + 0.00572 i
9
1.5241 + 0.3411 i
0.0213 - 0.00496 i
10
1.5241 - 0.3411 i
0.0213 + 0.00496 i
11
2.2876 + 0.2981 i
0.225 + 0.249 i
12
2.2876 - 0.2981 i
0.225 - 0.249 i
13
-2.646
0.000351
14
-3.1271
0.000741 i
15
-3.8365
0.0166
16
3.7583 + 4.8708 i
0.0101 - 0.0357 i
17
3.7583 - 4.8708 i
0.0101 + 0.0357 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
0.1576 + 0.4849 i
4.71e-9 + 8.24e-9 i
Singularities of quadratic [9, 9, 8] approximant
2
0.1576 - 0.4849 i
4.71e-9 - 8.24e-9 i
3
0.1576 + 0.4849 i
8.24e-9 - 4.71e-9 i
4
0.1576 - 0.4849 i
8.24e-9 + 4.71e-9 i
5
-1.5126 + 0.0004 i
2.4e-6 + 2.4e-6 i
6
-1.5126 - 0.0004 i
2.4e-6 - 2.4e-6 i
7
1.4571 + 0.4756 i
0.0103 - 0.00823 i
8
1.4571 - 0.4756 i
0.0103 + 0.00823 i
9
1.667 + 0.3576 i
0.0404 + 0.111 i
10
1.667 - 0.3576 i
0.0404 - 0.111 i
11
2.3967 + 0.7907 i
0.0524 + 0.0609 i
12
2.3967 - 0.7907 i
0.0524 - 0.0609 i
13
-2.6496
0.000271
14
-3.4922
0.00127 i
15
-4.6041
0.00418
16
3.5404 + 3.3216 i
0.0427 + 0.00373 i
17
3.5404 - 3.3216 i
0.0427 - 0.00373 i
18
-109.0062
0.177 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
-0.4707 + 0.6764 i
5.46e-8 - 2.54e-7 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.4707 - 0.6764 i
5.46e-8 + 2.54e-7 i
3
-0.4707 + 0.6764 i
2.54e-7 + 5.46e-8 i
4
-0.4707 - 0.6764 i
2.54e-7 - 5.46e-8 i
5
1.3562 + 0.0135 i
0.00215 - 0.00188 i
6
1.3562 - 0.0135 i
0.00215 + 0.00188 i
7
1.4954 + 0.4783 i
0.0254 + 0.00139 i
8
1.4954 - 0.4783 i
0.0254 - 0.00139 i
9
1.5849 + 0.2245 i
0.0464 - 0.0632 i
10
1.5849 - 0.2245 i
0.0464 + 0.0632 i
11
2.2809
0.838
12
-2.483
0.000561
13
-2.5509
0.000695 i
14
-3.1157
0.00304
15
3.0297 + 4.4261 i
0.0174 - 0.0457 i
16
3.0297 - 4.4261 i
0.0174 + 0.0457 i
17
4.9091 + 2.5177 i
0.2 - 0.0641 i
18
4.9091 - 2.5177 i
0.2 + 0.0641 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
-0.5747 + 0.6411 i
7.17e-8 - 4.9e-7 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.5747 - 0.6411 i
7.17e-8 + 4.9e-7 i
3
-0.5747 + 0.6411 i
4.9e-7 + 7.17e-8 i
4
-0.5747 - 0.6411 i
4.9e-7 - 7.17e-8 i
5
1.4399 + 0.4318 i
0.00186 + 0.0137 i
6
1.4399 - 0.4318 i
0.00186 - 0.0137 i
7
1.5538 + 0.3558 i
0.0406 - 0.00627 i
8
1.5538 - 0.3558 i
0.0406 + 0.00627 i
9
1.9328 + 0.6063 i
0.0301 - 0.0381 i
10
1.9328 - 0.6063 i
0.0301 + 0.0381 i
11
1.4853 + 1.8899 i
0.000154 + 0.00145 i
12
1.4853 - 1.8899 i
0.000154 - 0.00145 i
13
1.5665 + 1.8317 i
0.0016 - 0.000277 i
14
1.5665 - 1.8317 i
0.0016 + 0.000277 i
15
-2.5446
0.000477
16
-2.6741
0.000595 i
17
-3.2564
