Singularities of Møller-Plesset series: example "hf cc-pvdz 1.5re"

Molecule X 1^Sigma+ State of HF. Basis CC-PVDZ. Structure ""

Content


ExamplesAr cc-pVDZbh aug-cc-pVQZ 0.9r_ebh aug-cc-pVQZ 1.0r_ebh aug-cc-pVQZ 1.1r_ebh aug-cc-pVQZ 1.2r_ebh aug-cc-pVQZ 1.3r_ebh aug-cc-pVQZ 1.4r_ebh aug-cc-pVQZ 1.5r_ebh aug-cc-pVQZ 1.6r_ebh aug-cc-pVQZ 1.7r_ebh aug-cc-pVQZ 1.8r_ebh aug-cc-pVQZ 1.9r_ebh aug-cc-pVQZ 2.0r_ebh aug-cc-pVQZ 2.1r_ebh aug-cc-pVQZ 2.2r_ebh cc-pvdz 1.5rebh cc-pvdz 2rebh cc-pvdz rebh cc-pvqz 1.5rebh cc-pvqz 2rebh cc-pvqz rebh cc-pvtz 1.5rebh cc-pvtz 2rebh cc-pvtz reh- cc-pv5zh- cc-pvqzhf aug-cc-pVDZ 1.5r_ehf aug-cc-pVDZ 2.0r_ehf aug-cc-pVDZ r_ehf cc-pvdz 1.5rehf cc-pvdz 2rehf cc-pvdz 2rehf cc-pvdz rena-pl aug-cc-pvdzNe cc-pVDZo2- aug-cc-pvdz
MoleculeArX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHH- ionH- ionX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-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 [5, 5, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-1.1398
0.0218
Singularities of quadratic [5, 5, 4] approximant
2
-1.4732
0.0442 i
3
1.4094 + 0.6247 i
0.0367 - 0.00438 i
4
1.4094 - 0.6247 i
0.0367 + 0.00438 i
5
-1.9068 + 1.0629 i
0.0653 + 0.0414 i
6
-1.9068 - 1.0629 i
0.0653 - 0.0414 i
7
2.19 + 0.5611 i
0.0311 + 0.16 i
8
2.19 - 0.5611 i
0.0311 - 0.16 i
9
0.7158 + 2.6785 i
0.0798 - 0.0129 i
10
0.7158 - 2.6785 i
0.0798 + 0.0129 i
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Table 2. Singularities with their weights for the quadratic approximant [5, 5, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-1.1265 + 0.0237 i
0.0338 + 0.0388 i
Singularities of quadratic [5, 5, 5] approximant
2
-1.1265 - 0.0237 i
0.0338 - 0.0388 i
3
-1.3726
0.0957
4
1.6473 + 0.5058 i
0.161 - 0.249 i
5
1.6473 - 0.5058 i
0.161 + 0.249 i
6
2.5289
0.311
7
-1.701 + 2.5556 i
0.975 + 0.158 i
8
-1.701 - 2.5556 i
0.975 - 0.158 i
9
-2.7172 + 1.6934 i
0.108 - 0.434 i
10
-2.7172 - 1.6934 i
0.108 + 0.434 i
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Table 3. Singularities with their weights for the quadratic approximant [6, 5, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-1.0651
0.0104
Singularities of quadratic [6, 5, 5] approximant
2
-1.1832
0.0121 i
3
-1.5653 + 0.3897 i
0.00987 + 0.0425 i
4
-1.5653 - 0.3897 i
0.00987 - 0.0425 i
5
1.6375 + 0.5504 i
0.217 - 0.0891 i
6
1.6375 - 0.5504 i
0.217 + 0.0891 i
7
-1.5349 + 0.8927 i
0.0185 - 0.0391 i
8
-1.5349 - 0.8927 i
0.0185 + 0.0391 i
9
2.2106
0.269
10
-0.9623 + 2.9772 i
0.107 - 0.136 i
11
-0.9623 - 2.9772 i
0.107 + 0.136 i
