Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 2.2r_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
1.0791 + 0.4402 i
0.0803 - 0.0941 i
Singularities of quadratic [5, 5, 4] approximant
2
1.0791 - 0.4402 i
0.0803 + 0.0941 i
3
1.3848
0.12
4
1.5817
0.309 i
5
-2.1553 + 0.5761 i
0.121 + 0.243 i
6
-2.1553 - 0.5761 i
0.121 - 0.243 i
7
3.9971
1.63
8
6.2553
3.63 i
9
-8.1631
0.333
10
-2570.5441
10.5 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
1.0788 + 0.44 i
0.0794 - 0.0943 i
Singularities of quadratic [5, 5, 5] approximant
2
1.0788 - 0.44 i
0.0794 + 0.0943 i
3
1.3805
0.121
4
1.5934
0.344 i
5
-2.1555 + 0.5815 i
0.129 + 0.235 i
6
-2.1555 - 0.5815 i
0.129 - 0.235 i
7
4.4299 + 0.9281 i
0.121 + 1.95 i
8
4.4299 - 0.9281 i
0.121 - 1.95 i
9
-7.778
0.353
10
30.2276
1.81
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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
0.0542
5.98e-9
Singularities of quadratic [6, 5, 5] approximant
2
0.0542
5.98e-9 i
3
1.079 + 0.4416 i
0.0838 - 0.0901 i
4
1.079 - 0.4416 i
0.0838 + 0.0901 i
5
1.3824
0.11
6
1.5453
0.237 i
7
-2.1576 + 0.5828 i
0.136 + 0.236 i
8
-2.1576 - 0.5828 i
0.136 - 0.236 i
9
3.4613
0.888
10
-7.5832
0.312
11
7.996
1.12 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
1.0912 + 0.4042 i
0.0636 + 0.147 i
Singularities of quadratic [6, 6, 5] approximant
2
1.0912 - 0.4042 i
0.0636 - 0.147 i
3
1.2464 + 0.6138 i
0.122 - 0.0214 i
4
1.2464 - 0.6138 i
0.122 + 0.0214 i
5
1.5302
0.417
6
1.472 + 0.6298 i
0.00754 - 0.247 i
7
1.472 - 0.6298 i
0.00754 + 0.247 i
8
-2.1623 + 0.6293 i
0.195 + 0.155 i
9
-2.1623 - 0.6293 i
0.195 - 0.155 i
10
-5.2027
0.276
11
-22.8448
0.334 i
12
27.5221
0.381 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
0.2796 + 1.1038 i
0.00115 - 0.00185 i
Singularities of quadratic [6, 6, 6] approximant
2
0.2796 - 1.1038 i
0.00115 + 0.00185 i
3
0.2806 + 1.1044 i
0.00185 + 0.00115 i
4
0.2806 - 1.1044 i
0.00185 - 0.00115 i
5
1.076 + 0.4634 i
0.0888 - 0.0249 i
6
1.076 - 0.4634 i
0.0888 + 0.0249 i
7
1.2844 + 0.1022 i
0.0896 - 0.0297 i
8
1.2844 - 0.1022 i
0.0896 + 0.0297 i
9
2.0823
0.46
10
-2.1489 + 0.6146 i
0.14 + 0.174 i
11
-2.1489 - 0.6146 i
0.14 - 0.174 i
12
-7.5326
0.627
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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
1.0996 + 0.435 i
0.107 - 0.192 i
Singularities of quadratic [7, 6, 6] approximant
2
1.0996 - 0.435 i
0.107 + 0.192 i
3
1.3496 + 0.395 i
0.226 + 0.143 i
4
1.3496 - 0.395 i
0.226 - 0.143 i
5
1.4505 + 0.2667 i
0.289 - 1.08 i
6
1.4505 - 0.2667 i
0.289 + 1.08 i
7
-2.1488 + 0.6398 i
0.169 + 0.138 i
8
-2.1488 - 0.6398 i
0.169 - 0.138 i
9
2.5922
0.458
10
-5.4574 + 0.17 i
2.56 - 1.61 i
11
-5.4574 - 0.17 i
2.56 + 1.61 i
12
5.5234
3.01 i
13
-68.0107
3.
