Singularities of Møller-Plesset series: example "a1"

Molecule Ar. 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
-1.2869 + 0.0302 i
0.000666 + 0.00073 i
Singularities of quadratic [6, 6, 5] approximant
2
-1.2869 - 0.0302 i
0.000666 - 0.00073 i
3
-1.5415
0.00229
4
-0.4454 + 2.1561 i
0.00528 - 0.00375 i
5
-0.4454 - 2.1561 i
0.00528 + 0.00375 i
6
-0.4189 + 2.2157 i
0.00382 + 0.00559 i
7
-0.4189 - 2.2157 i
0.00382 - 0.00559 i
8
2.6073
0.305
9
0.3891 + 3.2607 i
0.0839 - 0.0242 i
10
0.3891 - 3.2607 i
0.0839 + 0.0242 i
11
-3.9611
1.74 i
12
39.2207
2.12 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
-1.2441 + 0.0143 i
0.000842 + 0.000888 i
Singularities of quadratic [6, 6, 6] approximant
2
-1.2441 - 0.0143 i
0.000842 - 0.000888 i
3
-1.5143
0.00353
4
-1.8233
0.0114 i
5
-2.1607
0.331
6
2.5747
0.232
7
0.0033 + 3.6511 i
0.0582 + 0.268 i
8
0.0033 - 3.6511 i
0.0582 - 0.268 i
9
-3.0654 + 3.5536 i
0.0123 + 0.172 i
10
-3.0654 - 3.5536 i
0.0123 - 0.172 i
11
5.7093
3.79 i
12
18.9284
2.46
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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
-1.2357 + 0.0212 i
0.000382 + 0.000416 i
Singularities of quadratic [7, 6, 6] approximant
2
-1.2357 - 0.0212 i
0.000382 - 0.000416 i
3
-1.4586
0.00137
4
-2.201
0.0157 i
5
2.5765
0.227
6
-3.0595
0.0462
7
-0.5928 + 3.0397 i
0.0299 - 0.00379 i
8
-0.5928 - 3.0397 i
0.0299 + 0.00379 i
9
-1.219 + 3.241 i
0.0145 - 0.0311 i
10
-1.219 - 3.241 i
0.0145 + 0.0311 i
11
1.154 + 3.9779 i
0.173 + 0.154 i
12
1.154 - 3.9779 i
0.173 - 0.154 i
13
114.4447
11.1 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
-0.9711
0.0000275
Singularities of quadratic [7, 7, 6] approximant
2
-0.9722
0.0000274 i
3
-1.2431 + 0.0486 i
0.000143 + 0.000127 i
4
-1.2431 - 0.0486 i
0.000143 - 0.000127 i
5
-1.4058
0.000435
6
2.5997 + 0.1291 i
0.114 - 0.2 i
7
2.5997 - 0.1291 i
0.114 + 0.2 i
8
2.712
0.196
9
0.3373 + 3.5701 i
0.147 + 0.00636 i
10
0.3373 - 3.5701 i
0.147 - 0.00636 i
11
-3.6341
7.98 i
12
-3.4095 + 5.8373 i
0.32 + 0.586 i
13
-3.4095 - 5.8373 i
0.32 - 0.586 i
14
66.4601
19.5 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
0.9356 + 0.e-5 i
0.0000231 - 0.0000231 i
Singularities of quadratic [7, 7, 7] approximant
2
0.9356 - 0.e-5 i
0.0000231 + 0.0000231 i
3
-1.0985
0.0000428
4
-1.1123
0.0000389 i
5
-1.2427 + 0.0677 i
0.000091 + 0.0000535 i
6
-1.2427 - 0.0677 i
