Singularities of Møller-Plesset series: example "a69"

Molecule HF. 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
-1.24 + 0.0106 i
0.00114 + 0.00127 i
Singularities of quadratic [6, 6, 5] approximant
2
-1.24 - 0.0106 i
0.00114 - 0.00127 i
3
-1.3245
0.00363
4
2.5005 + 0.3885 i
0.182 + 0.594 i
5
2.5005 - 0.3885 i
0.182 - 0.594 i
6
-2.6785
2.98 i
7
3.084
0.509
8
-1.8181 + 2.6489 i
0.0858 - 0.127 i
9
-1.8181 - 2.6489 i
0.0858 + 0.127 i
10
0.7762 + 5.7411 i
0.478 - 0.0863 i
11
0.7762 - 5.7411 i
0.478 + 0.0863 i
12
16.1916
1.3 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
-1.3013 + 0.0371 i
0.000427 + 0.0027 i
Singularities of quadratic [6, 6, 6] approximant
2
-1.3013 - 0.0371 i
0.000427 - 0.0027 i
3
-1.3115
0.00198
4
2.4785 + 0.311 i
0.522 + 0.323 i
5
2.4785 - 0.311 i
0.522 - 0.323 i
6
-2.7454
3.53 i
7
2.9607
0.543
8
-2.0807 + 2.6727 i
0.189 - 0.133 i
9
-2.0807 - 2.6727 i
0.189 + 0.133 i
10
-1.1453 + 5.2323 i
0.764 + 0.583 i
11
-1.1453 - 5.2323 i
0.764 - 0.583 i
12
-14.1423
3.98
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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
0.3706
6.57e-7
Singularities of quadratic [7, 6, 6] approximant
2
0.3706
6.57e-7 i
3
-1.2706
0.00103
4
-1.2843 + 0.0248 i
0.000308 - 0.00136 i
5
-1.2843 - 0.0248 i
0.000308 + 0.00136 i
6
2.5138 + 0.3717 i
0.0907 - 1.04 i
7
2.5138 - 0.3717 i
0.0907 + 1.04 i
8
2.786
0.497
9
-3.152
26.6 i
10
-2.027 + 3.2379 i
0.125 + 0.495 i
11
-2.027 - 3.2379 i
0.125 - 0.495 i
12
-3.4662 + 5.0077 i
5.24 + 3.17 i
13
-3.4662 - 5.0077 i
5.24 - 3.17 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
-1.2986 + 0.044 i
0.000144 + 0.00269 i
Singularities of quadratic [7, 7, 6] approximant
2
-1.2986 - 0.044 i
0.000144 - 0.00269 i
3
-1.2995
0.00191
4
2.4413 + 0.3113 i
0.246 + 0.0603 i
5
2.4413 - 0.3113 i
0.246 - 0.0603 i
6
3.0985 + 0.8629 i
0.291 + 0.0293 i
7
3.0985 - 0.8629 i
0.291 - 0.0293 i
8
-1.614 + 3.0946 i
0.0879 + 0.182 i
9
-1.614 - 3.0946 i
0.0879 - 0.182 i
10
-3.7137 + 0.7735 i
2.03 - 1.73 i
11
-3.7137 - 0.7735 i
2.03 + 1.73 i
12
4.9266
0.495
13
-5.7437
58.8 i
14
12.0981
3.25 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
-1.328 + 0.0532 i
0.00205 + 0.00555 i
Singularities of quadratic [7, 7, 7] approximant
2
-1.328 - 0.0532 i
0.00205 - 0.00555 i
3
-1.3696
0.00479
4
2.4876 + 0.4155 i
