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

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
1.1716 + 0.4577 i
0.0543 - 0.0857 i
Singularities of quadratic [5, 5, 4] approximant
2
1.1716 - 0.4577 i
0.0543 + 0.0857 i
3
1.271
0.0559
4
1.3686
0.0831 i
5
-2.7287 + 0.7388 i
0.0616 + 0.268 i
6
-2.7287 - 0.7388 i
0.0616 - 0.268 i
7
3.8908
3.99
8
5.6525
2.29 i
9
-15.5579
0.213
10
-81.7609
0.584 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
1.18 + 0.3935 i
0.0606 + 0.0502 i
Singularities of quadratic [5, 5, 5] approximant
2
1.18 - 0.3935 i
0.0606 - 0.0502 i
3
1.1159 + 0.6584 i
0.0138 - 0.0352 i
4
1.1159 - 0.6584 i
0.0138 + 0.0352 i
5
1.1756 + 0.642 i
0.0398 + 0.00838 i
6
1.1756 - 0.642 i
0.0398 - 0.00838 i
7
2.2068
0.546
8
-2.7409 + 0.8731 i
0.19 + 0.128 i
9
-2.7409 - 0.8731 i
0.19 - 0.128 i
10
-8.0514
0.312
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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
1.1915 + 0.4535 i
0.06 - 0.148 i
Singularities of quadratic [6, 5, 5] approximant
2
1.1915 - 0.4535 i
0.06 + 0.148 i
3
1.4693
0.184
4
2.043 + 0.2704 i
0.531 + 1.24 i
5
2.043 - 0.2704 i
0.531 - 1.24 i
6
2.0459 + 1.2303 i
0.212 + 0.0939 i
7
2.0459 - 1.2303 i
0.212 - 0.0939 i
8
-2.7321 + 0.8353 i
0.171 + 0.169 i
9
-2.7321 - 0.8353 i
0.171 - 0.169 i
10
-7.1887
0.278
11
-25.5878
0.324 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
1.2011 + 0.4557 i
0.0811 - 0.186 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2011 - 0.4557 i
0.0811 + 0.186 i
3
1.6346
0.306
4
1.574 + 0.5098 i
0.298 + 0.0923 i
5
1.574 - 0.5098 i
0.298 - 0.0923 i
6
1.876 + 0.7363 i
0.507 - 0.0495 i
7
1.876 - 0.7363 i
0.507 + 0.0495 i
8
-2.7369 + 0.7936 i
0.146 + 0.225 i
9
-2.7369 - 0.7936 i
0.146 - 0.225 i
10
-8.8372
0.22
11
32.0625
0.347 i
12
-136.8165
0.591 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
1.1917 + 0.4688 i
0.102 - 0.117 i
Singularities of quadratic [6, 6, 6] approximant
2
1.1917 - 0.4688 i
0.102 + 0.117 i
3
1.4166 + 0.2348 i
0.225 + 0.16 i
4
1.4166 - 0.2348 i
0.225 - 0.16 i
5
1.5351 + 0.3158 i
0.421 + 0.0896 i
6
1.5351 - 0.3158 i
0.421 - 0.0896 i
7
2.4354 + 1.2131 i
0.221 + 0.28 i
8
2.4354 - 1.2131 i
0.221 - 0.28 i
9
-2.7329 + 0.8036 i
0.147 + 0.21 i
10
-2.7329 - 0.8036 i
0.147 - 0.21 i
11
3.4541
0.431
12
-8.6519
0.265
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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
1.2196 + 0.4597 i
0.157 - 0.361 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2196 - 0.4597 i
0.157 + 0.361 i
3
1.3527 + 0.4498 i
0.384 + 0.322 i
4
1.3527 - 0.4498 i
0.384 - 0.322 i
5
1.4781 + 0.4041 i
1.33 + 0.982 i
6
1.4781 - 0.4041 i
1.33 - 0.982 i
7
2.6865
0.485
8
-2.7311 + 0.8248 i
0.169 + 0.179 i
9
-2.7311 - 0.8248 i
0.169 - 0.179 i