0.000091 - 0.0000535 i
7
-1.3592
0.000193
8
2.5673
0.2
9
0.3092 + 3.7717 i
0.325 - 0.0531 i
10
0.3092 - 3.7717 i
0.325 + 0.0531 i
11
-4.6716
0.251 i
12
-4.3657 + 5.2864 i
0.22 + 0.0803 i
13
-4.3657 - 5.2864 i
0.22 - 0.0803 i
14
9.0292
1.88 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
-1.1826
0.000193
Singularities of quadratic [8, 7, 7] approximant
2
-1.2447
0.000132 i
3
-1.357 + 0.1193 i
0.000239 + 0.000171 i
4
-1.357 - 0.1193 i
0.000239 - 0.000171 i
5
-1.3944
0.000209
6
1.6598 + 0.0005 i
0.00149 - 0.00149 i
7
1.6598 - 0.0005 i
0.00149 + 0.00149 i
8
2.5676
0.188
9
0.5112 + 3.721 i
0.182 - 0.13 i
10
0.5112 - 3.721 i
0.182 + 0.13 i
11
-2.0318 + 3.9972 i
0.152 - 0.0806 i
12
-2.0318 - 3.9972 i
0.152 + 0.0806 i
13
-3.7187 + 2.5319 i
0.0152 - 0.166 i
14
-3.7187 - 2.5319 i
0.0152 + 0.166 i
15
-23.1426
4.54 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
-1.1928 + 0.0123 i
0.000274 + 0.000278 i
Singularities of quadratic [8, 8, 7] approximant
2
-1.1928 - 0.0123 i
0.000274 - 0.000278 i
3
0.785 + 1.0145 i
0.0000908 + 0.000017 i
4
0.785 - 1.0145 i
0.0000908 - 0.000017 i
5
0.785 + 1.0145 i
0.000017 - 0.0000908 i
6
0.785 - 1.0145 i
0.000017 + 0.0000908 i
7
-1.3938
0.00232
8
-1.435
0.142 i
9
-1.586
0.00296
10
2.5452
0.151
11
0.4201 + 3.5723 i
0.104 - 0.0365 i
12
0.4201 - 3.5723 i
0.104 + 0.0365 i
13
-3.7184
83.3 i
14
-0.7751 + 7.4636 i
0.287 - 0.757 i
15
-0.7751 - 7.4636 i
0.287 + 0.757 i
16
15.9345
8.27 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
-1.1861
0.00109
Singularities of quadratic [8, 8, 8] approximant
2
-1.1993
0.000854 i
3
0.8729 + 1.0538 i
0.000184 - 0.0000108 i
4
0.8729 - 1.0538 i
0.000184 + 0.0000108 i
5
0.873 + 1.0539 i
0.0000108 + 0.000184 i
6
0.873 - 1.0539 i
0.0000108 - 0.000184 i
7
-1.3772 + 0.0698 i
0.000466 + 0.000556 i
8
-1.3772 - 0.0698 i
0.000466 - 0.000556 i
9
-1.4987
0.0009
10
2.5495
0.16
11
0.3691 + 3.6322 i
0.142 - 0.0325 i
12
0.3691 - 3.6322 i
0.142 + 0.0325 i
13
-3.989
3.6 i
14
-1.8349 + 7.5558 i
0.202 + 0.727 i
15
-1.8349 - 7.5558 i
0.202 - 0.727 i
16
11.7684
2.71 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
-1.1916 + 0.0155 i
0.000185 + 0.000196 i
Singularities of quadratic [9, 8, 8] approximant
2
-1.1916 - 0.0155 i
0.000185 - 0.000196 i
3
-1.3622
0.000742
4
0.6898 + 1.1801 i
0.0000577 + 0.000106 i
5
0.6898 - 1.1801 i
0.0000577 - 0.000106 i
6
0.6897 + 1.1803 i
0.000106 - 0.0000577 i
