Singularities of Møller-Plesset series: example "bh cc-pvqz 2re"

Molecule X 1^Sigma+ State of BH. Basis 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
1.1783 + 0.4516 i
0.0521 - 0.0814 i
Singularities of quadratic [5, 5, 4] approximant
2
1.1783 - 0.4516 i
0.0521 + 0.0814 i
3
1.2731
0.0499
4
1.3621
0.0714 i
5
-2.4979 + 0.4998 i
0.0695 - 0.33 i
6
-2.4979 - 0.4998 i
0.0695 + 0.33 i
7
3.2274
1.35
8
-5.9464
0.181
9
6.5923
0.906 i
10
-261.9871
1.6 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
1.1796 + 0.4513 i
0.0527 - 0.086 i
Singularities of quadratic [5, 5, 5] approximant
2
1.1796 - 0.4513 i
0.0527 + 0.086 i
3
1.2905
0.0589
4
1.3986
0.0918 i
5
-2.5154 + 0.5455 i
0.0576 + 0.331 i
6
-2.5154 - 0.5455 i
0.0576 - 0.331 i
7
3.4429 + 1.1421 i
0.0167 - 0.876 i
8
3.4429 - 1.1421 i
0.0167 + 0.876 i
9
-6.0682
0.244
10
11.5789
0.923
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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
1.1898 + 0.4487 i
0.0552 - 0.114 i
Singularities of quadratic [6, 5, 5] approximant
2
1.1898 - 0.4487 i
0.0552 + 0.114 i
3
1.3824
0.108
4
1.5681
0.255 i
5
-2.5265 + 0.696 i
0.188 + 0.0992 i
6
-2.5265 - 0.696 i
0.188 - 0.0992 i
7
2.5433 + 1.6185 i
0.0761 + 0.245 i
8
2.5433 - 1.6185 i
0.0761 - 0.245 i
9
-5.9915 + 1.7529 i
0.299 + 0.394 i
10
-5.9915 - 1.7529 i
0.299 - 0.394 i
11
10.9231
0.321
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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
1.2053 + 0.4441 i
0.0463 - 0.182 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2053 - 0.4441 i
0.0463 + 0.182 i
3
1.5671
0.281
4
1.6059 + 0.573 i
0.221 + 0.107 i
5
1.6059 - 0.573 i
0.221 - 0.107 i
6
1.7982 + 0.8911 i
0.265 - 0.0843 i
7
1.7982 - 0.8911 i
0.265 + 0.0843 i
8
-2.5376 + 0.6034 i
0.196 + 0.256 i
9
-2.5376 - 0.6034 i
0.196 - 0.256 i
10
-5.7653
0.287
11
29.2217
0.353 i
12
-110.0327
0.65 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
1.2491 + 0.0271 i
0.0626 - 0.0427 i
Singularities of quadratic [6, 6, 6] approximant
2
1.2491 - 0.0271 i
0.0626 + 0.0427 i
3
1.1829 + 0.4562 i
0.0516 - 0.0885 i
4
1.1829 - 0.4562 i
0.0516 + 0.0885 i
5
1.4361
0.506
6
2.1816 + 0.3841 i
0.427 - 0.33 i
7
2.1816 - 0.3841 i
0.427 + 0.33 i
8
2.0549 + 1.3166 i
0.12 + 0.145 i
9
2.0549 - 1.3166 i
0.12 - 0.145 i
10
-2.5339 + 0.6026 i
0.177 + 0.253 i
11
-2.5339 - 0.6026 i
0.177 - 0.253 i
12
-6.3062
0.362
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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
1.2177 + 0.4507 i
0.0994 - 0.254 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2177 - 0.4507 i