0.021 - 0.563 i
5
2.4876 - 0.4155 i
0.021 + 0.563 i
6
-2.552
0.574 i
7
3.011
0.476
8
-3.5778
0.263
9
-2.0362 + 3.241 i
0.181 - 0.801 i
10
-2.0362 - 3.241 i
0.181 + 0.801 i
11
4.5365
32.7 i
12
-4.8148 + 2.4453 i
0.141 - 0.397 i
13
-4.8148 - 2.4453 i
0.141 + 0.397 i
14
6.956
2.73
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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
-1.304 + 0.049 i
0.00042 + 0.00314 i
Singularities of quadratic [8, 7, 7] approximant
2
-1.304 - 0.049 i
0.00042 - 0.00314 i
3
-1.3123
0.00228
4
2.0625
0.0174
5
2.0976
0.0176 i
6
2.4533
0.119
7
-2.6255
0.489 i
8
2.5857 + 0.4856 i
0.283 + 0.479 i
9
2.5857 - 0.4856 i
0.283 - 0.479 i
10
-2.7005 + 0.4201 i
0.169 + 2.56 i
11
-2.7005 - 0.4201 i
0.169 - 2.56 i
12
-1.8262 + 3.0363 i
0.0265 + 0.273 i
13
-1.8262 - 3.0363 i
0.0265 - 0.273 i
14
-3.8093 + 7.0559 i
2.81 - 0.00913 i
15
-3.8093 - 7.0559 i
2.81 + 0.00913 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
-1.3335 + 0.0495 i
0.00238 + 0.0068 i
Singularities of quadratic [8, 8, 7] approximant
2
-1.3335 - 0.0495 i
0.00238 - 0.0068 i
3
-1.3796
0.0058
4
0.3878 + 1.3988 i
0.00032 - 0.0000937 i
5
0.3878 - 1.3988 i
0.00032 + 0.0000937 i
6
0.3878 + 1.3989 i
0.0000937 + 0.00032 i
7
0.3878 - 1.3989 i
0.0000937 - 0.00032 i
8
2.5131 + 0.4955 i
0.388 - 0.0106 i
9
2.5131 - 0.4955 i
0.388 + 0.0106 i
10
2.6506
0.317
11
-2.8875
5.79 i
12
-1.73 + 3.0168 i
0.0131 + 0.171 i
13
-1.73 - 3.0168 i
0.0131 - 0.171 i
14
-4.6516 + 3.4933 i
4.39 + 1.29 i
15
-4.6516 - 3.4933 i
4.39 - 1.29 i
16
51.9465
177. 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
-0.8522 + 0.e-5 i
0.0000135 + 0.0000135 i
Singularities of quadratic [8, 8, 8] approximant
2
-0.8522 - 0.e-5 i
0.0000135 - 0.0000135 i
3
-1.342
0.0152
4
-1.4159
0.0705 i
5
-1.4829
0.0379
6
1.9454
0.00609
7
1.9604
0.00615 i
8
2.4292
0.0935
9
2.5712 + 0.5581 i
0.109 + 0.251 i
10
2.5712 - 0.5581 i
0.109 - 0.251 i
11
-2.7218
1.74 i
12
-1.8563 + 2.9922 i
0.0339 - 0.216 i
13
-1.8563 - 2.9922 i
0.0339 + 0.216 i
14
-4.5499 + 4.1636 i
1.85 + 1.6 i
15
-4.5499 - 4.1636 i
1.85 - 1.6 i
16
-21.7744
1.28
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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
-0.8816 + 0.e-5 i
0.0000247 + 0.0000247 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.8816 - 0.e-5 i
0.0000247 - 0.0000247 i