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Table 4. 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
-1.067
0.00753
Singularities of quadratic [6, 6, 5] approximant
2
-1.3167
0.0137 i
3
-1.2571 + 0.5817 i
0.00378 + 0.00888 i
4
-1.2571 - 0.5817 i
0.00378 - 0.00888 i
5
-1.2816 + 0.7322 i
0.00971 - 0.00691 i
6
-1.2816 - 0.7322 i
0.00971 + 0.00691 i
7
1.6412 + 0.5567 i
0.226 - 0.0628 i
8
1.6412 - 0.5567 i
0.226 + 0.0628 i
9
2.1717
0.259
10
-1.0188 + 2.7384 i
0.114 - 0.0628 i
11
-1.0188 - 2.7384 i
0.114 + 0.0628 i
12
396.2356
28.4 i
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Table 5. 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
-0.9916 + 0.0168 i
0.00181 + 0.00197 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.9916 - 0.0168 i
0.00181 - 0.00197 i
3
-1.1262
0.00626
4
1.6109 + 0.4935 i
0.0286 - 0.2 i
5
1.6109 - 0.4935 i
0.0286 + 0.2 i
6
-1.9518
1.07 i
7
-1.5973 + 2.0649 i
0.0181 - 0.127 i
8
-1.5973 - 2.0649 i
0.0181 + 0.127 i
9
2.864 + 0.9524 i
0.166 + 0.33 i
10
2.864 - 0.9524 i
0.166 - 0.33 i
11
2.6686 + 3.8801 i
0.0879 + 0.295 i
12
2.6686 - 3.8801 i
0.0879 - 0.295 i
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Table 6. 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
-0.991 + 0.0167 i
0.0018 + 0.00196 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.991 - 0.0167 i
0.0018 - 0.00196 i
3
-1.1257
0.00624
4
1.6111 + 0.4945 i
0.0321 - 0.2 i
5
1.6111 - 0.4945 i
0.0321 + 0.2 i
6
-1.949
1.04 i
7
-1.5904 + 2.062 i
0.0175 - 0.125 i
8
-1.5904 - 2.062 i
0.0175 + 0.125 i
9
2.9371 + 0.9381 i
0.173 + 0.368 i
10
2.9371 - 0.9381 i
0.173 - 0.368 i
11
2.5094 + 3.8315 i
0.0642 + 0.281 i
12
2.5094 - 3.8315 i
0.0642 - 0.281 i
13
297.3509
4.29
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Table 7. 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
-0.9902 + 0.0169 i
0.00172 + 0.00187 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.9902 - 0.0169 i
0.00172 - 0.00187 i
3
-1.1238
0.00599
4
1.6073 + 0.4763 i
0.028 + 0.184 i
5
1.6073 - 0.4763 i
0.028 - 0.184 i
6
-1.9667
1.29 i
7
2.2598 + 1.121 i
0.121 + 0.142 i
8
2.2598 - 1.121 i
0.121 - 0.142 i
9
-1.5844 + 2.0983 i
0.00224 - 0.133 i
10
-1.5844 - 2.0983 i
0.00224 + 0.133 i
11
3.2553 + 1.842 i
0.278 + 0.12 i
12
3.2553 - 1.842 i
0.278 - 0.12 i
13
4.2746
0.642
14
5.9686
0.72 i
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Table 8. 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
-0.173
1.31e-7
Singularities of quadratic [7, 7, 7] approximant
2
-0.173
1.31e-7 i
3
-0.9912 + 0.0169 i
0.00178 + 0.00194 i
4
-0.9912 - 0.0169 i
0.00178 - 0.00194 i
5
-1.1255
0.00617
6
1.6117 + 0.4947 i