10
4.9604
248. i
11
-5.8976
0.272
12
-9.3075
0.39 i
13
15.6645
0.741
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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
1.2004 + 0.4655 i
0.12 - 0.149 i
Singularities of quadratic [7, 7, 6] approximant
2
1.2004 - 0.4655 i
0.12 + 0.149 i
3
1.5527 + 0.399 i
0.335 + 0.0226 i
4
1.5527 - 0.399 i
0.335 - 0.0226 i
5
1.7907 + 0.4042 i
0.556 - 1.31 i
6
1.7907 - 0.4042 i
0.556 + 1.31 i
7
2.0022
0.324
8
-2.6893 + 0.804 i
0.0937 + 0.191 i
9
-2.6893 - 0.804 i
0.0937 - 0.191 i
10
-3.8279 + 0.2264 i
0.0399 - 0.337 i
11
-3.8279 - 0.2264 i
0.0399 + 0.337 i
12
-8.5367
0.124
13
16.5753
0.328 i
14
-38.1117
0.267 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
1.2001 + 0.4656 i
0.12 - 0.146 i
Singularities of quadratic [7, 7, 7] approximant
2
1.2001 - 0.4656 i
0.12 + 0.146 i
3
1.5611 + 0.3955 i
0.335 + 0.0109 i
4
1.5611 - 0.3955 i
0.335 - 0.0109 i
5
1.8221 + 0.4224 i
0.0225 - 1.33 i
6
1.8221 - 0.4224 i
0.0225 + 1.33 i
7
1.9284
0.302
8
-2.6916 + 0.8073 i
0.0946 + 0.189 i
9
-2.6916 - 0.8073 i
0.0946 - 0.189 i
10
-4.3116 + 0.4377 i
0.00258 - 0.207 i
11
-4.3116 - 0.4377 i
0.00258 + 0.207 i
12
-9.2355
0.0721
13
-13.6862
0.096 i
14
26.7282
0.258 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
1.2001 + 0.4659 i
0.122 - 0.145 i
Singularities of quadratic [8, 7, 7] approximant
2
1.2001 - 0.4659 i
0.122 + 0.145 i
3
1.5641 + 0.3934 i
0.333 + 0.00379 i
4
1.5641 - 0.3934 i
0.333 - 0.00379 i
5
1.8495
0.289
6
1.8528 + 0.4504 i
0.533 + 1.12 i
7
1.8528 - 0.4504 i
0.533 - 1.12 i
8
-2.688 + 0.7908 i
0.059 + 0.204 i
9
-2.688 - 0.7908 i
0.059 - 0.204 i
10
-4.1232 + 1.5176 i
0.081 - 0.0573 i
11
-4.1232 - 1.5176 i
0.081 + 0.0573 i
12
-4.9006 + 1.6963 i
0.065 + 0.0721 i
13
-4.9006 - 1.6963 i
0.065 - 0.0721 i
14
17.8439
0.41 i
15
-34.6588
16.6
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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
0.8971
0.00202
Singularities of quadratic [8, 8, 7] approximant
2
0.8972
0.00202 i
3
1.2022 + 0.4674 i
0.148 - 0.148 i
4
1.2022 - 0.4674 i
0.148 + 0.148 i
5
1.5668 + 0.3719 i
0.297 - 0.0192 i
6
1.5668 - 0.3719 i
0.297 + 0.0192 i
7
1.6331
0.221
8
1.9569 + 0.5382 i
0.704 + 0.271 i
9
1.9569 - 0.5382 i
0.704 - 0.271 i
10
-2.6945 + 0.8258 i
0.13 + 0.161 i
11
-2.6945 - 0.8258 i
0.13 - 0.161 i
12
-3.6817 + 0.1549 i
0.348 - 0.509 i
13
-3.6817 - 0.1549 i
0.348 + 0.509 i
14
-11.7928
0.215
15
15.3054
0.4 i
16
-97.1993
0.594 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
1.2014 + 0.4622 i
0.101 - 0.177 i
Singularities of quadratic [8, 8, 8] approximant
2
1.2014 - 0.4622 i
0.101 + 0.177 i
3
1.5282 + 0.3484 i
0.369 + 0.438 i
4
1.5282 - 0.3484 i
0.369 - 0.438 i
5
1.5183 + 0.4437 i
0.342 + 0.155 i
6
1.5183 - 0.4437 i