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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
1.0929 + 0.4378 i
0.102 - 0.138 i
Singularities of quadratic [7, 7, 6] approximant
2
1.0929 - 0.4378 i
0.102 + 0.138 i
3
1.505 + 0.4338 i
0.307 + 0.0408 i
4
1.505 - 0.4338 i
0.307 - 0.0408 i
5
1.6116
0.277
6
1.848 + 0.5507 i
0.817 + 0.0563 i
7
1.848 - 0.5507 i
0.817 - 0.0563 i
8
-2.1301 + 0.6136 i
0.103 + 0.187 i
9
-2.1301 - 0.6136 i
0.103 - 0.187 i
10
-3.4251
0.179
11
-3.6842 + 0.8405 i
0.0807 - 0.0744 i
12
-3.6842 - 0.8405 i
0.0807 + 0.0744 i
13
10.9355
0.33 i
14
-20.2045
0.254 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
1.0926 + 0.4359 i
0.0881 - 0.148 i
Singularities of quadratic [7, 7, 7] approximant
2
1.0926 - 0.4359 i
0.0881 + 0.148 i
3
1.4917 + 0.2981 i
0.313 + 0.236 i
4
1.4917 - 0.2981 i
0.313 - 0.236 i
5
1.5268 + 0.4082 i
0.402 + 0.104 i
6
1.5268 - 0.4082 i
0.402 - 0.104 i
7
-2.141 + 0.6448 i
0.163 + 0.126 i
8
-2.141 - 0.6448 i
0.163 - 0.126 i
9
2.3942 + 1.0419 i
0.211 + 0.233 i
10
2.3942 - 1.0419 i
0.211 - 0.233 i
11
-3.4768 + 0.1164 i
0.264 - 1.05 i
12
-3.4768 - 0.1164 i
0.264 + 1.05 i
13
4.1231
0.294
14
-8.5395
0.592
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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
1.0921 + 0.439 i
0.107 - 0.129 i
Singularities of quadratic [8, 7, 7] approximant
2
1.0921 - 0.439 i
0.107 + 0.129 i
3
1.525
0.22
4
1.5776 + 0.4617 i
0.296 + 0.0174 i
5
1.5776 - 0.4617 i
0.296 - 0.0174 i
6
1.788 + 0.7872 i
0.32 - 0.289 i
7
1.788 - 0.7872 i
0.32 + 0.289 i
8
-2.1284 + 0.6214 i
0.103 + 0.164 i
9
-2.1284 - 0.6214 i
0.103 - 0.164 i
10
-3.9595 + 2.4933 i
0.00399 + 0.0862 i
11
-3.9595 - 2.4933 i
0.00399 - 0.0862 i
12
-2.6148 + 4.7014 i
0.0604 - 0.00816 i
13
-2.6148 - 4.7014 i
0.0604 + 0.00816 i
14
-0.0875 + 6.6198 i
0.0224 + 0.0864 i
15
-0.0875 - 6.6198 i
0.0224 - 0.0864 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
1.0941 + 0.4353 i
0.0916 - 0.163 i
Singularities of quadratic [8, 8, 7] approximant
2
1.0941 - 0.4353 i
0.0916 + 0.163 i
3
1.3645 + 0.1864 i
0.107 + 0.221 i
4
1.3645 - 0.1864 i
0.107 - 0.221 i
5
1.5102
0.356
6
1.5669 + 0.4138 i
0.246 + 0.0897 i
7
1.5669 - 0.4138 i
0.246 - 0.0897 i
8
1.9381 + 0.8339 i
0.303 - 0.00132 i
9
1.9381 - 0.8339 i
0.303 + 0.00132 i
10
-2.1386 + 0.6343 i
0.15 + 0.15 i
11
-2.1386 - 0.6343 i
0.15 - 0.15 i
12
-3.5555 + 0.2753 i
0.0406 + 0.242 i
13
-3.5555 - 0.2753 i
0.0406 - 0.242 i
14
-5.3075
0.15
15
16.1675
0.352 i
16
-34.3058
0.408 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