0.0994 + 0.254 i
3
1.416 + 0.4735 i
0.338 + 0.109 i
4
1.416 - 0.4735 i
0.338 - 0.109 i
5
1.5987 + 0.4403 i
31.3 + 253. i
6
1.5987 - 0.4403 i
31.3 - 253. i
7
2.1788
0.419
8
-2.5358 + 0.617 i
0.199 + 0.226 i
9
-2.5358 - 0.617 i
0.199 - 0.226 i
10
5.6584
2.36 i
11
-5.9326
0.387
12
-18.2606
0.612 i
13
19.3361
1.31
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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
-1.0817
0.000465
Singularities of quadratic [7, 7, 6] approximant
2
-1.0817
0.000465 i
3
1.2057 + 0.4603 i
0.119 - 0.13 i
4
1.2057 - 0.4603 i
0.119 + 0.13 i
5
1.625
0.215
6
1.618 + 0.3748 i
0.311 - 0.0556 i
7
1.618 - 0.3748 i
0.311 + 0.0556 i
8
1.8834 + 0.6603 i
0.855 - 0.257 i
9
1.8834 - 0.6603 i
0.855 + 0.257 i
10
-2.5556 + 0.6183 i
0.294 + 0.231 i
11
-2.5556 - 0.6183 i
0.294 - 0.231 i
12
-5.0697
0.227
13
16.6234
0.309 i
14
-46.9239
0.425 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
0.7582 + 0.e-5 i
0.000188 - 0.000188 i
Singularities of quadratic [7, 7, 7] approximant
2
0.7582 - 0.e-5 i
0.000188 + 0.000188 i
3
1.2054 + 0.468 i
0.157 - 0.0823 i
4
1.2054 - 0.468 i
0.157 + 0.0823 i
5
1.4161
0.0574
6
1.5137
0.0858 i
7
2.174
30.9
8
1.9994 + 0.9402 i
0.304 - 0.0591 i
9
1.9994 - 0.9402 i
0.304 + 0.0591 i
10
-2.54 + 0.6479 i
0.244 + 0.139 i
11
-2.54 - 0.6479 i
0.244 - 0.139 i
12
-3.737
0.347
13
-4.466
0.51 i
14
-10.0263
3.13
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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
1.2072 + 0.458 i
0.11 - 0.155 i
Singularities of quadratic [8, 7, 7] approximant
2
1.2072 - 0.458 i
0.11 + 0.155 i
3
1.5362 + 0.3981 i
0.305 + 0.0619 i
4
1.5362 - 0.3981 i
0.305 - 0.0619 i
5
1.6265 + 0.3595 i
0.456 + 0.723 i
6
1.6265 - 0.3595 i
0.456 - 0.723 i
7
-2.5036 + 0.6213 i
0.146 + 0.203 i
8
-2.5036 - 0.6213 i
0.146 - 0.203 i
9
2.7982 + 0.5654 i
0.68 + 0.336 i
10
2.7982 - 0.5654 i
0.68 - 0.336 i
11
-2.989 + 0.078 i
0.463 - 0.619 i
12
-2.989 - 0.078 i
0.463 + 0.619 i
13
5.4652
0.534
14
-6.1586
0.28
15
69.6822
0.475 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
1.2062 + 0.4587 i
0.111 - 0.144 i
Singularities of quadratic [8, 8, 7] approximant
2
1.2062 - 0.4587 i
0.111 + 0.144 i
3
1.5715 + 0.3939 i
0.327 + 0.00175 i
4
1.5715 - 0.3939 i
0.327 - 0.00175 i
5
1.8083 + 0.4386 i
0.224 - 1.69 i
6
1.8083 - 0.4386 i
0.224 + 1.69 i
7
1.9105
0.306
8
-2.5178 + 0.6412 i
0.179 + 0.168 i
9
-2.5178 - 0.6412 i
0.179 - 0.168 i
10
-4.0611
0.571
11
-5.0644
0.445 i
12
-3.9237 + 4.2618 i
0.00616 - 0.154 i
13
-3.9237 - 4.2618 i
0.00616 + 0.154 i