7
0.6897 - 1.1803 i
0.000106 + 0.0000577 i
8
-1.5046
0.00355 i
9
-1.6393
0.00733
10
2.5402
0.143
11
-3.4903
2.22 i
12
0.4626 + 3.5238 i
0.0798 - 0.0438 i
13
0.4626 - 3.5238 i
0.0798 + 0.0438 i
14
8.8021
2.18 i
15
0.4647 + 9.7149 i
0.357 - 0.491 i
16
0.4647 - 9.7149 i
0.357 + 0.491 i
17
2815.4384
85.3
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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
-1.1918 + 0.0146 i
0.000204 + 0.000214 i
Singularities of quadratic [9, 9, 8] approximant
2
-1.1918 - 0.0146 i
0.000204 - 0.000214 i
3
0.6748 + 1.1663 i
0.0000538 + 0.0000989 i
4
0.6748 - 1.1663 i
0.0000538 - 0.0000989 i
5
0.6748 + 1.1665 i
0.0000989 - 0.0000538 i
6
0.6748 - 1.1665 i
0.0000989 + 0.0000538 i
7
-1.3679
0.000901
8
-1.4848
0.00468 i
9
-1.6199
0.00522
10
2.5387
0.142
11
-3.5793
5.52 i
12
0.4629 + 3.5497 i
0.088 - 0.0491 i
13
0.4629 - 3.5497 i
0.088 + 0.0491 i
14
5.2663
1.88 i
15
5.9713
1.15e3
16
-1.3059 + 8.4547 i
0.248 - 0.617 i
17
-1.3059 - 8.4547 i
0.248 + 0.617 i
18
25.7318
47.2 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
-0.022
0
Singularities of quadratic [9, 9, 9] approximant
2
-0.022
0
3
-1.1943 + 0.0051 i
0.0011 + 0.00104 i
4
-1.1943 - 0.0051 i
0.0011 - 0.00104 i
5
0.6815 + 1.1779 i
0.0000198 + 0.0000934 i
6
0.6815 - 1.1779 i
0.0000198 - 0.0000934 i
7
0.6814 + 1.1781 i
0.0000934 - 0.0000198 i
8
0.6814 - 1.1781 i
0.0000934 + 0.0000198 i
9
-1.4073 + 0.0488 i
0.000927 + 0.00164 i
10
-1.4073 - 0.0488 i
0.000927 - 0.00164 i
11
-1.5688
0.00213
12
2.5372
0.136
13
0.4494 + 3.4675 i
0.0677 - 0.0245 i
14
0.4494 - 3.4675 i
0.0677 + 0.0245 i
15
-3.6186
5.19 i
16
0.3304 + 6.656 i
0.603 - 0.292 i
17
0.3304 - 6.656 i
0.603 + 0.292 i
18
24.1199
76.9 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
0.6016
3.75e-8
Singularities of quadratic [10, 9, 9] approximant
2
0.6016
3.75e-8 i
3
-0.8946
7.98e-7
4
-0.8947
7.97e-7 i
5
-1.1644 + 0.048 i
0.000019 + 0.0000182 i
6
-1.1644 - 0.048 i
0.000019 - 0.0000182 i
7
-1.2443
0.00004
8
0.6273 + 1.2453 i
0.0000413 - 8.82e-7 i
9
0.6273 - 1.2453 i
0.0000413 + 8.82e-7 i
10
0.6274 + 1.2459 i
8.56e-7 + 0.0000413 i
11
0.6274 - 1.2459 i
8.56e-7 - 0.0000413 i
12
2.5228
0.105
13
-1.7549 + 2.5725 i
0.0034 - 0.0115 i
14
-1.7549 - 2.5725 i
0.0034 + 0.0115 i
15
-2.2325 + 2.2017 i
0.00764 + 0.0107 i
16
-2.2325 - 2.2017 i
0.00764 - 0.0107 i
17
0.025 + 3.6694 i
0.197 - 0.237 i
18
