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

Molecule X 1^Sigma+ State of BH. Basis CC-PVTZ. 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
1.3988 + 0.0332 i
0.0396 - 0.0368 i
Singularities of quadratic [5, 5, 4] approximant
2
1.3988 - 0.0332 i
0.0396 + 0.0368 i
3
1.6944 + 0.4471 i
0.0632 + 0.341 i
4
1.6944 - 0.4471 i
0.0632 - 0.341 i
5
2.193
1.23
6
-3.8032 + 0.0754 i
0.104 + 0.0985 i
7
-3.8032 - 0.0754 i
0.104 - 0.0985 i
8
-9.5739
1.18
9
-17.2736
1.07 i
10
33.7075
1.25 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
1.4094 + 0.037 i
0.0419 - 0.0382 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4094 - 0.037 i
0.0419 + 0.0382 i
3
1.7019 + 0.452 i
0.0277 + 0.345 i
4
1.7019 - 0.452 i
0.0277 - 0.345 i
5
2.1754
1.23
6
-3.8418 + 0.0998 i
0.0778 + 0.0725 i
7
-3.8418 - 0.0998 i
0.0778 - 0.0725 i
8
-10.5165 + 2.8855 i
0.378 + 0.91 i
9
-10.5165 - 2.8855 i
0.378 - 0.91 i
10
71.5882
0.386 i
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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
1.4256 + 0.051 i
0.0384 - 0.0308 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4256 - 0.051 i
0.0384 + 0.0308 i
3
1.743 + 0.4829 i
0.177 - 0.256 i
4
1.743 - 0.4829 i
0.177 + 0.256 i
5
1.9998
0.784
6
-3.3459 + 0.2289 i
0.00301 + 0.00388 i
7
-3.3459 - 0.2289 i
0.00301 - 0.00388 i
8
-4.201
0.00687
9
-1.0487 + 10.4445 i
0.14 + 0.0835 i
10
-1.0487 - 10.4445 i
0.14 - 0.0835 i
11
-13.0021
0.111 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
1.4451 + 0.0724 i
0.0397 - 0.0284 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4451 - 0.0724 i
0.0397 + 0.0284 i
3
1.7223 + 0.5549 i
0.103 - 0.116 i
4
1.7223 - 0.5549 i
0.103 + 0.116 i
5
1.8199
0.574
6
2.7438
0.589 i
7
3.6133
1.39
8
-3.6954 + 0.2236 i
0.015 + 0.0146 i
9
-3.6954 - 0.2236 i
0.015 - 0.0146 i
10
-6.9129
0.0876
11
18.0988
3.02 i
12
-27.2941
1.31 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
0.3947 + 0.e-5 i
2.03e-7 - 2.03e-7 i
Singularities of quadratic [6, 6, 6] approximant
2
0.3947 - 0.e-5 i
2.03e-7 + 2.03e-7 i
3
1.1884 + 0.0074 i
0.000656 - 0.000634 i
4
1.1884 - 0.0074 i
0.000656 + 0.000634 i
5
1.4094
0.0111
6
1.6954 + 0.6836 i
0.0401 - 0.00458 i
7
1.6954 - 0.6836 i
0.0401 + 0.00458 i
8
2.8647
0.486 i
9
-3.4469
0.00857
10
-4.4119
0.0123 i
11
5.0293
1.13
12
-14.548
0.217
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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
1.352 + 0.1442 i
0.0395 + 0.0209 i
Singularities of quadratic [7, 6, 6] approximant
2
1.352 - 0.1442 i
0.0395 - 0.0209 i
3
1.3698 + 0.1201 i
0.0222 - 0.0366 i
4
1.3698 - 0.1201 i
