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

Molecule X 1^Sigma+ State of BH. 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
0.972
0.00157
Singularities of quadratic [5, 5, 4] approximant
2
0.9739
0.00157 i
3
1.4111 + 0.4835 i
0.00157 - 0.086 i
4
1.4111 - 0.4835 i
0.00157 + 0.086 i
5
2.6915
0.948
6
-2.9049
0.00488
7
-3.1416
0.00488 i
8
-5.8025 + 1.3847 i
0.0318 + 0.00112 i
9
-5.8025 - 1.3847 i
0.0318 - 0.00112 i
10
155.0396
0.876 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
1.4316 + 0.4877 i
0.0253 + 0.127 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4316 - 0.4877 i
0.0253 - 0.127 i
3
1.9212
0.635
4
1.8932 + 1.7137 i
0.0152 + 0.0449 i
5
1.8932 - 1.7137 i
0.0152 - 0.0449 i
6
2.2427 + 1.3885 i
0.0715 - 0.0321 i
7
2.2427 - 1.3885 i
0.0715 + 0.0321 i
8
-3.3959 + 0.4592 i
0.00225 + 0.00279 i
9
-3.3959 - 0.4592 i
0.00225 - 0.00279 i
10
-5.1017
0.00521
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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
1.4321 + 0.4885 i
0.0236 + 0.13 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4321 - 0.4885 i
0.0236 - 0.13 i
3
1.8926
0.606
4
1.9756 + 1.7562 i
0.011 + 0.0521 i
5
1.9756 - 1.7562 i
0.011 - 0.0521 i
6
2.4436 + 1.3346 i
0.0961 - 0.0243 i
7
2.4436 - 1.3346 i
0.0961 + 0.0243 i
8
-3.415 + 0.4665 i
0.00238 + 0.00291 i
9
-3.415 - 0.4665 i
0.00238 - 0.00291 i
10
-5.2607
0.00564
11
91.0406
0.0939 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
1.4512 + 0.5119 i
0.0988 - 0.186 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4512 - 0.5119 i
0.0988 + 0.186 i
3
1.7326
0.18
4
1.9083
0.408 i
5
2.4811 + 1.3367 i
0.24 + 0.135 i
6
2.4811 - 1.3367 i
0.24 - 0.135 i
7
-3.5385
0.0198
8
-4.0547
0.0187 i
9
4.6669
0.263
10
9.0877
0.958 i
11
-9.6254 + 7.6876 i
0.0774 + 0.00656 i
12
-9.6254 - 7.6876 i
0.0774 - 0.00656 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
1.4477 + 0.5187 i
0.112 - 0.146 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4477 - 0.5187 i
0.112 + 0.146 i
3
1.7062 + 0.0229 i
0.0721 - 0.0595 i
4
1.7062 - 0.0229 i
0.0721 + 0.0595 i
5
2.7823 + 1.2586 i
0.474 + 0.145 i
6
2.7823 - 1.2586 i
0.474 - 0.145 i
7
-3.7198 + 0.0663 i
0.0751 + 0.104 i
8
-3.7198 - 0.0663 i
0.0751 - 0.104 i
9
3.8875 + 2.4762 i
0.183 - 0.261 i
10
3.8875 - 2.4762 i
0.183 + 0.261 i
11
-8.936
0.0677
12
16.7909
0.162
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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
1.4516 + 0.5179 i
0.132 - 0.161 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4516 - 0.5179 i
0.132 + 0.161 i
3