0.342 - 0.155 i
7
2.4756 + 0.8941 i
0.24 + 0.274 i
8
2.4756 - 0.8941 i
0.24 - 0.274 i
9
-2.687 + 0.8436 i
0.134 + 0.12 i
10
-2.687 - 0.8436 i
0.134 - 0.12 i
11
-3.3147 + 0.0209 i
0.317 + 0.189 i
12
-3.3147 - 0.0209 i
0.317 - 0.189 i
13
3.4099
0.442
14
5.9913
24.1 i
15
13.4006
0.576
16
-15.4888
0.643
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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
0.2073
5.82e-9
Singularities of quadratic [9, 8, 8] approximant
2
0.2073
5.82e-9 i
3
1.2007 + 0.4621 i
0.0964 - 0.171 i
4
1.2007 - 0.4621 i
0.0964 + 0.171 i
5
1.5347 + 0.3701 i
0.332 + 0.415 i
6
1.5347 - 0.3701 i
0.332 - 0.415 i
7
1.5305 + 0.4437 i
0.392 + 0.13 i
8
1.5305 - 0.4437 i
0.392 - 0.13 i
9
-2.6933 + 0.8297 i
0.127 + 0.153 i
10
-2.6933 - 0.8297 i
0.127 - 0.153 i
11
2.7669 + 0.8156 i
0.294 + 0.499 i
12
2.7669 - 0.8156 i
0.294 - 0.499 i
13
-3.7721 + 0.1357 i
0.475 - 0.588 i
14
-3.7721 - 0.1357 i
0.475 + 0.588 i
15
4.2385
0.643
16
9.7361
1.84 i
17
-20.0485
0.49
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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
1.2002 + 0.4627 i
0.0989 - 0.164 i
Singularities of quadratic [9, 9, 8] approximant
2
1.2002 - 0.4627 i
0.0989 + 0.164 i
3
1.5554 + 0.396 i
0.292 + 0.205 i
4
1.5554 - 0.396 i
0.292 - 0.205 i
5
1.5772 + 0.4354 i
0.484 - 0.192 i
6
1.5772 - 0.4354 i
0.484 + 0.192 i
7
2.55
0.732
8
-2.801 + 0.0173 i
0.0825 + 0.0668 i
9
-2.801 - 0.0173 i
0.0825 - 0.0668 i
10
-2.6782 + 0.8449 i
0.121 + 0.0968 i
11
-2.6782 - 0.8449 i
0.121 - 0.0968 i
12
0.3756 + 3.2293 i
0.00165 - 0.0197 i
13
0.3756 - 3.2293 i
0.00165 + 0.0197 i
14
0.346 + 3.2624 i
0.0197 + 0.00178 i
15
0.346 - 3.2624 i
0.0197 - 0.00178 i
16
-7.18
0.192
17
-15.6523
0.17 i
18
23.7568
0.265 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
0.955
0.00146
Singularities of quadratic [9, 9, 9] approximant
2
0.955
0.00146 i
3
1.1994 + 0.4623 i
0.0904 - 0.155 i
4
1.1994 - 0.4623 i
0.0904 + 0.155 i
5
1.513 + 0.4192 i
0.204 + 0.251 i
6
1.513 - 0.4192 i
0.204 - 0.251 i
7
1.5327 + 0.4324 i
0.384 - 0.144 i
8
1.5327 - 0.4324 i
0.384 + 0.144 i
9
2.7142 + 0.6573 i
0.651 + 0.326 i
10
2.7142 - 0.6573 i
0.651 - 0.326 i
11
-2.6935 + 0.8123 i
0.0973 + 0.183 i
12
-2.6935 - 0.8123 i
0.0973 - 0.183 i
13
3.5622
0.785
14
-4.8931 + 1.3779 i
0.0324 - 0.145 i
15
-4.8931 - 1.3779 i
0.0324 + 0.145 i
16
-5.7457 + 3.6488 i
0.123 + 0.0256 i
17
-5.7457 - 3.6488 i
0.123 - 0.0256 i
18
-27.8961
0.696
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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
-1.2044 + 0.e-5 i
0.000157 + 0.000157 i
Singularities of quadratic [10, 9, 9] approximant
2
-1.2044 - 0.e-5 i
0.000157 - 0.000157 i
3
1.1999 + 0.4628 i
0.0981 - 0.161 i
4
1.1999 - 0.4628 i