0.0222 + 0.0366 i
5
1.7021 + 0.4562 i
0.0394 - 0.36 i
6
1.7021 - 0.4562 i
0.0394 + 0.36 i
7
2.0811
0.765
8
-3.6231 + 0.2205 i
0.0111 + 0.0122 i
9
-3.6231 - 0.2205 i
0.0111 - 0.0122 i
10
-5.7083
0.0365
11
0.2127 + 13.7937 i
0.236 + 0.213 i
12
0.2127 - 13.7937 i
0.236 - 0.213 i
13
-42.5007
1.75 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
1.4598
0.0372
Singularities of quadratic [7, 7, 6] approximant
2
1.4202 + 0.3677 i
0.0121 + 0.00398 i
3
1.4202 - 0.3677 i
0.0121 - 0.00398 i
4
1.4087 + 0.4323 i
0.00605 - 0.0106 i
5
1.4087 - 0.4323 i
0.00605 + 0.0106 i
6
1.9186 + 0.6392 i
0.0494 + 0.101 i
7
1.9186 - 0.6392 i
0.0494 - 0.101 i
8
-3.3971
0.00718
9
-4.5308
0.00876 i
10
-5.8864 + 4.9359 i
0.00094 - 0.0268 i
11
-5.8864 - 4.9359 i
0.00094 + 0.0268 i
12
-3.9501 + 7.5184 i
0.0317 - 0.021 i
13
-3.9501 - 7.5184 i
0.0317 + 0.021 i
14
14.6777
11.1 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
1.4623
0.0377
Singularities of quadratic [7, 7, 7] approximant
2
1.4179 + 0.3577 i
0.0129 + 0.00304 i
3
1.4179 - 0.3577 i
0.0129 - 0.00304 i
4
1.4122 + 0.4236 i
0.00555 - 0.0118 i
5
1.4122 - 0.4236 i
0.00555 + 0.0118 i
6
1.9195 + 0.6244 i
0.057 + 0.107 i
7
1.9195 - 0.6244 i
0.057 - 0.107 i
8
-3.4047
0.00756
9
-4.4741
0.00912 i
10
-6.0843 + 5.144 i
0.000206 + 0.0303 i
11
-6.0843 - 5.144 i
0.000206 - 0.0303 i
12
-3.6867 + 7.576 i
0.0317 - 0.0244 i
13
-3.6867 - 7.576 i
0.0317 + 0.0244 i
14
16.2854
58.3 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
1.4138 + 0.3271 i
0.0153 + 0.000125 i
Singularities of quadratic [8, 7, 7] approximant
2
1.4138 - 0.3271 i
0.0153 - 0.000125 i
3
1.4696
0.0375
4
1.4294 + 0.3976 i
0.00416 - 0.0162 i
5
1.4294 - 0.3976 i
0.00416 + 0.0162 i
6
1.9296 + 0.5613 i
0.0931 + 0.152 i
7
1.9296 - 0.5613 i
0.0931 - 0.152 i
8
-2.395
0.000226
9
-2.4119
0.000223 i
10
-3.2741 + 0.5907 i
0.00164 + 0.000632 i
11
-3.2741 - 0.5907 i
0.00164 - 0.000632 i
12
-4.3174
0.00353
13
0.9733 + 18.7005 i
0.488 + 0.721 i
14
0.9733 - 18.7005 i
0.488 - 0.721 i
15
-60.7361
10.1 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
1.4141 + 0.3222 i
0.0158 - 0.000364 i
Singularities of quadratic [8, 8, 7] approximant
2
1.4141 - 0.3222 i
0.0158 + 0.000364 i
3
1.4713
0.0375
4
1.4336 + 0.3938 i
0.00398 - 0.0171 i
5
1.4336 - 0.3938 i
0.00398 + 0.0171 i
6
1.9332 + 0.5477 i
0.1 + 0.166 i
7
1.9332 - 0.5477 i
0.1 - 0.166 i
8
-3.1361
0.0016
9
-3.067 + 1.285 i
0.000458 - 0.00109 i
10
-3.067 - 1.285 i
0.000458 + 0.00109 i
11
-3.228 + 1.3525 i
0.0011 + 0.000637 i
12
-3.228 - 1.3525 i
0.0011 - 0.000637 i
13
6.215 + 12.5205 i
0.625 - 0.252 i
14
6.215 - 12.5205 i