1.6713
0.106
4
1.7593
0.155 i
5
2.5342 + 1.4232 i
0.159 + 0.123 i
6
2.5342 - 1.4232 i
0.159 - 0.123 i
7
-3.2781
0.00386
8
-3.8123 + 3.7461 i
0.00545 + 0.000249 i
9
-3.8123 - 3.7461 i
0.00545 - 0.000249 i
10
-4.7439 + 2.4758 i
0.000903 - 0.00352 i
11
-4.7439 - 2.4758 i
0.000903 + 0.00352 i
12
5.9997 + 3.5396 i
0.15 + 0.184 i
13
5.9997 - 3.5396 i
0.15 - 0.184 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
0.2022
3.19e-9
Singularities of quadratic [7, 7, 6] approximant
2
0.2022
3.19e-9 i
3
1.4437 + 0.5119 i
0.0607 - 0.145 i
4
1.4437 - 0.5119 i
0.0607 + 0.145 i
5
1.9383 + 0.1068 i
0.336 - 0.133 i
6
1.9383 - 0.1068 i
0.336 + 0.133 i
7
2.3828 + 0.959 i
0.274 - 0.535 i
8
2.3828 - 0.959 i
0.274 + 0.535 i
9
-3.3464
0.00529
10
-4.9106
0.00613 i
11
4.8175 + 1.2507 i
0.107 - 0.178 i
12
4.8175 - 1.2507 i
0.107 + 0.178 i
13
-4.2345 + 8.2295 i
0.0181 - 0.0211 i
14
-4.2345 - 8.2295 i
0.0181 + 0.0211 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
1.4524 + 0.517 i
0.133 - 0.168 i
Singularities of quadratic [7, 7, 7] approximant
2
1.4524 - 0.517 i
0.133 + 0.168 i
3
1.6803
0.121
4
1.7914
0.196 i
5
2.4583 + 1.3883 i
0.156 + 0.0933 i
6
2.4583 - 1.3883 i
0.156 - 0.0933 i
7
-3.3934
0.0072
8
-4.5117
0.00757 i
9
5.4869
0.408
10
1.1127 + 6.0039 i
0.0193 + 0.00724 i
11
1.1127 - 6.0039 i
0.0193 - 0.00724 i
12
-0.51 + 6.4645 i
0.00753 - 0.0134 i
13
-0.51 - 6.4645 i
0.00753 + 0.0134 i
14
-13.8354
0.824
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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
1.4504 + 0.5131 i
0.0952 - 0.179 i
Singularities of quadratic [8, 7, 7] approximant
2
1.4504 - 0.5131 i
0.0952 + 0.179 i
3
1.7814
0.178
4
1.9213
0.326 i
5
2.58 + 1.0554 i
0.731 + 0.26 i
6
2.58 - 1.0554 i
0.731 - 0.26 i
7
3.3041
1.25
8
-3.3881 + 0.0631 i
0.011 + 0.00876 i
9
-3.3881 - 0.0631 i
0.011 - 0.00876 i
10
-3.8464 + 0.2088 i
0.00784 + 0.0208 i
11
-3.8464 - 0.2088 i
0.00784 - 0.0208 i
12
6.3258
0.325 i
13
-9.5311
0.0367
14
3.467 + 9.8249 i
0.123 + 0.0729 i
15
3.467 - 9.8249 i
0.123 - 0.0729 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
1.4512 + 0.5143 i
0.108 - 0.179 i
Singularities of quadratic [8, 8, 7] approximant
2
1.4512 - 0.5143 i
0.108 + 0.179 i
3
1.7376
0.15
4
1.8577
0.254 i
5
-0.1006 + 2.1594 i
0.000793 - 0.0000656 i
6
-0.1006 - 2.1594 i
0.000793 + 0.0000656 i
7
-0.101 + 2.1601 i
0.0000651 + 0.000792 i
8
-0.101 - 2.1601 i
0.0000651 - 0.000792 i
9
2.5688 + 1.1807 i
0.495 + 0.184 i
10
2.5688 - 1.1807 i
0.495 - 0.184 i
11
-3.3582
0.00572
12
4.3992
0.269
13
-4.8409
0.0062 i
14
6.6907
0.256 i
15
-4.4362 + 8.2838 i