0.025 - 3.6694 i
0.197 + 0.237 i
19
-5.2897
0.937 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
0.6617
8.07e-8
Singularities of quadratic [10, 10, 9] approximant
2
0.6617
8.07e-8 i
3
-0.9763
1.58e-6
4
-0.9769
1.57e-6 i
5
-1.1586 + 0.0535 i
0.0000152 + 0.0000126 i
6
-1.1586 - 0.0535 i
0.0000152 - 0.0000126 i
7
-1.2296
0.0000286
8
0.6092 + 1.2599 i
0.0000389 + 4.82e-6 i
9
0.6092 - 1.2599 i
0.0000389 - 4.82e-6 i
10
0.6092 + 1.2606 i
4.86e-6 - 0.000039 i
11
0.6092 - 1.2606 i
4.86e-6 + 0.000039 i
12
2.5206
0.102
13
-1.3598 + 2.5469 i
0.00366 + 0.00609 i
14
-1.3598 - 2.5469 i
0.00366 - 0.00609 i
15
-1.8016 + 2.6218 i
0.0102 - 0.0014 i
16
-1.8016 - 2.6218 i
0.0102 + 0.0014 i
17
-0.0831 + 3.7332 i
0.334 + 0.0491 i
18
-0.0831 - 3.7332 i
0.334 - 0.0491 i
19
-5.1639
5.09 i
20
894.2199
10.3 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
0.7715 + 0.e-5 i
1.96e-7 - 1.96e-7 i
Singularities of quadratic [10, 10, 10] approximant
2
0.7715 - 0.e-5 i
1.96e-7 + 1.96e-7 i
3
-1.0224 + 0.3163 i
1.84e-6 - 2.35e-6 i
4
-1.0224 - 0.3163 i
1.84e-6 + 2.35e-6 i
5
-1.0234 + 0.3168 i
2.35e-6 + 1.86e-6 i
6
-1.0234 - 0.3168 i
2.35e-6 - 1.86e-6 i
7
-1.1257 + 0.0443 i
3.09e-6 + 6.59e-6 i
8
-1.1257 - 0.0443 i
3.09e-6 - 6.59e-6 i
9
-1.1467
6.1e-6
10
0.4918 + 1.2186 i
0.0000186 + 2.48e-6 i
11
0.4918 - 1.2186 i
0.0000186 - 2.48e-6 i
12
0.4921 + 1.2188 i
2.48e-6 - 0.0000186 i
13
0.4921 - 1.2188 i
2.48e-6 + 0.0000186 i
14
2.5452
0.175
15
0.9214 + 3.3618 i
0.0109 + 0.03 i
16
0.9214 - 3.3618 i
0.0109 - 0.03 i
17
-3.7105
2.01 i
18
2.8705 + 3.8799 i
0.0244 + 0.105 i
19
2.8705 - 3.8799 i
0.0244 - 0.105 i
20
8.371
1.32 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
0.4898 + 0.1091 i
6.57e-9 + 5.9e-9 i
Singularities of quadratic [11, 10, 10] approximant
2
0.4898 - 0.1091 i
6.57e-9 - 5.9e-9 i
3
0.4898 + 0.1091 i
5.9e-9 - 6.57e-9 i
4
0.4898 - 0.1091 i
5.9e-9 + 6.57e-9 i
5
-0.9196
1.02e-6
6
-0.9198
1.02e-6 i
7
-1.1636 + 0.049 i
0.0000184 + 0.0000171 i
8
-1.1636 - 0.049 i
0.0000184 - 0.0000171 i
9
-1.2423
0.0000381
10
0.6252 + 1.2375 i
0.0000394 - 8.78e-7 i
11
0.6252 - 1.2375 i
0.0000394 + 8.78e-7 i
12
0.6253 + 1.238 i
8.56e-7 + 0.0000395 i
13
0.6253 - 1.238 i
8.56e-7 - 0.0000395 i
14
2.523
0.106
15
-1.76 + 2.5908 i
0.00349 - 0.0121 i
16
-1.76 - 2.5908 i
0.00349 + 0.0121 i
17
-2.2492 + 2.2141 i
0.00805 + 0.0111 i
18
-2.2492 - 2.2141 i
0.00805 - 0.0111 i
19
0.0313 + 3.6685 i