0.625 + 0.252 i
15
-16.0276
0.704 i
16
43.264
0.544 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
-0.1823
0
Singularities of quadratic [8, 8, 8] approximant
2
-0.1823
0
3
1.4255 + 0.3225 i
0.0185 - 0.00448 i
4
1.4255 - 0.3225 i
0.0185 + 0.00448 i
5
1.429 + 0.3953 i
0.000514 + 0.0182 i
6
1.429 - 0.3953 i
0.000514 - 0.0182 i
7
1.4909
0.058
8
1.9156 + 0.599 i
0.0642 + 0.103 i
9
1.9156 - 0.599 i
0.0642 - 0.103 i
10
-3.3172
0.00404
11
-0.8161 + 4.002 i
0.00149 + 0.00348 i
12
-0.8161 - 4.002 i
0.00149 - 0.00348 i
13
-0.9386 + 4.1279 i
0.00367 - 0.00122 i
14
-0.9386 - 4.1279 i
0.00367 + 0.00122 i
15
-5.2611
0.00952 i
16
47.8115
0.225 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
-0.8448 + 0.e-5 i
6.59e-7 + 6.59e-7 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.8448 - 0.e-5 i
6.59e-7 - 6.59e-7 i
3
0.893
0.0000236
4
0.893
0.0000236 i
5
1.422
0.014
6
1.3912 + 0.3428 i
0.00719 + 0.00465 i
7
1.3912 - 0.3428 i
0.00719 - 0.00465 i
8
1.428 + 0.4078 i
0.00907 - 0.00784 i
9
1.428 - 0.4078 i
0.00907 + 0.00784 i
10
1.9337 + 0.4895 i
0.22 + 0.296 i
11
1.9337 - 0.4895 i
0.22 - 0.296 i
12
-3.4108
0.00745
13
-4.3088
0.012 i
14
-8.4517
334.
15
2.8985 + 10.8426 i
0.158 + 0.125 i
16
2.8985 - 10.8426 i
0.158 - 0.125 i
17
18.1275
0.791 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
-1.1071 + 0.6289 i
1.39e-6 + 3.24e-6 i
Singularities of quadratic [9, 9, 8] approximant
2
-1.1071 - 0.6289 i
1.39e-6 - 3.24e-6 i
3
-1.1071 + 0.6289 i
3.24e-6 - 1.39e-6 i
4
-1.1071 - 0.6289 i
3.24e-6 + 1.39e-6 i
5
1.4286
0.00579
6
1.4093 + 0.2626 i
0.00984 - 0.00359 i
7
1.4093 - 0.2626 i
0.00984 + 0.00359 i
8
1.4753
0.00852 i
9
1.5035 + 0.4276 i
0.0138 - 0.015 i
10
1.5035 - 0.4276 i
0.0138 + 0.015 i
11
2.3961 + 0.8888 i
0.102 + 0.0617 i
12
2.3961 - 0.8888 i
0.102 - 0.0617 i
13
-3.3431
0.00406
14
3.5638
47.2
15
-4.293
0.0196 i
16
-6.1181
0.0404
17
9.6095
1.67 i
18
-16.0901
4. 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
-0.7785 + 0.1516 i
1.59e-8 - 6.74e-8 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.7785 - 0.1516 i
1.59e-8 + 6.74e-8 i
3
-0.7785 + 0.1516 i
6.74e-8 + 1.59e-8 i
4
-0.7785 - 0.1516 i
6.74e-8 - 1.59e-8 i
5
1.3447 + 0.0052 i
0.000785 - 0.000737 i
6
1.3447 - 0.0052 i
0.000785 + 0.000737 i
7
1.4035 + 0.2471 i
0.00547 - 0.0048 i
8
1.4035 - 0.2471 i
0.00547 + 0.0048 i
9
1.4879 + 0.4423 i
0.00957 - 0.0101 i
10
1.4879 - 0.4423 i
0.00957 + 0.0101 i
11
2.2782 + 0.9288 i
0.0711 + 0.0317 i
12
2.2782 - 0.9288 i
0.0711 - 0.0317 i
13
2.9938
1.52
14
-3.4217 + 0.3148 i
0.000311 + 0.00519 i
15
-3.4217 - 0.3148 i
0.000311 - 0.00519 i
16
