Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 1.1r_e"

Molecule X 1^Sigma+ State of BH. Basis AUG-CC-PVQZ. 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
-1.5291 + 0.005 i
0.00112 + 0.00114 i
Singularities of quadratic [5, 5, 4] approximant
2
-1.5291 - 0.005 i
0.00112 - 0.00114 i
3
1.5654 + 0.4141 i
0.216 - 0.0489 i
4
1.5654 - 0.4141 i
0.216 + 0.0489 i
5
-1.9612 + 0.0326 i
0.00418 + 0.00346 i
6
-1.9612 - 0.0326 i
0.00418 - 0.00346 i
7
2.1227
0.555
8
-3.9711
0.179
9
-10.5803
0.198 i
10
25.5448
0.385 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
0.5936
0.00167
Singularities of quadratic [5, 5, 5] approximant
2
0.5936
0.00167 i
3
1.5638 + 0.416 i
0.21 - 0.0475 i
4
1.5638 - 0.416 i
0.21 + 0.0475 i
5
2.1277
0.572
6
-2.5589
0.0161
7
-2.959
0.0169 i
8
-4.2885 + 2.5121 i
0.0525 - 0.068 i
9
-4.2885 - 2.5121 i
0.0525 + 0.068 i
10
-71.1216
1.18
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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
1.3574 + 0.005 i
0.00578 - 0.00573 i
Singularities of quadratic [6, 5, 5] approximant
2
1.3574 - 0.005 i
0.00578 + 0.00573 i
3
1.6707
0.117
4
1.6301 + 0.5065 i
0.0155 - 0.193 i
5
1.6301 - 0.5065 i
0.0155 + 0.193 i
6
-2.5077 + 0.086 i
0.0125 + 0.0122 i
7
-2.5077 - 0.086 i
0.0125 - 0.0122 i
8
-4.1128
0.0976
9
5.1247
109. i
10
-7.2862
1.34 i
11
15.1725
0.695
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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
1.2008 + 0.0024 i
0.00308 - 0.00306 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2008 - 0.0024 i
0.00308 + 0.00306 i
3
1.6191 + 0.4822 i
0.0451 + 0.216 i
4
1.6191 - 0.4822 i
0.0451 - 0.216 i
5
1.7734
0.219
6
-2.4221 + 0.1297 i
0.00378 + 0.00417 i
7
-2.4221 - 0.1297 i
0.00378 - 0.00417 i
8
-3.232
0.0117
9
-5.4026
0.151 i
10
8.0796
0.737 i
11
-8.0346 + 9.5741 i
0.181 + 0.0188 i
12
-8.0346 - 9.5741 i
0.181 - 0.0188 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
1.2663 + 0.0044 i
0.00697 - 0.00693 i
Singularities of quadratic [6, 6, 6] approximant
2
1.2663 - 0.0044 i
0.00697 + 0.00693 i
3
1.6108 + 0.4654 i
0.134 + 0.229 i
4
1.6108 - 0.4654 i
0.134 - 0.229 i
5
1.8358
0.27
6
-2.4764 + 0.074 i
0.0125 + 0.0126 i
7
-2.4764 - 0.074 i
0.0125 - 0.0126 i
8
-3.8598
0.0707
9
10.1101
0.672 i
10
-12.2231
0.472 i
11
0.6234 + 13.5181 i
0.313 - 1.31 i
12
0.6234 - 13.5181 i
0.313 + 1.31 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
1.2863 + 0.0052 i
0.00886 - 0.00881 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2863 - 0.0052 i
0.00886 + 0.00881 i