0.0333 - 0.202 i
7
1.6117 - 0.4947 i
0.0333 + 0.202 i
8
-1.956
1.12 i
9
-1.5995 + 2.0703 i
0.0168 - 0.13 i
10
-1.5995 - 2.0703 i
0.0168 + 0.13 i
11
2.8667 + 0.9202 i
0.183 + 0.333 i
12
2.8667 - 0.9202 i
0.183 - 0.333 i
13
2.7515 + 3.9169 i
0.0948 + 0.31 i
14
2.7515 - 3.9169 i
0.0948 - 0.31 i
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Table 9. 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
-0.912
0.000438
Singularities of quadratic [8, 7, 7] approximant
2
-0.9268
0.000369 i
3
-1.0095 + 0.0432 i
0.000598 + 0.000427 i
4
-1.0095 - 0.0432 i
0.000598 - 0.000427 i
5
-1.0669
0.00104
6
1.6205 + 0.5205 i
0.154 - 0.182 i
7
1.6205 - 0.5205 i
0.154 + 0.182 i
8
2.2796 + 0.2632 i
0.331 + 0.121 i
9
2.2796 - 0.2632 i
0.331 - 0.121 i
10
-2.5155
2.57 i
11
2.616
0.503
12
-2.0866 + 2.5922 i
0.718 + 0.737 i
13
-2.0866 - 2.5922 i
0.718 - 0.737 i
14
-4.1146 + 2.9977 i
3.28 + 0.677 i
15
-4.1146 - 2.9977 i
3.28 - 0.677 i
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Table 10. 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
-0.8864
0.000339
Singularities of quadratic [8, 8, 7] approximant
2
-0.893
0.000317 i
3
-0.9997 + 0.0374 i
0.000663 + 0.000499 i
4
-0.9997 - 0.0374 i
0.000663 - 0.000499 i
5
-1.0792
0.00157
6
1.6186 + 0.5233 i
0.157 - 0.166 i
7
1.6186 - 0.5233 i
0.157 + 0.166 i
8
2.1962 + 0.1634 i
0.369 + 0.13 i
9
2.1962 - 0.1634 i
0.369 - 0.13 i
10
-2.3783
5.78 i
11
2.5411
0.392
12
-2.0811 + 2.3513 i
0.0343 + 0.821 i
13
-2.0811 - 2.3513 i
0.0343 - 0.821 i
14
-3.3303 + 4.9314 i
1.32 + 0.965 i
15
-3.3303 - 4.9314 i
1.32 - 0.965 i
16
119.7912
4.49 i
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Table 11. 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
-0.9506 + 0.0165 i
0.000419 + 0.000454 i
Singularities of quadratic [8, 8, 8] approximant
2
-0.9506 - 0.0165 i
0.000419 - 0.000454 i
3
-1.052
0.00144
4
-0.8329 + 0.6435 i
0.0000889 - 0.000349 i
5
-0.8329 - 0.6435 i
0.0000889 + 0.000349 i
6
-0.8331 + 0.6444 i
0.00035 + 0.000089 i
7
-0.8331 - 0.6444 i
0.00035 - 0.000089 i
8
1.6114 + 0.5158 i
0.0977 - 0.17 i
9
1.6114 - 0.5158 i
0.0977 + 0.17 i
10
2.4891
0.381
11
-2.2772 + 1.1693 i
0.0823 - 0.167 i
12
-2.2772 - 1.1693 i
0.0823 + 0.167 i
13
3.6044
10.1 i
14
-1.6394 + 3.4787 i
0.224 + 0.389 i
15
-1.6394 - 3.4787 i
0.224 - 0.389 i
16
6.7027
10.5
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Table 12. 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
-0.9355 + 0.0044 i
0.00153 + 0.00154 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.9355 - 0.0044 i
0.00153 - 0.00154 i
3
-1.0811 + 0.0093 i
0.0116 - 0.0316 i