14
8.4365
0.352 i
15
-4.3677 + 8.5412 i
0.152 + 0.0112 i
16
-4.3677 - 8.5412 i
0.152 - 0.0112 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
1.2058 + 0.4575 i
0.101 - 0.148 i
Singularities of quadratic [8, 8, 8] approximant
2
1.2058 - 0.4575 i
0.101 + 0.148 i
3
1.5996 + 0.4117 i
0.362 - 0.018 i
4
1.5996 - 0.4117 i
0.362 + 0.018 i
5
1.7051 + 0.5271 i
5.27 - 53. i
6
1.7051 - 0.5271 i
5.27 + 53. i
7
1.8271
0.342
8
-2.5088 + 0.6382 i
0.171 + 0.164 i
9
-2.5088 - 0.6382 i
0.171 - 0.164 i
10
2.3102 + 1.7062 i
0.049 + 0.169 i
11
2.3102 - 1.7062 i
0.049 - 0.169 i
12
2.671 + 1.5788 i
0.191 - 0.0241 i
13
2.671 - 1.5788 i
0.191 + 0.0241 i
14
-3.1222 + 0.0736 i
0.7 - 0.65 i
15
-3.1222 - 0.0736 i
0.7 + 0.65 i
16
-6.9873
0.447
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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
1.2065 + 0.4565 i
0.0963 - 0.158 i
Singularities of quadratic [9, 8, 8] approximant
2
1.2065 - 0.4565 i
0.0963 + 0.158 i
3
1.5871 + 0.379 i
0.361 + 0.198 i
4
1.5871 - 0.379 i
0.361 - 0.198 i
5
1.5852 + 0.4482 i
0.505 - 0.0411 i
6
1.5852 - 0.4482 i
0.505 + 0.0411 i
7
2.3584
0.806
8
-2.5076 + 0.6471 i
0.174 + 0.137 i
9
-2.5076 - 0.6471 i
0.174 - 0.137 i
10
-3.0178 + 0.0275 i
0.805 + 0.167 i
11
-3.0178 - 0.0275 i
0.805 - 0.167 i
12
2.6262 + 1.8299 i
0.0228 + 0.172 i
13
2.6262 - 1.8299 i
0.0228 - 0.172 i
14
3.0945 + 2.0111 i
0.171 + 0.0159 i
15
3.0945 - 2.0111 i
0.171 - 0.0159 i
16
-7.7169
0.788
17
-45.9896
0.5 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
1.2065 + 0.4564 i
0.0952 - 0.159 i
Singularities of quadratic [9, 9, 8] approximant
2
1.2065 - 0.4564 i
0.0952 + 0.159 i
3
1.5773 + 0.3805 i
0.328 + 0.213 i
4
1.5773 - 0.3805 i
0.328 - 0.213 i
5
1.5822 + 0.4408 i
0.483 - 0.0685 i
6
1.5822 - 0.4408 i
0.483 + 0.0685 i
7
2.4639
0.81
8
-2.5004 + 0.6537 i
0.16 + 0.112 i
9
-2.5004 - 0.6537 i
0.16 - 0.112 i
10
-2.7756
0.327
11
-2.8371
0.813 i
12
2.6268 + 2.7387 i
0.0564 - 0.0822 i
13
2.6268 - 2.7387 i
0.0564 + 0.0822 i
14
2.4721 + 3.1284 i
0.0727 + 0.0534 i
15
2.4721 - 3.1284 i
0.0727 - 0.0534 i
16
-7.7194
1.21
17
-28.595
0.418 i
18
99.7943
0.572 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
1.2061 + 0.4568 i
0.0984 - 0.152 i
Singularities of quadratic [9, 9, 9] approximant
2
1.2061 - 0.4568 i
0.0984 + 0.152 i
3
1.5715 + 0.5034 i
0.647 + 0.0737 i
4
1.5715 - 0.5034 i
0.647 - 0.0737 i
5
1.6057 + 0.4611 i
0.836 + 0.129 i
6
1.6057 - 0.4611 i
0.836 - 0.129 i
7
1.6983
0.229
8
1.7743
0.412 i
9
-2.5107 + 0.6384 i
0.171 + 0.17 i
10
-2.5107 - 0.6384 i
0.171 - 0.17 i
11