3
-1.3618
0.0389
4
-1.3739
0.347 i
5
-1.4571
0.022
6
2.1732
0.0218
7
2.2808 + 0.1113 i
0.00399 + 0.0325 i
8
2.2808 - 0.1113 i
0.00399 - 0.0325 i
9
2.6024 + 0.5499 i
0.0376 + 0.314 i
10
2.6024 - 0.5499 i
0.0376 - 0.314 i
11
-2.7185
1.51 i
12
-1.8831 + 3.0121 i
0.0542 - 0.256 i
13
-1.8831 - 3.0121 i
0.0542 + 0.256 i
14
-5.5347 + 1.5501 i
0.438 + 0.315 i
15
-5.5347 - 1.5501 i
0.438 - 0.315 i
16
-7.2614 + 7.2441 i
1.1 - 0.274 i
17
-7.2614 - 7.2441 i
1.1 + 0.274 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
-0.929 + 0.5784 i
0.0000237 + 0.0000912 i
Singularities of quadratic [9, 9, 8] approximant
2
-0.929 - 0.5784 i
0.0000237 - 0.0000912 i
3
-0.929 + 0.5784 i
0.0000912 - 0.0000237 i
4
-0.929 - 0.5784 i
0.0000912 + 0.0000237 i
5
-1.3351
0.0115
6
-1.4552
0.031 i
7
-1.5214
0.113
8
2.366
0.103
9
2.39 + 0.2217 i
0.0614 - 0.131 i
10
2.39 - 0.2217 i
0.0614 + 0.131 i
11
2.6103 + 0.4698 i
0.0641 + 0.694 i
12
2.6103 - 0.4698 i
0.0641 - 0.694 i
13
-2.7942
4.33 i
14
-1.8062 + 3.0825 i
0.0754 + 0.245 i
15
-1.8062 - 3.0825 i
0.0754 - 0.245 i
16
-4.2235 + 5.6813 i
6.34 - 0.43 i
17
-4.2235 - 5.6813 i
6.34 + 0.43 i
18
505.6042
28.1 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
-0.6164 + 0.4016 i
2.77e-7 - 3.59e-6 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.6164 - 0.4016 i
2.77e-7 + 3.59e-6 i
3
-0.6164 + 0.4016 i
3.59e-6 + 2.77e-7 i
4
-0.6164 - 0.4016 i
3.59e-6 - 2.77e-7 i
5
-1.3388
0.0134
6
-1.4309
0.045 i
7
-1.4968
0.0543
8
2.2117
0.0337
9
2.3199 + 0.1162 i
0.00651 + 0.0492 i
10
2.3199 - 0.1162 i
0.00651 - 0.0492 i
11
2.5943 + 0.5169 i
0.124 + 0.408 i
12
2.5943 - 0.5169 i
0.124 - 0.408 i
13
-2.7571
2.56 i
14
-1.8182 + 3.0322 i
0.0209 + 0.223 i
15
-1.8182 - 3.0322 i
0.0209 - 0.223 i
16
-4.3615 + 4.8764 i
0.315 + 7.35 i
17
-4.3615 - 4.8764 i
0.315 - 7.35 i
18
-47.8323
3.24
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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
0.3943
5.55e-9 - 5.55e-9 i
Singularities of quadratic [10, 9, 9] approximant
2
0.3943
5.55e-9 + 5.55e-9 i
3
-0.6421 + 0.8633 i
0.000013 + 0.0000264 i
4
-0.6421 - 0.8633 i
0.000013 - 0.0000264 i
5
-0.6422 + 0.8633 i
0.0000264 - 0.000013 i
6
-0.6422 - 0.8633 i
0.0000264 + 0.000013 i
7
-1.3326
0.0102
8
-1.4761
0.0274 i
9
-1.5446
0.246
10
2.3571 + 0.3189 i
0.104 - 0.0136 i
11
2.3571 - 0.3189 i