1.0888 + 0.4377 i
0.0853 - 0.115 i
Singularities of quadratic [8, 8, 8] approximant
2
1.0888 - 0.4377 i
0.0853 + 0.115 i
3
1.3632
0.115
4
1.3572 + 0.4884 i
1.11 - 1.39 i
5
1.3572 - 0.4884 i
1.11 + 1.39 i
6
1.4685
0.196 i
7
1.405 + 0.5489 i
0.105 - 0.391 i
8
1.405 - 0.5489 i
0.105 + 0.391 i
9
-2.1379 + 0.6375 i
0.149 + 0.141 i
10
-2.1379 - 0.6375 i
0.149 - 0.141 i
11
2.6513 + 1.2079 i
0.104 + 0.322 i
12
2.6513 - 1.2079 i
0.104 - 0.322 i
13
-3.647 + 0.2496 i
0.0689 + 0.408 i
14
-3.647 - 0.2496 i
0.0689 - 0.408 i
15
5.3991
0.323
16
-7.3567
0.321
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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
1.0915 + 0.4366 i
0.0891 - 0.138 i
Singularities of quadratic [9, 8, 8] approximant
2
1.0915 - 0.4366 i
0.0891 + 0.138 i
3
1.6151 + 0.4439 i
0.379 - 0.0696 i
4
1.6151 - 0.4439 i
0.379 + 0.0696 i
5
1.6485 + 0.5312 i
1.03 - 2.6 i
6
1.6485 - 0.5312 i
1.03 + 2.6 i
7
1.8243
0.319
8
-2.1369 + 0.6449 i
0.156 + 0.121 i
9
-2.1369 - 0.6449 i
0.156 - 0.121 i
10
2.3565
1.28e7 i
11
-2.9238 + 0.0369 i
1.3 - 0.654 i
12
-2.9238 - 0.0369 i
1.3 + 0.654 i
13
3.1504 + 1.5007 i
0.0659 + 0.344 i
14
3.1504 - 1.5007 i
0.0659 - 0.344 i
15
-8.1942
2.16
16
8.9627
0.317
17
-11.1582
3.32 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
1.0909 + 0.4362 i
0.082 - 0.135 i
Singularities of quadratic [9, 9, 8] approximant
2
1.0909 - 0.4362 i
0.082 + 0.135 i
3
-0.0431 + 1.3325 i
0.000343 + 0.000317 i
4
-0.0431 - 1.3325 i
0.000343 - 0.000317 i
5
-0.0431 + 1.3326 i
0.000317 - 0.000343 i
6
-0.0431 - 1.3326 i
0.000317 + 0.000343 i
7
1.5049 + 0.4141 i
0.348 + 0.0342 i
8
1.5049 - 0.4141 i
0.348 - 0.0342 i
9
1.7189 + 0.4925 i
5.52 + 3.71 i
10
1.7189 - 0.4925 i
5.52 - 3.71 i
11
-1.8414
0.0105
12
1.8431
0.369
13
-1.8434
0.0106 i
14
-2.1232 + 0.6513 i
0.123 + 0.0796 i
15
-2.1232 - 0.6513 i
0.123 - 0.0796 i
16
-5.0654
0.286
17
14.1477
0.286 i
18
-17.0909
0.268 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
1.0912 + 0.4372 i
0.0933 - 0.131 i
Singularities of quadratic [9, 9, 9] approximant
2
1.0912 - 0.4372 i
0.0933 + 0.131 i
3
1.3603 + 0.0141 i
0.114 - 0.0865 i
4
1.3603 - 0.0141 i
0.114 + 0.0865 i
5
1.4661 + 0.4801 i
0.39 + 0.102 i
6
1.4661 - 0.4801 i
0.39 - 0.102 i
7
1.6172 + 0.4658 i
0.38 - 15.7 i
8
1.6172 - 0.4658 i
0.38 + 15.7 i
9
2.1359
0.453
10
-2.1338 + 0.6404 i
0.136 + 0.134 i
11
-2.1338 - 0.6404 i
0.136 - 0.134 i
12
-3.1141 + 1.2684 i
0.0784 + 0.11 i
13
-3.1141 - 1.2684 i
0.0784 - 0.11 i
14
-3.348 + 1.498 i
0.0718 - 0.0724 i