0.0184 - 0.0218 i
16
-4.4362 - 8.2838 i
0.0184 + 0.0218 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
1.4508 + 0.5142 i
0.105 - 0.175 i
Singularities of quadratic [8, 8, 8] approximant
2
1.4508 - 0.5142 i
0.105 + 0.175 i
3
1.7446
0.16
4
1.8742
0.283 i
5
2.5061 + 1.1966 i
0.383 + 0.106 i
6
2.5061 - 1.1966 i
0.383 - 0.106 i
7
-3.1729
0.00436
8
-3.4157
0.00271 i
9
-3.6218 + 0.6216 i
0.00454 + 0.00178 i
10
-3.6218 - 0.6216 i
0.00454 - 0.00178 i
11
3.8347
0.433
12
-5.6673
0.00668
13
-0.4289 + 7.508 i
0.0148 + 0.0424 i
14
-0.4289 - 7.508 i
0.0148 - 0.0424 i
15
4.3044 + 10.7968 i
0.0905 + 0.0344 i
16
4.3044 - 10.7968 i
0.0905 - 0.0344 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
-0.6899 + 1.2136 i
0.0000314 - 0.0000198 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.6899 - 1.2136 i
0.0000314 + 0.0000198 i
3
-0.6899 + 1.2136 i
0.0000198 + 0.0000314 i
4
-0.6899 - 1.2136 i
0.0000198 - 0.0000314 i
5
1.451 + 0.5137 i
0.102 - 0.18 i
6
1.451 - 0.5137 i
0.102 + 0.18 i
7
1.7571
0.161
8
1.8846
0.281 i
9
2.5826 + 1.108 i
0.65 + 0.222 i
10
2.5826 - 1.108 i
0.65 - 0.222 i
11
-3.3602
0.00554
12
3.7372
0.547
13
-4.6626
0.0077 i
14
6.6423
0.282 i
15
-0.9913 + 12.7188 i
0.00771 - 0.077 i
16
-0.9913 - 12.7188 i
0.00771 + 0.077 i
17
-22.9674
12.6
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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
-0.3023
1.29e-9 + 1.29e-9 i
Singularities of quadratic [9, 9, 8] approximant
2
-0.3023
1.29e-9 - 1.29e-9 i
3
1.451 + 0.5138 i
0.104 - 0.181 i
4
1.451 - 0.5138 i
0.104 + 0.181 i
5
1.7508
0.156
6
1.8734
0.267 i
7
-1.6978 + 2.0331 i
0.000461 + 9.52e-6 i
8
-1.6978 - 2.0331 i
0.000461 - 9.52e-6 i
9
-1.6965 + 2.0375 i
0.0000102 - 0.000462 i
10
-1.6965 - 2.0375 i
0.0000102 + 0.000462 i
11
2.5736 + 1.126 i
0.626 + 0.173 i
12
2.5736 - 1.126 i
0.626 - 0.173 i
13
-3.3514
0.00591
14
4.0951
0.345
15
-5.1405
0.0051 i
16
6.5888
0.254 i
17
-3.1752 + 7.9992 i
0.00623 - 0.0222 i
18
-3.1752 - 7.9992 i
0.00623 + 0.0222 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
-0.5817 + 0.6691 i
2.75e-6 - 5.17e-7 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.5817 - 0.6691 i
2.75e-6 + 5.17e-7 i
3
-0.5817 + 0.6691 i
5.17e-7 + 2.75e-6 i
4
-0.5817 - 0.6691 i
5.17e-7 - 2.75e-6 i
5
1.4493 + 0.5147 i
0.0978 - 0.162 i
6
1.4493 - 0.5147 i
0.0978 + 0.162 i
7
1.7392
0.186
8
1.9064
0.414 i
9
2.2612 + 1.0648 i
0.158 - 0.188 i
10
2.2612 - 1.0648 i
0.158 + 0.188 i
11
2.6276 + 0.4991 i
0.151 + 0.418 i
12
2.6276 - 0.4991 i
0.151 - 0.418 i
13
-3.3673
0.00601
14
3.9014 + 2.5196 i
