Singularities of Møller-Plesset series: example "hf cc-pvdz 2re"

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
-0.7122 + 0.364 i
0.000179 + 0.00139 i
Singularities of quadratic [5, 5, 4] approximant
2
-0.7122 - 0.364 i
0.000179 - 0.00139 i
3
-0.7194 + 0.3572 i
0.0014 - 0.000155 i
4
-0.7194 - 0.3572 i
0.0014 + 0.000155 i
5
1.1318 + 0.49 i
0.031 + 0.118 i
6
1.1318 - 0.49 i
0.031 - 0.118 i
7
-1.7226 + 1.2192 i
0.0813 + 0.000878 i
8
-1.7226 - 1.2192 i
0.0813 - 0.000878 i
9
1.4642 + 2.2357 i
0.0217 - 0.154 i
10
1.4642 - 2.2357 i
0.0217 + 0.154 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
-1.0804 + 0.0513 i
0.0096 + 0.0109 i
Singularities of quadratic [5, 5, 5] approximant
2
-1.0804 - 0.0513 i
0.0096 - 0.0109 i
3
1.162 + 0.5473 i
0.113 - 0.193 i
4
1.162 - 0.5473 i
0.113 + 0.193 i
5
-1.3545 + 0.1126 i
0.0394 + 0.00295 i
6
-1.3545 - 0.1126 i
0.0394 - 0.00295 i
7
-1.5825 + 1.5339 i
0.119 - 0.173 i
8
-1.5825 - 1.5339 i
0.119 + 0.173 i
9
2.8527
0.401
10
-12.7017
0.656
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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
-1.1218 + 0.0325 i
0.0402 + 0.0364 i
Singularities of quadratic [6, 5, 5] approximant
2
-1.1218 - 0.0325 i
0.0402 - 0.0364 i
3
1.163 + 0.5483 i
0.119 - 0.196 i
4
1.163 - 0.5483 i
0.119 + 0.196 i
5
-1.5279 + 0.3081 i
0.0341 + 0.318 i
6
-1.5279 - 0.3081 i
0.0341 - 0.318 i
7
-1.5219 + 1.8391 i
0.0553 + 0.27 i
8
-1.5219 - 1.8391 i
0.0553 - 0.27 i
9
2.9541
0.411
10
7.9992
38.7 i
11
-10.2438
0.832
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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
-1.0151 + 0.0765 i
0.000768 + 0.00426 i
Singularities of quadratic [6, 6, 5] approximant
2
-1.0151 - 0.0765 i
0.000768 - 0.00426 i
3
-1.0747
0.00261
4
-1.1467
0.00461 i
5
1.1602 + 0.5504 i
0.118 - 0.182 i
6
1.1602 - 0.5504 i
0.118 + 0.182 i
7
-1.5997 + 1.3125 i
0.14 - 0.0448 i
8
-1.5997 - 1.3125 i
0.14 + 0.0448 i
9
2.5439
0.363
10
-0.7163 + 5.3288 i
0.684 + 0.222 i
11
-0.7163 - 5.3288 i
0.684 - 0.222 i
12
34.398
1.99 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
-0.4586 + 0.e-5 i
0.0000467 + 0.0000467 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.4586 - 0.e-5 i
0.0000467 - 0.0000467 i
3
-1.0633
0.0199
4
-1.1521
0.025 i
5
1.1609 + 0.5497 i
0.118 - 0.185 i
6
1.1609 - 0.5497 i
0.118 + 0.185 i
7
-1.9096 + 0.716 i
0.139 + 0.266 i
8
-1.9096 - 0.716 i
0.139 - 0.266 i
9
2.6741
0.371
10
-2.1102 + 2.0528 i
0.26 - 4.66 i
11
-2.1102 - 2.0528 i
0.26 + 4.66 i
12
-5.0786
0.542
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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