4
-1.0811 - 0.0093 i
0.0116 + 0.0316 i
5
-1.1885
0.0143
6
1.6078 + 0.5142 i
0.0801 - 0.165 i
7
1.6078 - 0.5142 i
0.0801 + 0.165 i
8
-2.0936
3.15 i
9
2.3994
0.357
10
1.7426 + 1.6842 i
0.0291 + 0.0282 i
11
1.7426 - 1.6842 i
0.0291 - 0.0282 i
12
1.7793 + 1.6603 i
0.0284 - 0.031 i
13
1.7793 - 1.6603 i
0.0284 + 0.031 i
14
-1.8691 + 2.1933 i
0.0504 - 0.241 i
15
-1.8691 - 2.1933 i
0.0504 + 0.241 i
16
-4.1725 + 4.1559 i
4.53 - 7.36 i
17
-4.1725 - 4.1559 i
4.53 + 7.36 i
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Table 13. 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
-0.9232
0.000854
Singularities of quadratic [9, 9, 8] approximant
2
-0.9375
0.000734 i
3
-1.0376 + 0.0479 i
0.00109 + 0.000906 i
4
-1.0376 - 0.0479 i
0.00109 - 0.000906 i
5
-1.0966
0.00181
6
1.6144 + 0.5219 i
0.136 - 0.163 i
7
1.6144 - 0.5219 i
0.136 + 0.163 i
8
2.2031 + 0.0848 i
0.492 + 0.0119 i
9
2.2031 - 0.0848 i
0.492 - 0.0119 i
10
-2.7474
1.74e3 i
11
-2.7375 + 0.2536 i
1.78 + 3.91 i
12
-2.7375 - 0.2536 i
1.78 - 3.91 i
13
2.7993
0.434
14
-1.8543 + 2.3303 i
0.0362 + 0.409 i
15
-1.8543 - 2.3303 i
0.0362 - 0.409 i
16
1.4154 + 7.7625 i
0.848 - 0.569 i
17
1.4154 - 7.7625 i
0.848 + 0.569 i
18
8.2021
1.91 i
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Table 14. 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
-0.9236
0.00108
Singularities of quadratic [9, 9, 9] approximant
2
-0.9355
0.000943 i
3
-1.0402 + 0.0444 i
0.00125 + 0.00112 i
4
-1.0402 - 0.0444 i
0.00125 - 0.00112 i
5
-1.1049
0.00225
6
1.6132 + 0.5175 i
0.112 - 0.176 i
7
1.6132 - 0.5175 i
0.112 + 0.176 i
8
2.4056
0.377
9
-2.5514
2.44 i
10
-1.7055 + 2.3843 i
0.115 + 0.212 i
11
-1.7055 - 2.3843 i
0.115 - 0.212 i
12
3.2198
9.91 i
13
-3.5185
1.38
14
1.7725 + 4.1579 i
0.0595 + 0.226 i
15
1.7725 - 4.1579 i
0.0595 - 0.226 i
16
3.8699 + 3.0213 i
0.327 - 0.293 i
17
3.8699 - 3.0213 i
0.327 + 0.293 i
18
-7.1793
5.62 i
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Table 15. 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
-0.9185
0.000527
Singularities of quadratic [10, 9, 9] approximant
2
-0.9364
0.000427 i
3
-1.0194 + 0.0478 i
0.000618 + 0.000511 i
4
-1.0194 - 0.0478 i
0.000618 - 0.000511 i
5
-1.0625
0.000883
6
1.6146 + 0.5206 i
0.132 - 0.17 i
7
1.6146 - 0.5206 i
0.132 + 0.17 i
8
-1.9555
0.573 i
9
-1.9978 + 0.3292 i
0.0224 - 0.638 i
10
-1.9978 - 0.3292 i
0.0224 + 0.638 i
11
2.3376 + 0.0147 i
0.204 - 0.157 i
12
2.3376 - 0.0147 i
0.204 + 0.157 i
13
-1.8518 + 2.2911 i
0.0475 + 0.348 i
14
-1.8518 - 2.2911 i
0.0475 - 0.348 i
15
3.2763 + 0.6819 i
0.59 + 0.268 i
16
3.2763 - 0.6819 i