-4.1569
0.00415
17
-9.0945
0.0615 i
18
14.0451
62.1 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
-0.8299 + 0.5408 i
1.01e-6 + 1.7e-6 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.8299 - 0.5408 i
1.01e-6 - 1.7e-6 i
3
-0.8299 + 0.5408 i
1.7e-6 - 1.01e-6 i
4
-0.8299 - 0.5408 i
1.7e-6 + 1.01e-6 i
5
1.4085 + 0.1273 i
0.0138 - 0.0149 i
6
1.4085 - 0.1273 i
0.0138 + 0.0149 i
7
1.5235
0.0327
8
1.4881 + 0.361 i
0.00517 + 0.025 i
9
1.4881 - 0.361 i
0.00517 - 0.025 i
10
1.4862 + 0.4577 i
0.0316 + 0.00388 i
11
1.4862 - 0.4577 i
0.0316 - 0.00388 i
12
1.9641 + 0.5517 i
0.172 + 0.254 i
13
1.9641 - 0.5517 i
0.172 - 0.254 i
14
-3.362
0.00525
15
-4.5631
0.0104 i
16
-10.0554
0.81
17
4.1437 + 10.0464 i
0.181 + 0.0956 i
18
4.1437 - 10.0464 i
0.181 - 0.0956 i
19
11.749
0.609 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
-0.5035 + 0.6304 i
2.67e-9 + 6.02e-8 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.5035 - 0.6304 i
2.67e-9 - 6.02e-8 i
3
-0.5035 + 0.6304 i
6.02e-8 - 2.67e-9 i
4
-0.5035 - 0.6304 i
6.02e-8 + 2.67e-9 i
5
1.424 + 0.1942 i
0.0128 + 0.0108 i
6
1.424 - 0.1942 i
0.0128 - 0.0108 i
7
1.4779 + 0.3958 i
0.0128 + 0.013 i
8
1.4779 - 0.3958 i
0.0128 - 0.013 i
9
-1.5845 + 0.0003 i
2.3e-6 + 2.3e-6 i
10
-1.5845 - 0.0003 i
2.3e-6 - 2.3e-6 i
11
1.8012 + 0.4758 i
0.0107 - 0.0623 i
12
1.8012 - 0.4758 i
0.0107 + 0.0623 i
13
1.9548 + 0.8386 i
0.00137 + 0.0345 i
14
1.9548 - 0.8386 i
0.00137 - 0.0345 i
15
2.1995
0.801
16
-3.0625 + 0.2272 i
0.00104 - 0.000188 i
17
-3.0625 - 0.2272 i
0.00104 + 0.000188 i
18
-3.2815
0.00334
19
-9.5393
0.0682 i
20
10.3099
1.71 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
-0.0705
0
Singularities of quadratic [10, 10, 10] approximant
2
-0.0705
0
3
-0.5048 + 0.8401 i
2.59e-8 + 2.57e-8 i
4
-0.5048 - 0.8401 i
2.59e-8 - 2.57e-8 i
5
-0.5048 + 0.8401 i
2.57e-8 - 2.59e-8 i
6
-0.5048 - 0.8401 i
2.57e-8 + 2.59e-8 i
7
1.4012 + 0.2111 i
0.00252 + 0.00641 i
8
1.4012 - 0.2111 i
0.00252 - 0.00641 i
9
1.4566 + 0.4322 i
0.000685 - 0.00723 i
10
1.4566 - 0.4322 i
0.000685 + 0.00723 i
11
-1.3792 + 1.5141 i
4.38e-6 - 1.89e-6 i
12
-1.3792 - 1.5141 i
4.38e-6 + 1.89e-6 i
13
-1.3885 + 1.5077 i
1.79e-6 + 4.41e-6 i
14
-1.3885 - 1.5077 i
1.79e-6 - 4.41e-6 i
15
2.4711 + 1.2308 i
0.0153 - 0.0303 i
16
2.4711 - 1.2308 i
0.0153 + 0.0303 i
17
-2.8734
0.000145
18
-3.4321
0.000734 i
19
5.9889
0.547
20
-7.3716
0.0248
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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
0.0254 + 0.9063 i
2.85e-8 - 6.23e-8 i
Singularities of quadratic [11, 10, 10] approximant
2
0.0254 - 0.9063 i