-0.8466 + 0.0017 i
0.00144 + 0.00146 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.8466 - 0.0017 i
0.00144 - 0.00146 i
3
-1.0756
0.0129
4
-1.2245
0.0248 i
5
1.1627 + 0.5499 i
0.124 - 0.191 i
6
1.1627 - 0.5499 i
0.124 + 0.191 i
7
-1.7739 + 0.8677 i
0.169 + 0.181 i
8
-1.7739 - 0.8677 i
0.169 - 0.181 i
9
2.9581
0.388
10
-1.7112 + 2.6694 i
1.01 - 0.249 i
11
-1.7112 - 2.6694 i
1.01 + 0.249 i
12
4.4855
3.65 i
13
18.711
1.97
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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
-0.767 + 0.0005 i
0.000635 + 0.000637 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.767 - 0.0005 i
0.000635 - 0.000637 i
3
-1.0579
0.0114
4
-1.1899
0.0193 i
5
1.1625 + 0.5498 i
0.123 - 0.19 i
6
1.1625 - 0.5498 i
0.123 + 0.19 i
7
-1.7112 + 1.0033 i
0.145 + 0.0944 i
8
-1.7112 - 1.0033 i
0.145 - 0.0944 i
9
-1.4093 + 3.08 i
0.222 - 0.729 i
10
-1.4093 - 3.08 i
0.222 + 0.729 i
11
3.4304 + 0.0549 i
0.147 - 0.128 i
12
3.4304 - 0.0549 i
0.147 + 0.128 i
13
12.9331 + 13.7921 i
1.24 - 0.272 i
14
12.9331 - 13.7921 i
1.24 + 0.272 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
-0.9054 + 0.0029 i
0.00498 + 0.00506 i
Singularities of quadratic [7, 7, 7] approximant
2
-0.9054 - 0.0029 i
0.00498 - 0.00506 i
3
-1.1331
0.0323
4
-1.2753
0.0567 i
5
1.1634 + 0.5509 i
0.131 - 0.192 i
6
1.1634 - 0.5509 i
0.131 + 0.192 i
7
-1.6897 + 0.5254 i
0.324 - 0.528 i
8
-1.6897 - 0.5254 i
0.324 + 0.528 i
9
2.4753 + 0.3234 i
0.373 + 0.179 i
10
2.4753 - 0.3234 i
0.373 - 0.179 i
11
2.5795
0.854
12
-1.762 + 2.0764 i
0.282 + 0.544 i
13
-1.762 - 2.0764 i
0.282 - 0.544 i
14
-11.4687
0.896
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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
-0.8997 + 0.0029 i
0.00421 + 0.00428 i
Singularities of quadratic [8, 7, 7] approximant
2
-0.8997 - 0.0029 i
0.00421 - 0.00428 i
3
-1.1232
0.0272
4
-1.2686
0.0487 i
5
1.1633 + 0.5511 i
0.132 - 0.191 i
6
1.1633 - 0.5511 i
0.132 + 0.191 i
7
-1.7143 + 0.5696 i
0.128 - 0.503 i
8
-1.7143 - 0.5696 i
0.128 + 0.503 i
9
2.3596
0.475
10
2.3913 + 0.1681 i
0.239 + 0.195 i
11
2.3913 - 0.1681 i
0.239 - 0.195 i
12
-1.7463 + 2.1387 i
0.385 + 0.52 i
13
-1.7463 - 2.1387 i
0.385 - 0.52 i
14
-11.8272
1.03
15
29.2323
2.91 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
-0.8943 + 0.0019 i
0.00625 + 0.00635 i
Singularities of quadratic [8, 8, 7] approximant
2
-0.8943 - 0.0019 i
0.00625 - 0.00635 i
3
-1.1222
0.0345
4
-1.2375
0.0489 i
5
1.1636 + 0.551 i
0.133 - 0.193 i
6
1.1636 - 0.551 i
0.133 + 0.193 i
7
-1.6708 + 0.6566 i
0.0795 - 0.247 i