2.7015 + 0.9967 i
0.313 + 0.359 i
12
2.7015 - 0.9967 i
0.313 - 0.359 i
13
-3.406 + 0.117 i
0.317 - 0.801 i
14
-3.406 - 0.117 i
0.317 + 0.801 i
15
5.0594
0.396
16
-6.4642 + 1.9985 i
0.389 - 0.256 i
17
-6.4642 - 1.9985 i
0.389 + 0.256 i
18
-7.6158
0.62
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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
1.0919
0.0123
Singularities of quadratic [10, 9, 9] approximant
2
1.092
0.0123 i
3
1.2061 + 0.4561 i
0.0906 - 0.155 i
4
1.2061 - 0.4561 i
0.0906 + 0.155 i
5
1.5529 + 0.3905 i
0.342 + 0.326 i
6
1.5529 - 0.3905 i
0.342 - 0.326 i
7
1.5557 + 0.4495 i
0.469 + 0.0553 i
8
1.5557 - 0.4495 i
0.469 - 0.0553 i
9
-2.5084 + 0.6448 i
0.174 + 0.145 i
10
-2.5084 - 0.6448 i
0.174 - 0.145 i
11
2.6883
1.11
12
-3.0867 + 0.0402 i
1.04 - 0.121 i
13
-3.0867 - 0.0402 i
1.04 + 0.121 i
14
3.4147 + 2.0503 i
0.133 - 0.2 i
15
3.4147 - 2.0503 i
0.133 + 0.2 i
16
3.6856 + 2.96 i
0.145 + 0.119 i
17
3.6856 - 2.96 i
0.145 - 0.119 i
18
-7.9249
0.859
19
-35.9386
0.552 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
-0.5583
7.09e-7 + 7.09e-7 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.5583
7.09e-7 - 7.09e-7 i
3
1.2055 + 0.4568 i
0.0953 - 0.145 i
4
1.2055 - 0.4568 i
0.0953 + 0.145 i
5
1.3435
0.0291
6
1.3452
0.0294 i
7
1.5181 + 0.4598 i
0.359 + 0.206 i
8
1.5181 - 0.4598 i
0.359 - 0.206 i
9
1.5451 + 0.4548 i
0.487 - 0.685 i
10
1.5451 - 0.4548 i
0.487 + 0.685 i
11
-2.5107 + 0.6419 i
0.179 + 0.157 i
12
-2.5107 - 0.6419 i
0.179 - 0.157 i
13
2.934 + 0.6965 i
0.581 + 0.558 i
14
2.934 - 0.6965 i
0.581 - 0.558 i
15
-3.1689 + 0.0717 i
0.793 - 0.638 i
16
-3.1689 - 0.0717 i
0.793 + 0.638 i
17
7.0928
0.603
18
-7.6542
0.548
19
-42.5256
1.11 i
20
63.0699
1.33 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
-0.6933
6.29e-6 + 6.29e-6 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.6933
6.29e-6 - 6.29e-6 i
3
1.2056 + 0.4568 i
0.0965 - 0.147 i
4
1.2056 - 0.4568 i
0.0965 + 0.147 i
5
1.4283
0.0618
6
1.4348
0.065 i
7
1.5264 + 0.4749 i
0.41 + 0.163 i
8
1.5264 - 0.4749 i
0.41 - 0.163 i
9
1.5456 + 0.4621 i
0.111 - 0.844 i
10
1.5456 - 0.4621 i
0.111 + 0.844 i
11
-2.5109 + 0.6391 i
0.175 + 0.167 i
12
-2.5109 - 0.6391 i
0.175 - 0.167 i
13
2.8717 + 0.7731 i
0.488 + 0.513 i
14
2.8717 - 0.7731 i
0.488 - 0.513 i
15
-3.2872 + 0.096 i
0.475 - 0.789 i
16
-3.2872 - 0.096 i
0.475 + 0.789 i
17
6.2473
0.525
18
-9.4983 + 1.025 i
0.755 + 0.169 i
19
-9.4983 - 1.025 i
0.755 - 0.169 i
20
-21.1678
0.507
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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