0.187 - 0.246 i
20
0.0313 - 3.6685 i
0.187 + 0.246 i
21
-5.3212
0.971 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
0.7369 + 0.2503 i
2.09e-8 - 1.9e-8 i
Singularities of quadratic [11, 11, 10] approximant
2
0.7369 - 0.2503 i
2.09e-8 + 1.9e-8 i
3
0.7369 + 0.2503 i
1.9e-8 + 2.09e-8 i
4
0.7369 - 0.2503 i
1.9e-8 - 2.09e-8 i
5
-0.6528 + 0.7634 i
6.39e-7 - 6.88e-8 i
6
-0.6528 - 0.7634 i
6.39e-7 + 6.88e-8 i
7
-0.6529 + 0.7634 i
6.88e-8 + 6.39e-7 i
8
-0.6529 - 0.7634 i
6.88e-8 - 6.39e-7 i
9
-1.1558 + 0.046 i
0.0000132 + 0.0000162 i
10
-1.1558 - 0.046 i
0.0000132 - 0.0000162 i
11
0.5244 + 1.08 i
2.07e-7 - 2.22e-6 i
12
0.5244 - 1.08 i
2.07e-7 + 2.22e-6 i
13
0.5247 + 1.0802 i
2.22e-6 + 2.06e-7 i
14
0.5247 - 1.0802 i
2.22e-6 - 2.06e-7 i
15
-1.2188
0.0000257
16
2.4688
0.0428
17
-3.2403
0.214 i
18
1.0017 + 3.949 i
0.119 - 0.00501 i
19
1.0017 - 3.949 i
0.119 + 0.00501 i
20
-4.8642
0.0961
21
-10.7366
1.71 i
22
15.8889
2.06 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
-1.0396
2.24e-6
Singularities of quadratic [11, 11, 11] approximant
2
-1.0432
2.17e-6 i
3
0.4625 + 0.9514 i
3.81e-7 - 8.e-7 i
4
0.4625 - 0.9514 i
3.81e-7 + 8.e-7 i
5
0.4626 + 0.9514 i
8.e-7 + 3.81e-7 i
6
0.4626 - 0.9514 i
8.e-7 - 3.81e-7 i
7
-0.4672 + 1.0393 i
2.67e-7 - 2.3e-6 i
8
-0.4672 - 1.0393 i
2.67e-7 + 2.3e-6 i
9
-0.4672 + 1.0394 i
2.3e-6 + 2.67e-7 i
10
-0.4672 - 1.0394 i
2.3e-6 - 2.67e-7 i
11
-1.1449 + 0.0616 i
9.71e-6 + 6.07e-6 i
12
-1.1449 - 0.0616 i
9.71e-6 - 6.07e-6 i
13
-1.1931
0.000013
14
1.1707 + 0.4024 i
2.75e-6 - 6.78e-7 i
15
1.1707 - 0.4024 i
2.75e-6 + 6.78e-7 i
16
1.171 + 0.4025 i
6.79e-7 + 2.75e-6 i
17
1.171 - 0.4025 i
6.79e-7 - 2.75e-6 i
18
2.4483
0.0287
19
-3.9965
6.95 i
20
1.2059 + 4.0349 i
0.0914 - 0.0278 i
21
1.2059 - 4.0349 i
0.0914 + 0.0278 i
22
7.3356
11.4 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
0.4523 + 0.9372 i
3.24e-7 - 5.95e-7 i
Singularities of quadratic [12, 11, 11] approximant
2
0.4523 - 0.9372 i
3.24e-7 + 5.95e-7 i
3
0.4524 + 0.9372 i
5.95e-7 + 3.24e-7 i
4
0.4524 - 0.9372 i
5.95e-7 - 3.24e-7 i
5
-1.1081
7.51e-6
6
-1.1531 + 0.0756 i
0.000013 + 1.01e-6 i
7
-1.1531 - 0.0756 i
0.000013 - 1.01e-6 i
8
-1.1608 + 0.0199 i
2.89e-6 - 4.67e-6 i
9
-1.1608 - 0.0199 i
2.89e-6 + 4.67e-6 i
10
-0.4746 + 1.0916 i
1.68e-7 - 3.13e-6 i
11
-0.4746 - 1.0916 i
1.68e-7 + 3.13e-6 i
12
-0.4747 + 1.0918 i
3.14e-6 + 1.67e-7 i
13