0.0134 - 0.146 i
15
3.9014 - 2.5196 i
0.0134 + 0.146 i
16
-4.7169
0.00673 i
17
-4.9907 + 10.0931 i
0.0209 - 0.0289 i
18
-4.9907 - 10.0931 i
0.0209 + 0.0289 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
-0.5838 + 0.6689 i
2.82e-6 - 5.82e-7 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.5838 - 0.6689 i
2.82e-6 + 5.82e-7 i
3
-0.5838 + 0.6689 i
5.82e-7 + 2.82e-6 i
4
-0.5838 - 0.6689 i
5.82e-7 - 2.82e-6 i
5
1.4493 + 0.5147 i
0.0976 - 0.162 i
6
1.4493 - 0.5147 i
0.0976 + 0.162 i
7
1.7385
0.186
8
1.9056
0.415 i
9
2.2612 + 1.0558 i
0.157 - 0.199 i
10
2.2612 - 1.0558 i
0.157 + 0.199 i
11
2.5956 + 0.4856 i
0.188 + 0.422 i
12
2.5956 - 0.4856 i
0.188 - 0.422 i
13
-3.3672
0.006
14
3.9195 + 2.4737 i
0.0112 - 0.152 i
15
3.9195 - 2.4737 i
0.0112 + 0.152 i
16
-4.7132
0.00677 i
17
-4.9602 + 10.2511 i
0.0211 - 0.03 i
18
-4.9602 - 10.2511 i
0.0211 + 0.03 i
19
-919.9734
0.205
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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
0.5322
4.57e-8
Singularities of quadratic [10, 10, 9] approximant
2
0.5322
4.57e-8 i
3
-0.5783 + 0.663 i
3.85e-7 + 5.41e-7 i
4
-0.5783 - 0.663 i
3.85e-7 - 5.41e-7 i
5
-0.5783 + 0.663 i
5.41e-7 - 3.85e-7 i
6
-0.5783 - 0.663 i
5.41e-7 + 3.85e-7 i
7
1.4485 + 0.5157 i
0.1 - 0.145 i
8
1.4485 - 0.5157 i
0.1 + 0.145 i
9
1.8106
0.294
10
2.1304 + 0.2729 i
0.99 + 0.0775 i
11
2.1304 - 0.2729 i
0.99 - 0.0775 i
12
2.4053 + 1.131 i
0.212 + 0.0096 i
13
2.4053 - 1.131 i
0.212 - 0.0096 i
14
3.2846
0.909 i
15
-3.3561
0.00519
16
-4.6316
0.00825 i
17
5.1097 + 3.8095 i
0.213 + 0.0283 i
18
5.1097 - 3.8095 i
0.213 - 0.0283 i
19
-7.5406 + 9.7736 i
0.0638 - 0.0184 i
20
-7.5406 - 9.7736 i
0.0638 + 0.0184 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
-0.0602
0
Singularities of quadratic [10, 10, 10] approximant
2
-0.0602
0
3
-0.5878 + 0.6722 i
6.05e-7 - 1.26e-7 i
4
-0.5878 - 0.6722 i
6.05e-7 + 1.26e-7 i
5
-0.5878 + 0.6722 i
1.26e-7 + 6.05e-7 i
6
-0.5878 - 0.6722 i
1.26e-7 - 6.05e-7 i
7
1.45 + 0.5144 i
0.1 - 0.173 i
8
1.45 - 0.5144 i
0.1 + 0.173 i
9
1.6975
0.135
10
1.8005
0.216 i
11
2.1872 + 1.0165 i
0.0105 - 0.274 i
12
2.1872 - 1.0165 i
0.0105 + 0.274 i
13
2.4868 + 0.6845 i
0.261 + 0.197 i
14
2.4868 - 0.6845 i
0.261 - 0.197 i
15
-3.3737
0.00657
16
3.5339 + 2.2339 i
0.0707 + 0.11 i
17
3.5339 - 2.2339 i
0.0707 - 0.11 i
18
-4.7611
0.00616 i
19
-4.1233 + 10.0214 i
0.0118 - 0.0275 i
20
-4.1233 - 10.0214 i
0.0118 + 0.0275 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
-0.4684
2.7e-10
Singularities of quadratic [11, 10, 10] approximant
2
-0.4684
2.7e-10 i
3