3
1.6078 + 0.4622 i
0.159 + 0.22 i
4
1.6078 - 0.4622 i
0.159 - 0.22 i
5
1.8523
0.284
6
-2.4828 + 0.0551 i
0.02 + 0.0203 i
7
-2.4828 - 0.0551 i
0.02 - 0.0203 i
8
-3.9696
0.109
9
8.8904
1.19 i
10
-9.893 + 8.9531 i
0.136 - 0.306 i
11
-9.893 - 8.9531 i
0.136 + 0.306 i
12
2.7199 + 13.8219 i
1.07 + 0.214 i
13
2.7199 - 13.8219 i
1.07 - 0.214 i
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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
1.2179 + 0.4909 i
0.00282 - 0.00321 i
Singularities of quadratic [7, 7, 6] approximant
2
1.2179 - 0.4909 i
0.00282 + 0.00321 i
3
1.2242 + 0.4927 i
0.00325 + 0.00283 i
4
1.2242 - 0.4927 i
0.00325 - 0.00283 i
5
1.6653
0.144
6
1.648 + 0.5439 i
0.0746 - 0.0908 i
7
1.648 - 0.5439 i
0.0746 + 0.0908 i
8
-2.4701 + 0.0674 i
0.013 + 0.0145 i
9
-2.4701 - 0.0674 i
0.013 - 0.0145 i
10
-3.6773
0.0459
11
-7.0501
1.8 i
12
8.291
0.582 i
13
-7.829 + 9.0126 i
0.195 + 0.0656 i
14
-7.829 - 9.0126 i
0.195 - 0.0656 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
1.5118
0.104
Singularities of quadratic [7, 7, 7] approximant
2
1.5218 + 0.4519 i
0.0784 - 0.0202 i
3
1.5218 - 0.4519 i
0.0784 + 0.0202 i
4
1.6691
0.682 i
5
2.173 + 0.7942 i
0.101 - 0.137 i
6
2.173 - 0.7942 i
0.101 + 0.137 i
7
-2.4553 + 0.0514 i
0.0148 + 0.0208 i
8
-2.4553 - 0.0514 i
0.0148 - 0.0208 i
9
2.9628
0.556
10
-3.2203
0.0217
11
-3.8871
0.0348 i
12
6.0079
0.718 i
13
-6.7105
0.166
14
-13.434
0.111 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
1.4984
0.0638
Singularities of quadratic [8, 7, 7] approximant
2
1.516 + 0.4641 i
0.0637 + 0.0019 i
3
1.516 - 0.4641 i
0.0637 - 0.0019 i
4
1.7404
0.771 i
5
2.1223 + 0.65 i
0.17 - 0.585 i
6
2.1223 - 0.65 i
0.17 + 0.585 i
7
-2.2305
0.00112
8
-2.0778 + 0.922 i
0.0000611 + 0.000421 i
9
-2.0778 - 0.922 i
0.0000611 - 0.000421 i
10
-2.0854 + 0.9552 i
0.000438 - 0.0000611 i
11
-2.0854 - 0.9552 i
0.000438 + 0.0000611 i
12
2.3081
0.525
13
3.3849
0.578 i
14
-4.0061
0.014 i
15
8.7203
0.247
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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
1.5421
0.119
Singularities of quadratic [8, 8, 7] approximant
2
1.5015 + 0.4509 i
0.0544 - 0.028 i
3
1.5015 - 0.4509 i
0.0544 + 0.028 i
4
1.8946 + 0.2722 i
0.137 - 0.228 i
5
1.8946 - 0.2722 i
0.137 + 0.228 i
6
1.9458 + 0.7779 i
0.00236 - 0.0912 i
7
1.9458 - 0.7779 i
0.00236 + 0.0912 i
8
-2.2388 + 0.1578 i
0.000179 + 0.00103 i
9
-2.2388 - 0.1578 i
0.000179 - 0.00103 i
10
-2.3057
0.000757
11
-3.3896
0.00755 i
12
-1.6084 + 5.9672 i
0.0298 + 0.00443 i