8
-1.6708 - 0.6566 i
0.0795 + 0.247 i
9
-1.5145 + 2.1877 i
0.328 + 0.122 i
10
-1.5145 - 2.1877 i
0.328 - 0.122 i
11
2.7818 + 0.3606 i
0.548 + 0.15 i
12
2.7818 - 0.3606 i
0.548 - 0.15 i
13
3.9163
0.621
14
-4.2684
0.496
15
-5.4663
1.54 i
16
13.344
197. 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
-0.749 + 0.e-4 i
0.000859 + 0.000859 i
Singularities of quadratic [8, 8, 8] approximant
2
-0.749 - 0.e-4 i
0.000859 - 0.000859 i
3
-0.9294
0.0199
4
-0.9341
0.0218 i
5
-1.1631
0.0699
6
-1.2754
0.0813 i
7
1.1633 + 0.551 i
0.131 - 0.191 i
8
1.1633 - 0.551 i
0.131 + 0.191 i
9
-1.6567 + 0.5146 i
0.392 - 0.378 i
10
-1.6567 - 0.5146 i
0.392 + 0.378 i
11
2.4391 + 0.287 i
0.346 + 0.184 i
12
2.4391 - 0.287 i
0.346 - 0.184 i
13
2.4818
0.83
14
-1.7514 + 2.0701 i
0.281 + 0.529 i
15
-1.7514 - 2.0701 i
0.281 - 0.529 i
16
-11.0751
0.877
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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
-0.704 + 0.e-5 i
0.00196 + 0.00196 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.704 - 0.e-5 i
0.00196 - 0.00196 i
3
-0.921 + 0.0031 i
0.00724 + 0.00743 i
4
-0.921 - 0.0031 i
0.00724 - 0.00743 i
5
-1.1453
0.0392
6
-1.2848
0.0652 i
7
1.1634 + 0.551 i
0.131 - 0.191 i
8
1.1634 - 0.551 i
0.131 + 0.191 i
9
-1.6722 + 0.5204 i
0.381 - 0.462 i
10
-1.6722 - 0.5204 i
0.381 + 0.462 i
11
2.4522 + 0.2845 i
0.348 + 0.189 i
12
2.4522 - 0.2845 i
0.348 - 0.189 i
13
2.5143
0.749
14
-1.7421 + 2.0774 i
0.28 + 0.507 i
15
-1.7421 - 2.0774 i
0.28 - 0.507 i
16
-11.7353
0.936
17
98.5828
2.03 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
-0.7341
0.000103
Singularities of quadratic [9, 9, 8] approximant
2
-0.7345
0.000102 i
3
0.9071
0.00488
4
0.9072
0.00488 i
5
-0.913 + 0.0149 i
0.000526 + 0.00048 i
6
-0.913 - 0.0149 i
0.000526 - 0.00048 i
7
-1.0664
0.00335
8
1.1632 + 0.5516 i
0.136 - 0.186 i
9
1.1632 - 0.5516 i
0.136 + 0.186 i
10
-1.5799 + 0.2882 i
0.202 + 0.0859 i
11
-1.5799 - 0.2882 i
0.202 - 0.0859 i
12
-1.8676
0.334 i
13
-1.5714 + 1.9941 i
0.116 + 0.195 i
14
-1.5714 - 1.9941 i
0.116 - 0.195 i
15
2.8924 + 0.5802 i
0.497 + 0.166 i
16
2.8924 - 0.5802 i
0.497 - 0.166 i
17
4.988
0.713
18
18.258
137. 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
-0.7248
0.0000387
Singularities of quadratic [9, 9, 9] approximant
2
-0.7252
0.0000386 i
3
-0.8855 + 0.0155 i
0.000177 + 0.000163 i
4
-0.8855 - 0.0155 i
0.000177 - 0.000163 i
5
-1.0043
0.000894
6
1.1639 + 0.5511 i
0.135 - 0.196 i
7
1.1639 - 0.5511 i
0.135 + 0.196 i
8
-1.3804 + 0.3825 i
0.0206 - 0.0181 i
9
-1.3804 - 0.3825 i
0.0206 + 0.0181 i
10
1.7563 + 0.0098 i