0.5897 + 0.e-5 i
3.01e-8 - 3.01e-8 i
4
0.5897 - 0.e-5 i
3.01e-8 + 3.01e-8 i
5
-0.6687 + 0.654 i
9.93e-8 - 2.4e-8 i
6
-0.6687 - 0.654 i
9.93e-8 + 2.4e-8 i
7
-0.6687 + 0.6541 i
2.4e-8 + 9.93e-8 i
8
-0.6687 - 0.6541 i
2.4e-8 - 9.93e-8 i
9
1.4479 + 0.5215 i
0.129 - 0.0881 i
10
1.4479 - 0.5215 i
0.129 + 0.0881 i
11
1.8988 + 0.598 i
0.279 + 0.206 i
12
1.8988 - 0.598 i
0.279 - 0.206 i
13
2.1058 + 0.3955 i
0.478 - 1.03 i
14
2.1058 - 0.3955 i
0.478 + 1.03 i
15
2.7458 + 1.5666 i
0.0163 - 0.0992 i
16
2.7458 - 1.5666 i
0.0163 + 0.0992 i
17
-3.4247
0.0155
18
-5.104
0.00398 i
19
-1.4536 + 8.9583 i
0.00826 + 0.0152 i
20
-1.4536 - 8.9583 i
0.00826 - 0.0152 i
21
116.7885
0.0962
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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
-0.6191 + 0.4357 i
2.97e-9 + 9.59e-9 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.6191 - 0.4357 i
2.97e-9 - 9.59e-9 i
3
-0.6191 + 0.4357 i
9.59e-9 - 2.97e-9 i
4
-0.6191 - 0.4357 i
9.59e-9 + 2.97e-9 i
5
1.19
0.000207
6
1.1902
0.000207 i
7
1.464 + 0.5208 i
0.52 - 0.0923 i
8
1.464 - 0.5208 i
0.52 + 0.0923 i
9
-0.7717 + 1.7407 i
6.16e-6 - 3.79e-6 i
10
-0.7717 - 1.7407 i
6.16e-6 + 3.79e-6 i
11
-0.7735 + 1.7401 i
3.77e-6 + 6.16e-6 i
12
-0.7735 - 1.7401 i
3.77e-6 - 6.16e-6 i
13
1.7644 + 0.948 i
0.0103 - 0.033 i
14
1.7644 - 0.948 i
0.0103 + 0.033 i
15
1.9571 + 0.9096 i
0.0245 + 0.0599 i
16
1.9571 - 0.9096 i
0.0245 - 0.0599 i
17
-3.0538
0.000402
18
2.6542 + 2.3103 i
0.0248 + 0.00248 i
19
2.6542 - 2.3103 i
0.0248 - 0.00248 i
20
-3.5608
0.00181 i
21
-7.3981 + 4.6053 i
0.00203 - 0.0092 i
22
-7.3981 - 4.6053 i
0.00203 + 0.0092 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
-0.7008 + 0.5277 i
4.65e-9 - 3.35e-8 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.7008 - 0.5277 i
4.65e-9 + 3.35e-8 i
3
-0.7008 + 0.5277 i
3.35e-8 + 4.65e-9 i
4
-0.7008 - 0.5277 i
3.35e-8 - 4.65e-9 i
5
-0.8904
1.9e-8
6
-0.8904
1.9e-8 i
7
0.5654 + 0.7842 i
1.75e-6 + 5.56e-7 i
8
0.5654 - 0.7842 i
1.75e-6 - 5.56e-7 i
9
0.5654 + 0.7842 i
5.56e-7 - 1.75e-6 i
10
0.5654 - 0.7842 i
5.56e-7 + 1.75e-6 i
11
1.4476 + 0.5133 i
0.0709 - 0.153 i
12
1.4476 - 0.5133 i
0.0709 + 0.153 i
13
1.7689
0.205
14
2.0758 + 0.2098 i
0.764 - 0.458 i
15
2.0758 - 0.2098 i
0.764 + 0.458 i
16
2.5211 + 1.3465 i
0.0738 + 0.0845 i
17
2.5211 - 1.3465 i
0.0738 - 0.0845 i
18
3.2404
2.5 i
19
-3.4672
0.044
20
-5.3018
0.00345 i
21
-0.0005 + 8.6225 i
0.0151 + 0.00937 i
22
-0.0005 - 8.6225 i
0.0151 - 0.00937 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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