13
-1.6084 - 5.9672 i
0.0298 - 0.00443 i
14
-4.5873 + 8.621 i
0.0262 - 0.0438 i
15
-4.5873 - 8.621 i
0.0262 + 0.0438 i
16
19.4963
0.193 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
1.4861 + 0.4396 i
0.0436 - 0.0268 i
Singularities of quadratic [8, 8, 8] approximant
2
1.4861 - 0.4396 i
0.0436 + 0.0268 i
3
1.5527
0.0834
4
1.6051 + 0.3241 i
0.0734 + 0.0498 i
5
1.6051 - 0.3241 i
0.0734 - 0.0498 i
6
1.9063 + 0.5002 i
0.12 + 0.278 i
7
1.9063 - 0.5002 i
0.12 - 0.278 i
8
-2.3495
0.00554
9
-2.7103
0.00463 i
10
-3.3675 + 0.334 i
0.0104 + 0.00253 i
11
-3.3675 - 0.334 i
0.0104 - 0.00253 i
12
3.7809
0.829 i
13
-4.3738
0.0798
14
6.0125 + 1.9185 i
0.0642 - 0.317 i
15
6.0125 - 1.9185 i
0.0642 + 0.317 i
16
-9.2051
0.195 i
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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
1.2479 + 0.0021 i
0.0011 - 0.00109 i
Singularities of quadratic [9, 8, 8] approximant
2
1.2479 - 0.0021 i
0.0011 + 0.00109 i
3
1.5444 + 0.1063 i
0.0805 + 0.0318 i
4
1.5444 - 0.1063 i
0.0805 - 0.0318 i
5
1.4976 + 0.432 i
0.0291 - 0.0336 i
6
1.4976 - 0.432 i
0.0291 + 0.0336 i
7
-2.3807
0.00896
8
2.3408 + 0.8217 i
0.143 + 0.0126 i
9
2.3408 - 0.8217 i
0.143 - 0.0126 i
10
-2.5571
0.0174 i
11
-3.1383
0.0157
12
-3.9749
0.0233 i
13
-1.1151 + 4.1818 i
0.00513 + 0.00343 i
14
-1.1151 - 4.1818 i
0.00513 - 0.00343 i
15
4.6414
0.568
16
-1.1057 + 4.524 i
0.0038 - 0.00566 i
17
-1.1057 - 4.524 i
0.0038 + 0.00566 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
0.6691
5.02e-7
Singularities of quadratic [9, 9, 8] approximant
2
0.6691
5.02e-7 i
3
1.2561
0.000448
4
-1.2564
6.44e-6
5
-1.2564
6.44e-6 i
6
1.2657
0.000468 i
7
1.5021 + 0.2252 i
0.00554 - 0.0156 i
8
1.5021 - 0.2252 i
0.00554 + 0.0156 i
9
1.4535 + 0.4415 i
0.0107 - 0.00768 i
10
1.4535 - 0.4415 i
0.0107 + 0.00768 i
11
-2.3119
0.00256
12
2.4214
6.65
13
-2.7978
0.0064 i
14
3.4759
0.476 i
15
-3.8496
0.111
16
-5.744
0.407 i
17
28.56 + 16.3195 i
0.755 + 0.297 i
18
28.56 - 16.3195 i
0.755 - 0.297 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
-0.4434 + 0.9797 i
1.43e-6 + 2.03e-6 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.4434 - 0.9797 i
1.43e-6 - 2.03e-6 i
3
-0.4434 + 0.9797 i
2.03e-6 - 1.43e-6 i
4
-0.4434 - 0.9797 i
2.03e-6 + 1.43e-6 i
5
1.2873 + 0.0035 i
0.000591 - 0.000579 i
6
1.2873 - 0.0035 i
0.000591 + 0.000579 i
7
1.5117 + 0.1792 i
0.00631 + 0.0245 i
8
1.5117 - 0.1792 i
0.00631 - 0.0245 i
9
1.4726 + 0.4315 i
0.0142 - 0.0164 i
10
1.4726 - 0.4315 i
0.0142 + 0.0164 i
11
-2.3272
0.00326
12