1.5 - 0.00413 i
11
1.7563 - 0.0098 i
1.5 + 0.00413 i
12
-1.3076 + 1.5347 i
0.0151 - 0.0297 i
13
-1.3076 - 1.5347 i
0.0151 + 0.0297 i
14
-1.5985 + 1.4373 i
0.0274 + 0.0306 i
15
-1.5985 - 1.4373 i
0.0274 - 0.0306 i
16
2.7309
0.386
17
-1.3989 + 3.6468 i
0.365 + 0.00194 i
18
-1.3989 - 3.6468 i
0.365 - 0.00194 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
-0.7897
0.000155
Singularities of quadratic [10, 9, 9] approximant
2
-0.7918
0.000153 i
3
-0.9286 + 0.0231 i
0.000402 + 0.000341 i
4
-0.9286 - 0.0231 i
0.000402 - 0.000341 i
5
-1.0453
0.00167
6
1.1638 + 0.5512 i
0.135 - 0.195 i
7
1.1638 - 0.5512 i
0.135 + 0.195 i
8
-1.4361 + 0.351 i
0.0535 - 0.0315 i
9
-1.4361 - 0.351 i
0.0535 + 0.0315 i
10
1.8481 + 0.0125 i
1.49 + 0.0814 i
11
1.8481 - 0.0125 i
1.49 - 0.0814 i
12
-1.5234 + 1.8094 i
0.00657 + 0.126 i
13
-1.5234 - 1.8094 i
0.00657 - 0.126 i
14
2.8301
0.4
15
-3.4907 + 0.2391 i
0.156 - 0.265 i
16
-3.4907 - 0.2391 i
0.156 + 0.265 i
17
-0.7553 + 5.3209 i
0.312 - 0.454 i
18
-0.7553 - 5.3209 i
0.312 + 0.454 i
19
11.6234
2.92 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
-0.726
0.0000293
Singularities of quadratic [10, 10, 9] approximant
2
-0.7264
0.0000292 i
3
-0.8677 + 0.0128 i
0.000109 + 0.000103 i
4
-0.8677 - 0.0128 i
0.000109 - 0.000103 i
5
-0.9771
0.000552
6
1.1639 + 0.5512 i
0.137 - 0.195 i
7
1.1639 - 0.5512 i
0.137 + 0.195 i
8
-1.2798 + 0.365 i
0.011 - 0.00304 i
9
-1.2798 - 0.365 i
0.011 + 0.00304 i
10
1.584 + 0.0032 i
0.705 - 0.423 i
11
1.584 - 0.0032 i
0.705 + 0.423 i
12
-1.6512 + 0.8098 i
0.0633 + 0.000977 i
13
-1.6512 - 0.8098 i
0.0633 - 0.000977 i
14
-1.8438
2.45 i
15
-1.812 + 1.7192 i
0.241 - 0.087 i
16
-1.812 - 1.7192 i
0.241 + 0.087 i
17
2.845
0.415
18
6.5262
9.99 i
19
2.2826 + 11.1158 i
0.806 - 0.847 i
20
2.2826 - 11.1158 i
0.806 + 0.847 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
-0.7663
0.0000696
Singularities of quadratic [10, 10, 10] approximant
2
-0.7677
0.0000688 i
3
-0.8989 + 0.0192 i
0.000193 + 0.00017 i
4
-0.8989 - 0.0192 i
0.000193 - 0.00017 i
5
-1.0053
0.000818
6
1.1638 + 0.5512 i
0.136 - 0.195 i
7
1.1638 - 0.5512 i
0.136 + 0.195 i
8
-1.3643 + 0.3778 i
0.0205 - 0.0153 i
9
-1.3643 - 0.3778 i
0.0205 + 0.0153 i
10
1.6319 + 0.0031 i
0.774 - 0.454 i
11
1.6319 - 0.0031 i
0.774 + 0.454 i
12
-1.7309 + 1.1173 i
0.00998 - 0.059 i
13
-1.7309 - 1.1173 i
0.00998 + 0.059 i
14
-1.5585 + 1.5046 i
0.0589 - 0.0341 i
15
-1.5585 - 1.5046 i
0.0589 + 0.0341 i
16
2.9671 + 0.3798 i
0.566 + 0.0177 i
17
2.9671 - 0.3798 i
0.566 - 0.0177 i
18
3.6901
1.25
19
-2.6986 + 3.5676 i
0.778 - 0.294 i
20
-2.6986 - 3.5676 i