0.00905
18
4.0096 + 4.2326 i
0.000713 + 0.0329 i
19
4.0096 - 4.2326 i
0.000713 - 0.0329 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
0.3095
0
Singularities of quadratic [10, 10, 9] approximant
2
0.3095
0
3
-0.7041 + 0.6566 i
1.8e-8 + 7.61e-8 i
4
-0.7041 - 0.6566 i
1.8e-8 - 7.61e-8 i
5
-0.7041 + 0.6566 i
7.61e-8 - 1.8e-8 i
6
-0.7041 - 0.6566 i
7.61e-8 + 1.8e-8 i
7
1.4447 + 0.4507 i
0.00426 - 0.00734 i
8
1.4447 - 0.4507 i
0.00426 + 0.00734 i
9
1.5249 + 0.2601 i
0.00622 - 0.0265 i
10
1.5249 - 0.2601 i
0.00622 + 0.0265 i
11
1.7215
0.159
12
-2.579
0.000154
13
0.156 + 2.8887 i
0.0000749 + 0.00017 i
14
0.156 - 2.8887 i
0.0000749 - 0.00017 i
15
-0.0065 + 2.9944 i
0.000174 - 0.0000352 i
16
-0.0065 - 2.9944 i
0.000174 + 0.0000352 i
17
3.0417
0.462 i
18
-3.9883
0.004 i
19
-4.1607 + 4.3156 i
0.0013 + 0.00149 i
20
-4.1607 - 4.3156 i
0.0013 - 0.00149 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
-0.7037 + 0.e-5 i
6.97e-9 + 6.97e-9 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.7037 - 0.e-5 i
6.97e-9 - 6.97e-9 i
3
-0.4782 + 0.8589 i
1.34e-7 - 1.91e-7 i
4
-0.4782 - 0.8589 i
1.34e-7 + 1.91e-7 i
5
-0.4782 + 0.859 i
1.91e-7 + 1.34e-7 i
6
-0.4782 - 0.859 i
1.91e-7 - 1.34e-7 i
7
1.2944 + 0.0084 i
0.000414 - 0.000382 i
8
1.2944 - 0.0084 i
0.000414 + 0.000382 i
9
1.5265 + 0.2299 i
0.00805 - 0.0164 i
10
1.5265 - 0.2299 i
0.00805 + 0.0164 i
11
1.4695 + 0.4909 i
0.0104 + 0.00178 i
12
1.4695 - 0.4909 i
0.0104 - 0.00178 i
13
1.7907
0.142
14
-2.2825 + 0.0351 i
0.0000452 + 0.0000419 i
15
-2.2825 - 0.0351 i
0.0000452 - 0.0000419 i
16
-2.8495
0.000435
17
1.9093 + 5.3552 i
0.0124 - 0.00199 i
18
1.9093 - 5.3552 i
0.0124 + 0.00199 i
19
6.0866 + 1.3128 i
0.135 + 0.0995 i
20
6.0866 - 1.3128 i
0.135 - 0.0995 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
-0.8304 + 0.3081 i
2.71e-10 + 9.96e-9 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.8304 - 0.3081 i
2.71e-10 - 9.96e-9 i
3
-0.8304 + 0.3081 i
9.96e-9 - 2.71e-10 i
4
-0.8304 - 0.3081 i
9.96e-9 + 2.71e-10 i
5
-0.3761 + 0.8355 i
3.89e-8 - 2.33e-9 i
6
-0.3761 - 0.8355 i
3.89e-8 + 2.33e-9 i
7
-0.3761 + 0.8355 i
2.32e-9 + 3.89e-8 i
8
-0.3761 - 0.8355 i
2.32e-9 - 3.89e-8 i
9
1.3549
0.00219
10
1.3913
0.00289 i
11
1.4644 + 0.4496 i
0.00372 - 0.0119 i
12
1.4644 - 0.4496 i
0.00372 + 0.0119 i
13
1.6238
0.0695
14
2.2816
0.118 i
15
-2.4405 + 0.121 i
0.0000355 + 0.0000241 i
16
-2.4405 - 0.121 i
0.0000355 - 0.0000241 i
17
-2.7852
0.000137
18
2.6742 + 1.4095 i
0.0217 - 0.0143 i
19