-2.741
0.00687 i
13
2.7894 + 0.3758 i
0.0105 - 0.412 i
14
2.7894 - 0.3758 i
0.0105 + 0.412 i
15
-3.6585
0.0591
16
-5.2927
0.17 i
17
14.5703
0.223
18
62.9586
3.35 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
-0.876 + 0.4879 i
8.86e-7 + 4.04e-7 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.876 - 0.4879 i
8.86e-7 - 4.04e-7 i
3
-0.876 + 0.4879 i
4.04e-7 - 8.86e-7 i
4
-0.876 - 0.4879 i
4.04e-7 + 8.86e-7 i
5
1.2761 + 0.0035 i
0.000673 - 0.000659 i
6
1.2761 - 0.0035 i
0.000673 + 0.000659 i
7
1.5199 + 0.1627 i
0.0146 + 0.0289 i
8
1.5199 - 0.1627 i
0.0146 - 0.0289 i
9
1.4791 + 0.4315 i
0.0168 - 0.0195 i
10
1.4791 - 0.4315 i
0.0168 + 0.0195 i
11
-2.3041
0.00227
12
2.6315 + 0.6081 i
0.166 + 0.261 i
13
2.6315 - 0.6081 i
0.166 - 0.261 i
14
-2.84
0.00632 i
15
-4.2286
0.411
16
-6.3214 + 3.2178 i
0.168 + 0.0682 i
17
-6.3214 - 3.2178 i
0.168 - 0.0682 i
18
7.5807
0.185
19
-14.1385
0.155 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
-0.8293 + 0.5203 i
6.75e-8 - 8.78e-7 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.8293 - 0.5203 i
6.75e-8 + 8.78e-7 i
3
-0.8293 + 0.5203 i
8.78e-7 + 6.75e-8 i
4
-0.8293 - 0.5203 i
8.78e-7 - 6.75e-8 i
5
1.2775 + 0.0036 i
0.000699 - 0.000685 i
6
1.2775 - 0.0036 i
0.000699 + 0.000685 i
7
1.5204 + 0.1613 i
0.0152 + 0.0293 i
8
1.5204 - 0.1613 i
0.0152 - 0.0293 i
9
1.4797 + 0.4317 i
0.0172 - 0.0198 i
10
1.4797 - 0.4317 i
0.0172 + 0.0198 i
11
-2.3085
0.00243
12
2.6034 + 0.6239 i
0.185 + 0.239 i
13
2.6034 - 0.6239 i
0.185 - 0.239 i
14
-2.8194
0.00636 i
15
-4.0351
0.19
16
6.5913
0.22
17
-7.9585
2.86 i
18
-14.0513
0.886
19
-35.3987
2.78 i
20
73.5125
0.758 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
-0.7531 + 0.5478 i
3.79e-7 - 1.77e-6 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.7531 - 0.5478 i
3.79e-7 + 1.77e-6 i
3
-0.7531 + 0.5478 i
1.77e-6 + 3.79e-7 i
4
-0.7531 - 0.5478 i
1.77e-6 - 3.79e-7 i
5
1.4679 + 0.3501 i
0.0276 - 0.0000303 i
6
1.4679 - 0.3501 i
0.0276 + 0.0000303 i
7
1.5114 + 0.2051 i
0.035 + 0.0261 i
8
1.5114 - 0.2051 i
0.035 - 0.0261 i
9
1.5998 + 0.5543 i
0.0316 - 0.0083 i
10
1.5998 - 0.5543 i
0.0316 + 0.0083 i
11
1.7554 + 0.6096 i
0.0189 - 0.0478 i
12
1.7554 - 0.6096 i
0.0189 + 0.0478 i
13
-2.318
0.00298
14
2.4673
0.996
15
-2.8289
0.00513 i
16
-4.3873
0.313
17
4.4557
7.28 i
18
-4.7959
0.0932 i
19
-13.9588 + 4.9191 i
0.0597 + 0.042 i
20
-13.9588 - 4.9191 i
0.0597 - 0.042 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
-0.7801 + 0.5515 i
2.2e-7 - 1.43e-6 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.7801 - 0.5515 i