0.104 + 0.0136 i
12
2.603
0.317
13
-2.7662
3.65 i
14
2.7211 + 0.5708 i
0.223 - 0.19 i
15
2.7211 - 0.5708 i
0.223 + 0.19 i
16
-1.8248 + 3.1208 i
0.141 + 0.28 i
17
-1.8248 - 3.1208 i
0.141 - 0.28 i
18
-3.6072 + 6.4499 i
2.6 + 1.08 i
19
-3.6072 - 6.4499 i
2.6 - 1.08 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
0.6153 + 0.e-5 i
3.92e-8 - 3.92e-8 i
Singularities of quadratic [10, 10, 9] approximant
2
0.6153 - 0.e-5 i
3.92e-8 + 3.92e-8 i
3
0.2701 + 1.2615 i
0.000014 - 0.0000119 i
4
0.2701 - 1.2615 i
0.000014 + 0.0000119 i
5
0.27 + 1.2615 i
0.0000119 + 0.000014 i
6
0.27 - 1.2615 i
0.0000119 - 0.000014 i
7
-1.3306
0.00934
8
-1.5026
0.0251 i
9
-1.5778
1.53
10
2.3335 + 0.4091 i
0.0317 + 0.0484 i
11
2.3335 - 0.4091 i
0.0317 - 0.0484 i
12
-2.72
3.07 i
13
-1.8917 + 3.5752 i
0.0217 - 0.442 i
14
-1.8917 - 3.5752 i
0.0217 + 0.442 i
15
-0.026 + 4.5443 i
0.0162 + 0.039 i
16
-0.026 - 4.5443 i
0.0162 - 0.039 i
17
4.5083 + 0.8035 i
0.589 + 0.542 i
18
4.5083 - 0.8035 i
0.589 - 0.542 i
19
1.0957 + 5.2041 i
0.0276 - 0.0463 i
20
1.0957 - 5.2041 i
0.0276 + 0.0463 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
0.8626 + 0.e-5 i
9.6e-7 - 9.6e-7 i
Singularities of quadratic [10, 10, 10] approximant
2
0.8626 - 0.e-5 i
9.6e-7 + 9.6e-7 i
3
-1.3307
0.00938
4
-0.01 + 1.3624 i
0.0000276 - 0.0000161 i
5
-0.01 - 1.3624 i
0.0000276 + 0.0000161 i
6
-0.0101 + 1.3624 i
0.0000161 + 0.0000276 i
7
-0.0101 - 1.3624 i
0.0000161 - 0.0000276 i
8
-1.5035
0.0249 i
9
-1.5793
1.85
10
2.3893 + 0.4258 i
0.03 + 0.109 i
11
2.3893 - 0.4258 i
0.03 - 0.109 i
12
-2.7433
4.3 i
13
3.1982
0.804
14
0.2071 + 3.5446 i
0.00164 - 0.0111 i
15
0.2071 - 3.5446 i
0.00164 + 0.0111 i
16
0.2485 + 3.7814 i
0.0135 + 0.00127 i
17
0.2485 - 3.7814 i
0.0135 - 0.00127 i
18
-2.0372 + 3.7172 i
0.612 + 0.345 i
19
-2.0372 - 3.7172 i
0.612 - 0.345 i
20
17.989
13.1 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
-0.1405
0
Singularities of quadratic [11, 10, 10] approximant
2
-0.1405
0
3
1.1687
0.000018
4
1.1688
0.000018 i
5
-1.3309
0.00943
6
-1.4942
0.026 i
7
-1.5659
0.638
8
-0.4093 + 1.8102 i
0.000381 + 0.000718 i
9
-0.4093 - 1.8102 i
0.000381 - 0.000718 i
10
-0.4097 + 1.8115 i
0.00072 - 0.000382 i
11
-0.4097 - 1.8115 i
0.00072 + 0.000382 i
12
2.2591
0.0219
13
2.3642 + 0.6097 i
0.044 + 0.014 i
14
2.3642 - 0.6097 i
0.044 - 0.014 i
15
2.6384