0.59 - 0.268 i
17
5.1586
0.817
18
-4.5114 + 6.5419 i
2.51 - 0.362 i
19
-4.5114 - 6.5419 i
2.51 + 0.362 i
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Table 16. 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
-0.9013 + 0.0047 i
0.0000931 + 0.000124 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.9013 - 0.0047 i
0.0000931 - 0.000124 i
3
-0.9328
0.000171
4
-1.0186 + 0.0092 i
0.000105 - 0.000129 i
5
-1.0186 - 0.0092 i
0.000105 + 0.000129 i
6
-1.0325 + 0.0728 i
0.0007 + 0.000152 i
7
-1.0325 - 0.0728 i
0.0007 - 0.000152 i
8
1.6141 + 0.5202 i
0.128 - 0.169 i
9
1.6141 - 0.5202 i
0.128 + 0.169 i
10
2.3243 + 0.0867 i
0.514 - 0.0345 i
11
2.3243 - 0.0867 i
0.514 + 0.0345 i
12
-2.3719
3.31 i
13
-2.5314 + 0.3893 i
1.05 + 1.12 i
14
-2.5314 - 0.3893 i
1.05 - 1.12 i
15
-1.8832 + 2.2896 i
0.063 - 0.425 i
16
-1.8832 - 2.2896 i
0.063 + 0.425 i
17
3.0041
0.518
18
1.1852 + 7.5004 i
0.72 - 0.477 i
19
1.1852 - 7.5004 i
0.72 + 0.477 i
20
8.105
2.06 i
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Table 17. 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
-0.9164
0.000507
Singularities of quadratic [10, 10, 10] approximant
2
-0.9329
0.000405 i
3
-1.01 + 0.0404 i
0.000495 + 0.000452 i
4
-1.01 - 0.0404 i
0.000495 - 0.000452 i
5
-1.0498
0.000742
6
-1.3511
0.0551 i
7
-1.3896
0.434
8
1.6143 + 0.52 i
0.128 - 0.171 i
9
1.6143 - 0.52 i
0.128 + 0.171 i
10
-2.198
18.7 i
11
2.3683 + 0.0621 i
0.456 - 0.135 i
12
2.3683 - 0.0621 i
0.456 + 0.135 i
13
-1.8497 + 2.3039 i
0.00315 + 0.34 i
14
-1.8497 - 2.3039 i
0.00315 - 0.34 i
15
3.2743
0.607
16
-3.9085 + 0.8964 i
1.48 + 1.22 i
17
-3.9085 - 0.8964 i
1.48 - 1.22 i
18
6.0077
9.54 i
19
2.9143 + 7.1689 i
0.307 - 0.894 i
20
2.9143 - 7.1689 i
0.307 + 0.894 i
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Table 18. 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
-0.9156
0.000426
Singularities of quadratic [11, 10, 10] approximant
2
-0.9344
0.000328 i
3
-1.0059 + 0.0419 i
0.000408 + 0.000373 i
4
-1.0059 - 0.0419 i
0.000408 - 0.000373 i
5
-1.0394
0.00056
6
-1.3638
0.066 i
7
-1.4028
0.262
8
1.6145 + 0.52 i
0.129 - 0.172 i
9
1.6145 - 0.52 i
0.129 + 0.172 i
10
-2.2623
3.84e3 i
11
2.3515
0.327
12
2.4466
0.714 i
13
-1.8307 + 2.3178 i
0.0552 + 0.331 i
14
-1.8307 - 2.3178 i
0.0552 - 0.331 i
15
3.619 + 0.7099 i
0.748 + 0.398 i
16
3.619 - 0.7099 i
0.748 - 0.398 i
17
-3.8034 + 0.2256 i
6.89 + 6.48 i
18
-3.8034 - 0.2256 i
6.89 - 6.48 i
19
8.8412
1.28
20
-4.2373 + 12.8965 i
2.4 - 2.34 i
21
-4.2373 - 12.8965 i
2.4 + 2.34 i
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Table 19. 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