2.2e-7 + 1.43e-6 i
3
-0.7801 + 0.5515 i
1.43e-6 + 2.2e-7 i
4
-0.7801 - 0.5515 i
1.43e-6 - 2.2e-7 i
5
1.1586 + 0.5021 i
0.000186 - 0.000137 i
6
1.1586 - 0.5021 i
0.000186 + 0.000137 i
7
1.1597 + 0.5021 i
0.000137 + 0.000186 i
8
1.1597 - 0.5021 i
0.000137 - 0.000186 i
9
1.449 + 0.4292 i
0.00453 - 0.0106 i
10
1.449 - 0.4292 i
0.00453 + 0.0106 i
11
1.5382 + 0.1843 i
0.0212 + 0.0365 i
12
1.5382 - 0.1843 i
0.0212 - 0.0365 i
13
-2.3137
0.00273
14
-2.8343
0.00548 i
15
2.8708 + 0.3443 i
0.117 - 0.336 i
16
2.8708 - 0.3443 i
0.117 + 0.336 i
17
-4.2481
7.98
18
-6.2428
0.391 i
19
-9.8941 + 3.17 i
0.292 + 0.0764 i
20
-9.8941 - 3.17 i
0.292 - 0.0764 i
21
12.2628
0.291
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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
-0.6951 + 0.e-5 i
1.09e-8 + 1.09e-8 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.6951 - 0.e-5 i
1.09e-8 - 1.09e-8 i
3
-0.729 + 0.5906 i
3.63e-7 - 9.95e-8 i
4
-0.729 - 0.5906 i
3.63e-7 + 9.95e-8 i
5
-0.729 + 0.5906 i
9.95e-8 + 3.63e-7 i
6
-0.729 - 0.5906 i
9.95e-8 - 3.63e-7 i
7
1.4497 + 0.3735 i
0.0132 + 0.00851 i
8
1.4497 - 0.3735 i
0.0132 - 0.00851 i
9
1.5145 + 0.203 i
0.0218 + 0.0258 i
10
1.5145 - 0.203 i
0.0218 - 0.0258 i
11
1.5532 + 0.6562 i
0.0099 + 0.0023 i
12
1.5532 - 0.6562 i
0.0099 - 0.0023 i
13
1.6201 + 0.6777 i
0.00443 - 0.0125 i
14
1.6201 - 0.6777 i
0.00443 + 0.0125 i
15
-2.3138
0.00249
16
2.3805
2.75
17
-2.7579
0.00785 i
18
-3.7178
0.0479
19
4.1664
1.76 i
20
-5.928
0.736 i
21
26.7898 + 27.4691 i
0.545 + 1.48 i
22
26.7898 - 27.4691 i
0.545 - 1.48 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
0.9344
4.38e-6
Singularities of quadratic [11, 11, 11] approximant
2
0.9344
4.38e-6 i
3
-0.8076 + 0.6216 i
7.95e-8 - 1.59e-7 i
4
-0.8076 - 0.6216 i
7.95e-8 + 1.59e-7 i
5
-0.8076 + 0.6216 i
1.59e-7 + 7.95e-8 i
6
-0.8076 - 0.6216 i
1.59e-7 - 7.95e-8 i
7
1.134 + 0.8618 i
0.0000464 + 0.0000831 i
8
1.134 - 0.8618 i
0.0000464 - 0.0000831 i
9
1.1347 + 0.8636 i
0.0000836 - 0.0000461 i
10
1.1347 - 0.8636 i
0.0000836 + 0.0000461 i
11
1.448 + 0.4022 i
0.00637 + 0.0111 i
12
1.448 - 0.4022 i
0.00637 - 0.0111 i
13
-1.5788 + 0.0009 i
2.16e-6 + 2.16e-6 i
14
-1.5788 - 0.0009 i
2.16e-6 - 2.16e-6 i
15
1.5796 + 0.1685 i
0.121 + 0.0551 i
16
1.5796 - 0.1685 i
0.121 - 0.0551 i
17
-2.2155
0.000239
18
-2.3656
0.000767 i
19
-3.
0.00221
20
3.0785
0.272
21
3.7555
0.516 i
22
-7.1458
0.536 i
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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.