15
-3.348 - 1.498 i
0.0718 + 0.0724 i
16
-3.9542
0.158
17
7.3493
0.465 i
18
-170.8485
0.286 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
1.0914 + 0.4366 i
0.0889 - 0.137 i
Singularities of quadratic [10, 9, 9] approximant
2
1.0914 - 0.4366 i
0.0889 + 0.137 i
3
1.578 + 0.4596 i
0.416 - 0.0795 i
4
1.578 - 0.4596 i
0.416 + 0.0795 i
5
1.6708
0.28
6
1.6109 + 0.5739 i
3.89 + 4.65 i
7
1.6109 - 0.5739 i
3.89 - 4.65 i
8
2.1707
110. i
9
-2.1358 + 0.6461 i
0.155 + 0.117 i
10
-2.1358 - 0.6461 i
0.155 - 0.117 i
11
-2.7994 + 0.0063 i
0.662 + 0.406 i
12
-2.7994 - 0.0063 i
0.662 - 0.406 i
13
2.821 + 1.1789 i
0.0747 + 0.307 i
14
2.821 - 1.1789 i
0.0747 - 0.307 i
15
3.9509
0.368
16
5.644
75.8 i
17
-8.159 + 1.6557 i
0.661 + 1.11 i
18
-8.159 - 1.6557 i
0.661 - 1.11 i
19
18.9871
0.64
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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
1.0912 + 0.4369 i
0.0906 - 0.133 i
Singularities of quadratic [10, 10, 9] approximant
2
1.0912 - 0.4369 i
0.0906 + 0.133 i
3
1.4002 + 0.0142 i
0.15 - 0.107 i
4
1.4002 - 0.0142 i
0.15 + 0.107 i
5
1.488 + 0.47 i
0.406 + 0.0892 i
6
1.488 - 0.47 i
0.406 - 0.0892 i
7
1.631 + 0.476 i
10.1 - 13.5 i
8
1.631 - 0.476 i
10.1 + 13.5 i
9
2.0773
0.471
10
-2.1349 + 0.647 i
0.153 + 0.112 i
11
-2.1349 - 0.647 i
0.153 - 0.112 i
12
-2.6624 + 0.0128 i
0.768 + 0.29 i
13
-2.6624 - 0.0128 i
0.768 - 0.29 i
14
0.5642 + 3.8959 i
0.00254 + 0.0431 i
15
0.5642 - 3.8959 i
0.00254 - 0.0431 i
16
0.6423 + 3.9997 i
0.0433 - 0.00225 i
17
0.6423 - 3.9997 i
0.0433 + 0.00225 i
18
-5.9092
0.499
19
-15.3818
0.319 i
20
15.9645
0.259 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
-1.0296 + 0.e-5 i
0.0000362 + 0.0000362 i
Singularities of quadratic [10, 10, 10] approximant
2
-1.0296 - 0.e-5 i
0.0000362 - 0.0000362 i
3
1.0914 + 0.4368 i
0.0903 - 0.135 i
4
1.0914 - 0.4368 i
0.0903 + 0.135 i
5
1.5176 + 0.506 i
0.479 + 0.0708 i
6
1.5176 - 0.506 i
0.479 - 0.0708 i
7
1.6043 + 0.0565 i
0.254 - 0.106 i
8
1.6043 - 0.0565 i
0.254 + 0.106 i
9
1.6146 + 0.5224 i
4.22 - 8.56 i
10
1.6146 - 0.5224 i
4.22 + 8.56 i
11
-2.1259 + 0.6392 i
0.108 + 0.123 i
12
-2.1259 - 0.6392 i
0.108 - 0.123 i
13
2.4417
0.569
14
-2.5871 + 1.4943 i
0.014 + 0.0552 i
15
-2.5871 - 1.4943 i
0.014 - 0.0552 i
16
-2.6605 + 1.5522 i
0.0541 - 0.0197 i
17
-2.6605 - 1.5522 i
0.0541 + 0.0197 i
18
-4.563
0.163
19
6.2336
0.646 i
20
86.1147
0.971
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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
-1.1608
0.000192