-0.6308
9.09e-7 + 9.09e-7 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.6308
9.09e-7 - 9.09e-7 i
3
1.2421 + 0.0005 i
0.0113 - 0.0112 i
4
1.2421 - 0.0005 i
0.0113 + 0.0112 i
5
1.2051 + 0.4569 i
0.0939 - 0.14 i
6
1.2051 - 0.4569 i
0.0939 + 0.14 i
7
1.5003 + 0.4519 i
0.39 + 0.239 i
8
1.5003 - 0.4519 i
0.39 - 0.239 i
9
1.5505 + 0.4529 i
1.24 - 0.666 i
10
1.5505 - 0.4529 i
1.24 + 0.666 i
11
-2.5124 + 0.6436 i
0.191 + 0.15 i
12
-2.5124 - 0.6436 i
0.191 - 0.15 i
13
2.8681 + 0.659 i
0.66 + 0.38 i
14
2.8681 - 0.659 i
0.66 - 0.38 i
15
-3.0857 + 0.0728 i
0.757 - 0.469 i
16
-3.0857 - 0.0728 i
0.757 + 0.469 i
17
6.0643
0.444
18
-6.7143
0.326
19
-6.1044 + 16.6026 i
0.0124 + 0.528 i
20
-6.1044 - 16.6026 i
0.0124 - 0.528 i
21
-27.0367
1.54 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
0.0367
0
Singularities of quadratic [11, 11, 10] approximant
2
0.0367
0
3
-0.6371
1.74e-6
4
-0.6371
1.74e-6 i
5
1.2047 + 0.0003 i
0.00708 - 0.00706 i
6
1.2047 - 0.0003 i
0.00708 + 0.00706 i
7
1.2051 + 0.457 i
0.0942 - 0.14 i
8
1.2051 - 0.457 i
0.0942 + 0.14 i
9
1.5028 + 0.4511 i
0.369 + 0.231 i
10
1.5028 - 0.4511 i
0.369 - 0.231 i
11
1.5489 + 0.4485 i
0.969 - 0.73 i
12
1.5489 - 0.4485 i
0.969 + 0.73 i
13
-2.5098 + 0.6408 i
0.173 + 0.16 i
14
-2.5098 - 0.6408 i
0.173 - 0.16 i
15
2.9211 + 0.6626 i
0.635 + 0.487 i
16
2.9211 - 0.6626 i
0.635 - 0.487 i
17
-3.2165 + 0.0738 i
0.756 - 0.746 i
18
-3.2165 - 0.0738 i
0.756 + 0.746 i
19
6.9904
0.567
20
-7.8574
0.613
21
-37.4152
1.11 i
22
70.0859
1.42 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
-0.5018 + 0.1404 i
8.33e-9 + 6.2e-8 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.5018 - 0.1404 i
8.33e-9 - 6.2e-8 i
3
-0.5018 + 0.1404 i
6.2e-8 - 8.33e-9 i
4
-0.5018 - 0.1404 i
6.2e-8 + 8.33e-9 i
5
1.0081 + 0.e-4 i
0.00081 - 0.00081 i
6
1.0081 - 0.e-4 i
0.00081 + 0.00081 i
7
1.2047 + 0.4566 i
0.0875 - 0.138 i
8
1.2047 - 0.4566 i
0.0875 + 0.138 i
9
1.5007 + 0.4347 i
0.353 + 0.22 i
10
1.5007 - 0.4347 i
0.353 - 0.22 i
11
1.5583 + 0.4398 i
1.03 - 0.606 i
12
1.5583 - 0.4398 i
1.03 + 0.606 i
13
-2.5083 + 0.6423 i
0.169 + 0.153 i
14
-2.5083 - 0.6423 i
0.169 - 0.153 i
15
2.9781 + 0.5407 i
0.81 + 0.399 i
16
2.9781 - 0.5407 i
0.81 - 0.399 i
17
-3.1757 + 0.0562 i
1.02 - 0.586 i
18
-3.1757 - 0.0562 i
1.02 + 0.586 i
19
-7.6657
0.644
20
9.4072 + 2.2769 i
0.784 - 0.0716 i
21
9.4072 - 2.2769 i
0.784 + 0.0716 i
22
35.2436
0.365
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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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