2.6742 - 1.4095 i
0.0217 + 0.0143 i
20
2.4858 + 3.7473 i
0.0065 + 0.00522 i
21
2.4858 - 3.7473 i
0.0065 - 0.00522 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
-0.843 + 0.e-5 i
1.03e-8 + 1.03e-8 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.843 - 0.e-5 i
1.03e-8 - 1.03e-8 i
3
-0.4071 + 0.9268 i
1.94e-8 - 1.34e-7 i
4
-0.4071 - 0.9268 i
1.94e-8 + 1.34e-7 i
5
-0.4071 + 0.9268 i
1.34e-7 + 1.94e-8 i
6
-0.4071 - 0.9268 i
1.34e-7 - 1.94e-8 i
7
1.4002 + 0.3578 i
0.00253 - 0.00362 i
8
1.4002 - 0.3578 i
0.00253 + 0.00362 i
9
1.5357 + 0.348 i
0.00368 + 0.0201 i
10
1.5357 - 0.348 i
0.00368 - 0.0201 i
11
1.5075 + 0.6227 i
0.00247 - 0.00255 i
12
1.5075 - 0.6227 i
0.00247 + 0.00255 i
13
-1.8023 + 0.0071 i
2.35e-6 + 2.29e-6 i
14
-1.8023 - 0.0071 i
2.35e-6 - 2.29e-6 i
15
1.8797 + 0.789 i
0.00853 - 0.00418 i
16
1.8797 - 0.789 i
0.00853 + 0.00418 i
17
2.2412 + 1.3563 i
0.0103 + 0.00209 i
18
2.2412 - 1.3563 i
0.0103 - 0.00209 i
19
-2.6605
0.000156
20
0.4242 + 6.6447 i
0.00361 + 0.00378 i
21
0.4242 - 6.6447 i
0.00361 - 0.00378 i
22
-13.9748
0.00769 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
-0.8378 + 0.e-5 i
1.47e-8 + 1.47e-8 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.8378 - 0.e-5 i
1.47e-8 - 1.47e-8 i
3
-0.4094 + 0.9319 i
6.27e-8 - 1.98e-7 i
4
-0.4094 - 0.9319 i
6.27e-8 + 1.98e-7 i
5
-0.4094 + 0.9319 i
1.98e-7 + 6.27e-8 i
6
-0.4094 - 0.9319 i
1.98e-7 - 6.27e-8 i
7
1.4649 + 0.3914 i
0.0187 + 0.01 i
8
1.4649 - 0.3914 i
0.0187 - 0.01 i
9
1.5227 + 0.2473 i
0.0346 + 0.0504 i
10
1.5227 - 0.2473 i
0.0346 - 0.0504 i
11
-1.8596 + 0.0082 i
3.91e-6 + 3.81e-6 i
12
-1.8596 - 0.0082 i
3.91e-6 - 3.81e-6 i
13
1.5667 + 1.1389 i
0.00056 + 0.0014 i
14
1.5667 - 1.1389 i
0.00056 - 0.0014 i
15
1.6575 + 1.1219 i
0.0018 - 0.00061 i
16
1.6575 - 1.1219 i
0.0018 + 0.00061 i
17
2.0883 + 0.0267 i
0.0826 - 0.135 i
18
2.0883 - 0.0267 i
0.0826 + 0.135 i
19
-2.6905
0.000194
20
0.0032 + 6.371 i
0.00237 + 0.00447 i
21
0.0032 - 6.371 i
0.00237 - 0.00447 i
22
-21.5628
0.00826 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
0.4381
0
Singularities of quadratic [12, 11, 11] approximant
2
0.4381
0
3
-0.8492
1.83e-9
4
-0.8492
1.83e-9 i
5
-0.4069 + 0.9143 i
1.51e-8 - 1.63e-8 i
6
-0.4069 - 0.9143 i
1.51e-8 + 1.63e-8 i
7
-0.4069 + 0.9143 i
1.63e-8 + 1.51e-8 i
8
-0.4069 - 0.9143 i
1.63e-8 - 1.51e-8 i
9
1.1683 + 0.3814 i
0.0000151 - 0.0000232 i
10
1.1683 - 0.3814 i
0.0000151 + 0.0000232 i
11
1.1716 + 0.3906 i
0.0000227 + 0.000017 i
12