0.778 + 0.294 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
-0.593 + 0.e-5 i
1.23e-6 + 1.23e-6 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.593 - 0.e-5 i
1.23e-6 - 1.23e-6 i
3
-0.7645
0.0000245
4
-0.767
0.0000243 i
5
-0.8896 + 0.0249 i
0.0000999 + 0.0000733 i
6
-0.8896 - 0.0249 i
0.0000999 - 0.0000733 i
7
-0.9818
0.000391
8
1.1637 + 0.5512 i
0.135 - 0.193 i
9
1.1637 - 0.5512 i
0.135 + 0.193 i
10
-1.3839 + 0.4003 i
0.0164 - 0.0302 i
11
-1.3839 - 0.4003 i
0.0164 + 0.0302 i
12
2.2705 + 0.0414 i
1.14 + 0.201 i
13
2.2705 - 0.0414 i
1.14 - 0.201 i
14
-1.5676 + 1.8685 i
0.0503 + 0.143 i
15
-1.5676 - 1.8685 i
0.0503 - 0.143 i
16
-3.0949
0.262 i
17
3.5093
0.389
18
4.1199
0.854 i
19
-4.7573
0.706
20
-8.7222 + 13.4009 i
0.0146 - 1.41 i
21
-8.7222 - 13.4009 i
0.0146 + 1.41 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
-0.7303 + 0.0003 i
8.03e-6 + 8.15e-6 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.7303 - 0.0003 i
8.03e-6 - 8.15e-6 i
3
-0.8009
0.0000196
4
-0.8102
0.0000197 i
5
-0.8942 + 0.0343 i
0.0000778 + 0.0000342 i
6
-0.8942 - 0.0343 i
0.0000778 - 0.0000342 i
7
-0.9715
0.000242
8
1.1637 + 0.5512 i
0.134 - 0.193 i
9
1.1637 - 0.5512 i
0.134 + 0.193 i
10
-1.405 + 0.4018 i
0.0181 - 0.0423 i
11
-1.405 - 0.4018 i
0.0181 + 0.0423 i
12
-2.2857
0.342 i
13
2.4106 + 0.0365 i
0.88 - 0.208 i
14
2.4106 - 0.0365 i
0.88 + 0.208 i
15
-1.6206 + 1.9097 i
0.0844 + 0.197 i
16
-1.6206 - 1.9097 i
0.0844 - 0.197 i
17
3.3825 + 0.9186 i
0.584 + 0.12 i
18
3.3825 - 0.9186 i
0.584 - 0.12 i
19
-4.1022 + 6.4282 i
5.02 - 1.66 i
20
-4.1022 - 6.4282 i
5.02 + 1.66 i
21
15.1547 + 7.0509 i
0.889 - 0.458 i
22
15.1547 - 7.0509 i
0.889 + 0.458 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
-0.7495
0.0000532
Singularities of quadratic [11, 11, 11] approximant
2
-0.7502
0.0000528 i
3
-0.8797 + 0.0139 i
0.000147 + 0.000138 i
4
-0.8797 - 0.0139 i
0.000147 - 0.000138 i
5
-0.986
0.000678
6
1.1637 + 0.5511 i
0.133 - 0.194 i
7
1.1637 - 0.5511 i
0.133 + 0.194 i
8
-1.2903 + 0.312 i
0.0149 + 0.00386 i
9
-1.2903 - 0.312 i
0.0149 - 0.00386 i
10
-1.4036
0.0326 i
11
1.7288 + 0.542 i
1.37 + 0.137 i
12
1.7288 - 0.542 i
1.37 - 0.137 i
13
1.7386 + 0.5494 i
9.24 - 11.3 i
14
1.7386 - 0.5494 i
9.24 + 11.3 i
15
-1.734 + 0.6291 i
0.232 + 0.0671 i
16
-1.734 - 0.6291 i
0.232 - 0.0671 i
17
-1.6621 + 1.7577 i
0.103 - 0.164 i
18
-1.6621 - 1.7577 i
0.103 + 0.164 i
19
2.6935
0.388
20
-1.0424 + 5.2224 i
0.466 - 0.292 i
21
-1.0424 - 5.2224 i
0.466 + 0.292 i
22
-14.2606
2.16
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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.