-0.4747 - 1.0918 i
3.14e-6 - 1.67e-7 i
14
1.216 + 0.3681 i
2.43e-6 - 1.57e-6 i
15
1.216 - 0.3681 i
2.43e-6 + 1.57e-6 i
16
1.2166 + 0.368 i
1.57e-6 + 2.43e-6 i
17
1.2166 - 0.368 i
1.57e-6 - 2.43e-6 i
18
2.4137
0.0177
19
-4.0906
11.2 i
20
1.3982 + 4.1278 i
0.0686 - 0.0505 i
21
1.3982 - 4.1278 i
0.0686 + 0.0505 i
22
5.5238
9.48 i
23
43.3288
3.66
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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
0.9986 + 0.1727 i
1.29e-7 - 7.46e-8 i
Singularities of quadratic [12, 12, 11] approximant
2
0.9986 - 0.1727 i
1.29e-7 + 7.46e-8 i
3
0.9987 + 0.1727 i
7.46e-8 + 1.29e-7 i
4
0.9987 - 0.1727 i
7.46e-8 - 1.29e-7 i
5
0.4241 + 0.9399 i
1.68e-7 - 3.3e-7 i
6
0.4241 - 0.9399 i
1.68e-7 + 3.3e-7 i
7
0.4242 + 0.94 i
3.3e-7 + 1.68e-7 i
8
0.4242 - 0.94 i
3.3e-7 - 1.68e-7 i
9
-1.1582 + 0.0205 i
0.0000103 + 0.0000142 i
10
-1.1582 - 0.0205 i
0.0000103 - 0.0000142 i
11
-1.1795 + 0.0113 i
0.0000292 - 6.47e-6 i
12
-1.1795 - 0.0113 i
0.0000292 + 6.47e-6 i
13
-0.4306 + 1.157 i
1.11e-6 + 2.35e-6 i
14
-0.4306 - 1.157 i
1.11e-6 - 2.35e-6 i
15
-0.4304 + 1.1574 i
2.35e-6 - 1.12e-6 i
16
-0.4304 - 1.1574 i
2.35e-6 + 1.12e-6 i
17
-1.2689
0.0000709
18
2.3694
0.0113
19
-3.8965
0.781 i
20
1.831 + 3.8114 i
0.0201 - 0.0459 i
21
1.831 - 3.8114 i
0.0201 + 0.0459 i
22
5.3999
2.88 i
23
-8.2343 + 3.7975 i
0.231 - 0.0532 i
24
-8.2343 - 3.7975 i
0.231 + 0.0532 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
-0.3112
0
Singularities of quadratic [12, 12, 12] approximant
2
-0.3112
0
3
-1.0306
2.38e-6
4
-1.0329
2.33e-6 i
5
0.4587 + 0.9445 i
2.88e-7 - 8.9e-7 i
6
0.4587 - 0.9445 i
2.88e-7 + 8.9e-7 i
7
0.4588 + 0.9445 i
8.9e-7 + 2.88e-7 i
8
0.4588 - 0.9445 i
8.9e-7 - 2.88e-7 i
9
-1.1485 + 0.0584 i
0.0000108 + 7.86e-6 i
10
-1.1485 - 0.0584 i
0.0000108 - 7.86e-6 i
11
-0.4633 + 1.0536 i
1.72e-7 + 2.33e-6 i
12
-0.4633 - 1.0536 i
1.72e-7 - 2.33e-6 i
13
-0.4634 + 1.0537 i
2.33e-6 - 1.73e-7 i
14
-0.4634 - 1.0537 i
2.33e-6 + 1.73e-7 i
15
-1.2022
0.0000161
16
1.223 + 0.4006 i
4.54e-6 - 1.78e-6 i
17
1.223 - 0.4006 i
4.54e-6 + 1.78e-6 i
18
1.2236 + 0.4006 i
1.78e-6 + 4.54e-6 i
19
1.2236 - 0.4006 i
1.78e-6 - 4.54e-6 i
20
2.4551
0.031
21
-3.9814
5.58 i
22
1.2002 + 4.064 i
0.0962 - 0.0309 i
23
1.2002 - 4.064 i
0.0962 + 0.0309 i
24
7.314
10.8 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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