Singularities of quadratic [11, 10, 10] approximant
2
-1.1608
0.000192 i
3
1.0914 + 0.4368 i
0.0904 - 0.135 i
4
1.0914 - 0.4368 i
0.0904 + 0.135 i
5
1.5941 + 0.0523 i
0.246 - 0.109 i
6
1.5941 - 0.0523 i
0.246 + 0.109 i
7
1.5159 + 0.5047 i
0.479 + 0.0736 i
8
1.5159 - 0.5047 i
0.479 - 0.0736 i
9
1.6111 + 0.5199 i
6.35 - 8.8 i
10
1.6111 - 0.5199 i
6.35 + 8.8 i
11
-2.1303 + 0.6412 i
0.125 + 0.124 i
12
-2.1303 - 0.6412 i
0.125 - 0.124 i
13
2.4235
0.573
14
-3.6592
0.214
15
-3.6432 + 1.7078 i
0.084 + 0.0163 i
16
-3.6432 - 1.7078 i
0.084 - 0.0163 i
17
-3.5346 + 2.3307 i
0.0221 - 0.0682 i
18
-3.5346 - 2.3307 i
0.0221 + 0.0682 i
19
6.7663
0.458 i
20
7.9373 + 26.035 i
0.364 + 0.28 i
21
7.9373 - 26.035 i
0.364 - 0.28 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
0.1508
0
Singularities of quadratic [11, 11, 10] approximant
2
0.1508
0
3
1.0913 + 0.4368 i
0.0901 - 0.135 i
4
1.0913 - 0.4368 i
0.0901 + 0.135 i
5
1.5132 + 0.5043 i
0.457 + 0.0758 i
6
1.5132 - 0.5043 i
0.457 - 0.0758 i
7
1.6014 + 0.0644 i
0.276 - 0.0977 i
8
1.6014 - 0.0644 i
0.276 + 0.0977 i
9
1.6262 + 0.5189 i
0.363 + 6.65 i
10
1.6262 - 0.5189 i
0.363 - 6.65 i
11
-2.1293 + 0.6286 i
0.0952 + 0.164 i
12
-2.1293 - 0.6286 i
0.0952 - 0.164 i
13
2.365
0.53
14
-2.4726 + 0.829 i
0.174 - 0.127 i
15
-2.4726 - 0.829 i
0.174 + 0.127 i
16
-2.5123 + 0.7553 i
0.0913 + 0.357 i
17
-2.5123 - 0.7553 i
0.0913 - 0.357 i
18
-5.7206
0.232
19
6.6552
0.596 i
20
-16.9312
3.71 i
21
-6.0648 + 23.2066 i
0.612 + 0.249 i
22
-6.0648 - 23.2066 i
0.612 - 0.249 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
0.0387 + 0.7771 i
8.7e-6 + 7.73e-6 i
Singularities of quadratic [11, 11, 11] approximant
2
0.0387 - 0.7771 i
8.7e-6 - 7.73e-6 i
3
0.0387 + 0.7771 i
7.73e-6 - 8.7e-6 i
4
0.0387 - 0.7771 i
7.73e-6 + 8.7e-6 i
5
1.0914 + 0.4368 i
0.0905 - 0.136 i
6
1.0914 - 0.4368 i
0.0905 + 0.136 i
7
1.5219 + 0.5065 i
0.501 + 0.0598 i
8
1.5219 - 0.5065 i
0.501 - 0.0598 i
9
1.6046 + 0.0474 i
0.227 - 0.112 i
10
1.6046 - 0.0474 i
0.227 + 0.112 i
11
1.604 + 0.5275 i
13.4 - 5.4 i
12
1.604 - 0.5275 i
13.4 + 5.4 i
13
-2.1235 + 0.6357 i
0.0939 + 0.129 i
14
-2.1235 - 0.6357 i
0.0939 - 0.129 i
15
2.4958
0.608
16
-2.3651 + 1.2347 i
0.0292 - 0.0447 i
17
-2.3651 - 1.2347 i
0.0292 + 0.0447 i
18
-2.4205 + 1.2338 i
0.05 + 0.0305 i
19
-2.4205 - 1.2338 i
0.05 - 0.0305 i
20
-4.8059
0.174
21
6.1033
0.655 i
22
66.1369
1.31
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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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