2.85e-8 + 6.23e-8 i
3
0.0254 + 0.9063 i
6.23e-8 + 2.85e-8 i
4
0.0254 - 0.9063 i
6.23e-8 - 2.85e-8 i
5
-0.9048 + 0.683 i
1.28e-7 + 1.03e-7 i
6
-0.9048 - 0.683 i
1.28e-7 - 1.03e-7 i
7
-0.9049 + 0.683 i
1.03e-7 - 1.28e-7 i
8
-0.9049 - 0.683 i
1.03e-7 + 1.28e-7 i
9
1.4039 + 0.21 i
0.00305 + 0.00681 i
10
1.4039 - 0.21 i
0.00305 - 0.00681 i
11
1.455 + 0.4279 i
0.000129 + 0.00739 i
12
1.455 - 0.4279 i
0.000129 - 0.00739 i
13
2.4136 + 1.2333 i
0.0094 - 0.0243 i
14
2.4136 - 1.2333 i
0.0094 + 0.0243 i
15
-3.4264
0.0268
16
0.4865 + 4.9516 i
0.000408 - 0.00226 i
17
0.4865 - 4.9516 i
0.000408 + 0.00226 i
18
6.0232
0.736
19
-0.2949 + 6.1323 i
0.00221 + 0.00251 i
20
-0.2949 - 6.1323 i
0.00221 - 0.00251 i
21
-6.206
0.00827 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
0.7058
5.55e-8
Singularities of quadratic [11, 11, 10] approximant
2
0.7058
5.55e-8 i
3
-0.0859 + 0.8903 i
3.32e-9 - 6.78e-8 i
4
-0.0859 - 0.8903 i
3.32e-9 + 6.78e-8 i
5
-0.0859 + 0.8903 i
6.78e-8 + 3.32e-9 i
6
-0.0859 - 0.8903 i
6.78e-8 - 3.32e-9 i
7
-0.9422 + 0.6326 i
2.e-7 + 3.89e-8 i
8
-0.9422 - 0.6326 i
2.e-7 - 3.89e-8 i
9
-0.9422 + 0.6326 i
3.89e-8 - 2.e-7 i
10
-0.9422 - 0.6326 i
3.89e-8 + 2.e-7 i
11
1.3965 + 0.2171 i
0.00101 + 0.00568 i
12
1.3965 - 0.2171 i
0.00101 - 0.00568 i
13
1.4615 + 0.4417 i
0.00285 - 0.00682 i
14
1.4615 - 0.4417 i
0.00285 + 0.00682 i
15
2.3782 + 0.9986 i
0.0285 + 0.0662 i
16
2.3782 - 0.9986 i
0.0285 - 0.0662 i
17
3.2883
142.
18
-3.3255
0.00167
19
-3.6388
0.01 i
20
-4.6395
0.0051
21
12.262
17.7 i
22
-12.8899
0.511 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
-0.1398 + 1.026 i
5.94e-8 - 6.41e-8 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.1398 - 1.026 i
5.94e-8 + 6.41e-8 i
3
-0.1398 + 1.026 i
6.41e-8 + 5.94e-8 i
4
-0.1398 - 1.026 i
6.41e-8 - 5.94e-8 i
5
-1.1458 + 0.5671 i
5.45e-8 + 6.4e-8 i
6
-1.1458 - 0.5671 i
5.45e-8 - 6.4e-8 i
7
-1.1459 + 0.5673 i
6.4e-8 - 5.45e-8 i
8
-1.1459 - 0.5673 i
6.4e-8 + 5.45e-8 i
9
1.396
0.0201
10
1.4047
0.0136 i
11
1.3995 + 0.2154 i
0.00197 + 0.00664 i
12
1.3995 - 0.2154 i
0.00197 - 0.00664 i
13
1.4585 + 0.4296 i
0.000572 - 0.00749 i
14
1.4585 - 0.4296 i
0.000572 + 0.00749 i
15
-2.0947 + 1.1505 i
4.28e-6 + 5.87e-6 i
16
-2.0947 - 1.1505 i
4.28e-6 - 5.87e-6 i
17
-2.0681 + 1.2098 i
5.37e-6 - 5.27e-6 i
18
-2.0681 - 1.2098 i
5.37e-6 + 5.27e-6 i
19
2.5944 + 1.263 i
0.0293 - 0.0266 i
20
2.5944 - 1.263 i
0.0293 + 0.0266 i
21
-4.7765
0.00236
22
8.925
52.3
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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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