0.176 i
16
-2.7177
2.43 i
17
3.6037
1.73
18
-1.9038 + 3.0937 i
0.116 + 0.428 i
19
-1.9038 - 3.0937 i
0.116 - 0.428 i
20
-3.4316 + 6.8732 i
2.6 - 0.0433 i
21
-3.4316 - 6.8732 i
2.6 + 0.0433 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
-0.0884 + 0.4921 i
5.84e-9 + 9.94e-9 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.0884 - 0.4921 i
5.84e-9 - 9.94e-9 i
3
-0.0884 + 0.4921 i
9.94e-9 - 5.84e-9 i
4
-0.0884 - 0.4921 i
9.94e-9 + 5.84e-9 i
5
0.8208 + 0.8314 i
5.78e-6 - 3.89e-6 i
6
0.8208 - 0.8314 i
5.78e-6 + 3.89e-6 i
7
0.8208 + 0.8314 i
3.89e-6 + 5.78e-6 i
8
0.8208 - 0.8314 i
3.89e-6 - 5.78e-6 i
9
-1.3304
0.00929
10
-1.507
0.0248 i
11
-1.5839
2.89
12
2.3088 + 0.4182 i
0.0195 + 0.0369 i
13
2.3088 - 0.4182 i
0.0195 - 0.0369 i
14
-2.721
3.41 i
15
-0.5545 + 3.8101 i
0.000278 + 0.018 i
16
-0.5545 - 3.8101 i
0.000278 - 0.018 i
17
-0.2533 + 3.9024 i
0.0163 - 0.00402 i
18
-0.2533 - 3.9024 i
0.0163 + 0.00402 i
19
4.175
1.92e3
20
-2.2318 + 4.0095 i
0.347 - 0.175 i
21
-2.2318 - 4.0095 i
0.347 + 0.175 i
22
7.4629
0.6 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
0.6256 + 0.3353 i
7.54e-8 - 2.05e-8 i
Singularities of quadratic [11, 11, 11] approximant
2
0.6256 - 0.3353 i
7.54e-8 + 2.05e-8 i
3
0.6256 + 0.3353 i
2.05e-8 + 7.54e-8 i
4
0.6256 - 0.3353 i
2.05e-8 - 7.54e-8 i
5
-0.3416 + 0.6313 i
5.2e-8 - 1.81e-7 i
6
-0.3416 - 0.6313 i
5.2e-8 + 1.81e-7 i
7
-0.3416 + 0.6313 i
1.81e-7 + 5.2e-8 i
8
-0.3416 - 0.6313 i
1.81e-7 - 5.2e-8 i
9
-1.3303
0.00936
10
-1.5201
0.0238 i
11
-1.6035
46.6
12
2.3873 + 0.4383 i
0.00805 + 0.103 i
13
2.3873 - 0.4383 i
0.00805 - 0.103 i
14
-0.4057 + 2.55 i
0.00188 - 0.00171 i
15
-0.4057 - 2.55 i
0.00188 + 0.00171 i
16
-0.3769 + 2.5764 i
0.00185 + 0.00183 i
17
-0.3769 - 2.5764 i
0.00185 - 0.00183 i
18
-2.7972
22. i
19
3.0948
0.718
20
-2.6895 + 3.4471 i
0.918 + 0.833 i
21
-2.6895 - 3.4471 i
0.918 - 0.833 i
22
3162.3486
0.217 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
0.5471 + 0.4662 i
2.7e-7 - 1.76e-7 i
Singularities of quadratic [12, 11, 11] approximant
2
0.5471 - 0.4662 i
2.7e-7 + 1.76e-7 i
3
0.5471 + 0.4662 i
1.76e-7 + 2.7e-7 i
4
0.5471 - 0.4662 i
1.76e-7 - 2.7e-7 i
5
-0.3218 + 0.8923 i
1.35e-6 - 3.96e-6 i
6
-0.3218 - 0.8923 i
1.35e-6 + 3.96e-6 i
7
-0.3218 + 0.8923 i
3.96e-6 + 1.35e-6 i
8
-0.3218 - 0.8923 i
3.96e-6 - 1.35e-6 i
9
-1.3171
0.00562