1.1716 - 0.3906 i
0.0000227 - 0.000017 i
13
1.3902 + 0.511 i
0.000949 - 0.000109 i
14
1.3902 - 0.511 i
0.000949 + 0.000109 i
15
1.5969
0.0231
16
-1.6933 + 0.3592 i
2.34e-7 + 1.98e-7 i
17
-1.6933 - 0.3592 i
2.34e-7 - 1.98e-7 i
18
-1.7162 + 0.3562 i
2.22e-7 - 2.33e-7 i
19
-1.7162 - 0.3562 i
2.22e-7 + 2.33e-7 i
20
-2.3765
0.0000123
21
3.1321 + 3.6074 i
0.0229 - 0.0106 i
22
3.1321 - 3.6074 i
0.0229 + 0.0106 i
23
5.1591
1.45 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
-0.2551
0
Singularities of quadratic [12, 12, 11] approximant
2
-0.2551
0
3
-0.8372 + 0.e-5 i
1.29e-9 + 1.29e-9 i
4
-0.8372 - 0.e-5 i
1.29e-9 - 1.29e-9 i
5
-0.419 + 0.9251 i
2.3e-8 + 1.15e-8 i
6
-0.419 - 0.9251 i
2.3e-8 - 1.15e-8 i
7
-0.419 + 0.9251 i
1.15e-8 - 2.3e-8 i
8
-0.419 - 0.9251 i
1.15e-8 + 2.3e-8 i
9
0.9147 + 0.7713 i
6.03e-7 - 2.42e-6 i
10
0.9147 - 0.7713 i
6.03e-7 + 2.42e-6 i
11
0.9153 + 0.7711 i
2.43e-6 + 6.e-7 i
12
0.9153 - 0.7711 i
2.43e-6 - 6.e-7 i
13
1.2644
0.000119
14
1.2969
0.000154 i
15
1.4854
0.00339
16
1.4087 + 0.4837 i
0.00146 - 0.00101 i
17
1.4087 - 0.4837 i
0.00146 + 0.00101 i
18
-1.7582 + 0.0108 i
6.57e-7 + 6.17e-7 i
19
-1.7582 - 0.0108 i
6.57e-7 - 6.17e-7 i
20
-2.5687
0.0000643
21
3.9101
1.03e3 i
22
2.5418 + 4.8619 i
0.000638 + 0.0122 i
23
2.5418 - 4.8619 i
0.000638 - 0.0122 i
24
-76.6342
0.038 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
-0.4981 + 0.7028 i
1.05e-9 - 2.02e-10 i
Singularities of quadratic [12, 12, 12] approximant
2
-0.4981 - 0.7028 i
1.05e-9 + 2.02e-10 i
3
-0.4981 + 0.7028 i
2.02e-10 + 1.05e-9 i
4
-0.4981 - 0.7028 i
2.02e-10 - 1.05e-9 i
5
-0.2659 + 0.9666 i
2.27e-9 + 7.85e-9 i
6
-0.2659 - 0.9666 i
2.27e-9 - 7.85e-9 i
7
-0.2658 + 0.9666 i
7.85e-9 - 2.28e-9 i
8
-0.2658 - 0.9666 i
7.85e-9 + 2.28e-9 i
9
-1.0127 + 0.1512 i
2.38e-9 + 9.99e-10 i
10
-1.0127 - 0.1512 i
2.38e-9 - 9.99e-10 i
11
-1.0127 + 0.1515 i
9.98e-10 - 2.38e-9 i
12
-1.0127 - 0.1515 i
9.98e-10 + 2.38e-9 i
13
1.4425 + 0.3603 i
0.0043 - 0.00507 i
14
1.4425 - 0.3603 i
0.0043 + 0.00507 i
15
1.5083 + 0.0953 i
0.0111 + 0.00382 i
16
1.5083 - 0.0953 i
0.0111 - 0.00382 i
17
1.7169 + 0.5943 i
0.00654 - 0.0128 i
18
1.7169 - 0.5943 i
0.00654 + 0.0128 i
19
2.0513 + 1.236 i
0.00373 + 0.00188 i
20
2.0513 - 1.236 i
0.00373 - 0.00188 i
21
-2.4599
0.0000329
22
2.3462 + 3.0695 i
0.00248 - 0.00146 i
23
2.3462 - 3.0695 i
0.00248 + 0.00146 i
24
-9.5137
0.00673 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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