0.6574
4.19e-6
Singularities of quadratic [11, 11, 10] approximant
2
0.6574
4.19e-6 i
3
-0.9207 + 0.0078 i
0.000266 + 0.000322 i
4
-0.9207 - 0.0078 i
0.000266 - 0.000322 i
5
-0.9913
0.000577
6
-1.0799 + 0.0958 i
0.000152 + 0.00087 i
7
-1.0799 - 0.0958 i
0.000152 - 0.00087 i
8
-1.0847 + 0.1077 i
0.00104 - 0.000235 i
9
-1.0847 - 0.1077 i
0.00104 + 0.000235 i
10
1.6147 + 0.5198 i
0.129 - 0.175 i
11
1.6147 - 0.5198 i
0.129 + 0.175 i
12
-2.1711
2.68 i
13
2.3278
0.327
14
2.4216
0.73 i
15
-1.8901 + 2.2554 i
0.128 - 0.336 i
16
-1.8901 - 2.2554 i
0.128 + 0.336 i
17
-2.9538 + 0.5839 i
0.538 + 0.293 i
18
-2.9538 - 0.5839 i
0.538 - 0.293 i
19
3.5709
0.787
20
4.8445
181. i
21
3.221 + 7.3241 i
0.322 - 0.792 i
22
3.221 - 7.3241 i
0.322 + 0.792 i
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Table 20. 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
-0.9048 + 0.0146 i
0.0000167 + 0.0000536 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.9048 - 0.0146 i
0.0000167 - 0.0000536 i
3
-0.9232
0.0000423
4
-0.9727 + 0.0827 i
0.0000368 + 0.000109 i
5
-0.9727 - 0.0827 i
0.0000368 - 0.000109 i
6
-0.9816 + 0.0914 i
0.00014 - 0.000037 i
7
-0.9816 - 0.0914 i
0.00014 + 0.000037 i
8
1.6141 + 0.52 i
0.126 - 0.17 i
9
1.6141 - 0.52 i
0.126 + 0.17 i
10
-1.9487
0.443 i
11
-2.1997 + 0.2603 i
0.508 - 1.4 i
12
-2.1997 - 0.2603 i
0.508 + 1.4 i
13
2.3676 + 0.092 i
0.51 - 0.0478 i
14
2.3676 - 0.092 i
0.51 + 0.0478 i
15
-1.9447 + 2.3425 i
0.0312 - 0.652 i
16
-1.9447 - 2.3425 i
0.0312 + 0.652 i
17
3.1243
0.544
18
3.2843 + 6.8956 i
1.67 - 1.19 i
19
3.2843 - 6.8956 i
1.67 + 1.19 i
20
7.0483 + 5.4186 i
2.49 + 1.75 i
21
7.0483 - 5.4186 i
2.49 - 1.75 i
22
-33.8803
0.623
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ExamplesAr cc-pVDZbh aug-cc-pVQZ 0.9r_ebh aug-cc-pVQZ 1.0r_ebh aug-cc-pVQZ 1.1r_ebh aug-cc-pVQZ 1.2r_ebh aug-cc-pVQZ 1.3r_ebh aug-cc-pVQZ 1.4r_ebh aug-cc-pVQZ 1.5r_ebh aug-cc-pVQZ 1.6r_ebh aug-cc-pVQZ 1.7r_ebh aug-cc-pVQZ 1.8r_ebh aug-cc-pVQZ 1.9r_ebh aug-cc-pVQZ 2.0r_ebh aug-cc-pVQZ 2.1r_ebh aug-cc-pVQZ 2.2r_ebh cc-pvdz 1.5rebh cc-pvdz 2rebh cc-pvdz rebh cc-pvqz 1.5rebh cc-pvqz 2rebh cc-pvqz rebh cc-pvtz 1.5rebh cc-pvtz 2rebh cc-pvtz reh- cc-pv5zh- cc-pvqzhf aug-cc-pVDZ 1.5r_ehf aug-cc-pVDZ 2.0r_ehf aug-cc-pVDZ r_ehf cc-pvdz 1.5rehf cc-pvdz 2rehf cc-pvdz 2rehf cc-pvdz rena-pl aug-cc-pvdzNe cc-pVDZo2- aug-cc-pvdz
MoleculeArX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHH- ionH- ionX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

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Designed by A. Sergeev.