10
-1.4091
0.00755 i
11
-1.4107 + 0.0718 i
0.00937 - 0.0178 i
12
-1.4107 - 0.0718 i
0.00937 + 0.0178 i
13
-1.4619
0.0164
14
2.267
0.0349
15
2.2917 + 0.197 i
0.0191 - 0.0441 i
16
2.2917 - 0.197 i
0.0191 + 0.0441 i
17
2.6258 + 0.5742 i
0.0438 - 0.254 i
18
2.6258 - 0.5742 i
0.0438 + 0.254 i
19
-2.791
4.98 i
20
-1.8374 + 3.1489 i
0.184 + 0.306 i
21
-1.8374 - 3.1489 i
0.184 - 0.306 i
22
-3.6798 + 6.6646 i
2.21 + 0.784 i
23
-3.6798 - 6.6646 i
2.21 - 0.784 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
0.5847 + 0.4592 i
9.78e-8 - 2.39e-8 i
Singularities of quadratic [12, 12, 11] approximant
2
0.5847 - 0.4592 i
9.78e-8 + 2.39e-8 i
3
0.5847 + 0.4592 i
2.39e-8 + 9.78e-8 i
4
0.5847 - 0.4592 i
2.39e-8 - 9.78e-8 i
5
-0.2453 + 0.8523 i
2.12e-7 - 6.18e-7 i
6
-0.2453 - 0.8523 i
2.12e-7 + 6.18e-7 i
7
-0.2453 + 0.8523 i
6.18e-7 + 2.12e-7 i
8
-0.2453 - 0.8523 i
6.18e-7 - 2.12e-7 i
9
-1. + 0.00002 i
0.0000129 + 0.0000129 i
10
-1. - 0.00002 i
0.0000129 - 0.0000129 i
11
-1.3304
0.00796
12
-1.4526
0.0477 i
13
-1.5144
0.0607
14
2.3585 + 0.4285 i
0.0192 + 0.0705 i
15
2.3585 - 0.4285 i
0.0192 - 0.0705 i
16
-2.5557
0.66 i
17
-1.368 + 2.7161 i
0.00161 + 0.0157 i
18
-1.368 - 2.7161 i
0.00161 - 0.0157 i
19
-1.5748 + 2.8468 i
0.0234 - 0.000881 i
20
-1.5748 - 2.8468 i
0.0234 + 0.000881 i
21
3.3326
1.02
22
-3.7606 + 3.5992 i
0.105 + 0.403 i
23
-3.7606 - 3.5992 i
0.105 - 0.403 i
24
15.0241
3.59 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
-0.0463
0
Singularities of quadratic [12, 12, 12] approximant
2
-0.0463
0
3
0.588 + 0.458 i
4.83e-8 + 9.87e-9 i
4
0.588 - 0.458 i
4.83e-8 - 9.87e-9 i
5
0.588 + 0.458 i
9.87e-9 - 4.83e-8 i
6
0.588 - 0.458 i
9.87e-9 + 4.83e-8 i
7
-0.8811
1.76e-6
8
-0.8811
1.76e-6 i
9
-0.2457 + 0.8502 i
3.31e-7 + 9.71e-8 i
10
-0.2457 - 0.8502 i
3.31e-7 - 9.71e-8 i
11
-0.2457 + 0.8502 i
9.71e-8 - 3.31e-7 i
12
-0.2457 - 0.8502 i
9.71e-8 + 3.31e-7 i
13
-1.3325
0.0115
14
-1.5344
0.0222 i
15
-1.6251
0.661
16
2.3611 + 0.4358 i
0.00989 + 0.0716 i
17
2.3611 - 0.4358 i
0.00989 - 0.0716 i
18
-3.0252
8.73 i
19
3.2525
0.869
20
-2.0211 + 3.1482 i
0.539 - 0.716 i
21
-2.0211 - 3.1482 i
0.539 + 0.716 i
22
-9.8492 + 6.021 i
1.05 + 0.5 i
23
-9.8492 - 6.021 i
1.05 - 0.5 i
24
14.4666
2.72 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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