0.0981 + 0.161 i
5
1.5546 + 0.4065 i
0.394 + 0.0987 i
6
1.5546 - 0.4065 i
0.394 - 0.0987 i
7
1.6253 + 0.4825 i
2.19 - 0.297 i
8
1.6253 - 0.4825 i
2.19 + 0.297 i
9
2.079
0.514
10
1.9715 + 1.4714 i
0.0688 + 0.0977 i
11
1.9715 - 1.4714 i
0.0688 - 0.0977 i
12
2.0362 + 1.3921 i
0.107 - 0.0777 i
13
2.0362 - 1.3921 i
0.107 + 0.0777 i
14
-2.6908 + 0.828 i
0.117 + 0.152 i
15
-2.6908 - 0.828 i
0.117 - 0.152 i
16
-3.9044 + 0.1375 i
0.429 - 0.694 i
17
-3.9044 - 0.1375 i
0.429 + 0.694 i
18
11.5484
0.947 i
19
-21.6937
0.59
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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
1.1999 + 0.4628 i
0.0987 - 0.161 i
Singularities of quadratic [10, 10, 9] approximant
2
1.1999 - 0.4628 i
0.0987 + 0.161 i
3
-1.3194 + 0.e-5 i
0.000381 + 0.000381 i
4
-1.3194 - 0.e-5 i
0.000381 - 0.000381 i
5
1.557 + 0.4051 i
0.384 + 0.1 i
6
1.557 - 0.4051 i
0.384 - 0.1 i
7
1.6273 + 0.4739 i
1.88 - 0.695 i
8
1.6273 - 0.4739 i
1.88 + 0.695 i
9
2.1346
0.521
10
1.8347 + 1.4844 i
0.0702 + 0.0687 i
11
1.8347 - 1.4844 i
0.0702 - 0.0687 i
12
1.8758 + 1.44 i
0.0715 - 0.0761 i
13
1.8758 - 1.44 i
0.0715 + 0.0761 i
14
-2.6915 + 0.8306 i
0.123 + 0.148 i
15
-2.6915 - 0.8306 i
0.123 - 0.148 i
16
-3.8003 + 0.1192 i
0.576 - 0.629 i
17
-3.8003 - 0.1192 i
0.576 + 0.629 i
18
12.9185
0.689 i
19
-18.8287
0.484
20
-2923.2142
6.55 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
1.1998 + 0.4625 i
0.0933 - 0.162 i
Singularities of quadratic [10, 10, 10] approximant
2
1.1998 - 0.4625 i
0.0933 + 0.162 i
3
1.5287 + 0.4029 i
0.381 + 0.148 i
4
1.5287 - 0.4029 i
0.381 - 0.148 i
5
1.6075 + 0.4595 i
1.81 - 0.303 i
6
1.6075 - 0.4595 i
1.81 + 0.303 i
7
-1.8005 + 0.0002 i
0.0024 + 0.0024 i
8
-1.8005 - 0.0002 i
0.0024 - 0.0024 i
9
2.1988
0.53
10
1.3327 + 2.3599 i
0.013 - 0.0151 i
11
1.3327 - 2.3599 i
0.013 + 0.0151 i
12
1.3071 + 2.383 i
0.0149 + 0.013 i
13
1.3071 - 2.383 i
0.0149 - 0.013 i
14
-2.6762 + 0.8496 i
0.11 + 0.102 i
15
-2.6762 - 0.8496 i
0.11 - 0.102 i
16
3.1932
0.751 i
17
-3.278
0.408
18
-3.4729
22.4 i
19
4.2199
1.33
20
-20.216
3.76
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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
-0.4185
1.17e-7 + 1.17e-7 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.4185
1.17e-7 - 1.17e-7 i
3
-1.1598 + 0.e-5 i
0.000104 + 0.000104 i
4
-1.1598 - 0.e-5 i
0.000104 - 0.000104 i
5
1.1999 + 0.4628 i
0.0983 - 0.161 i
6
1.1999 - 0.4628 i
0.0983 + 0.161 i
7
1.5554 + 0.4061 i
0.392 + 0.0987 i
8
1.5554 - 0.4061 i
0.392 - 0.0987 i
9
1.6258 + 0.4809 i
2.13 - 0.383 i
10
1.6258 - 0.4809 i
2.13 + 0.383 i
11
2.0878
0.515
12
1.9509 + 1.4802 i
0.0678 + 0.0924 i
13
1.9509 - 1.4802 i
0.0678 - 0.0924 i
14
2.0131 + 1.408 i
0.101 - 0.076 i
15
2.0131 - 1.408 i
0.101 + 0.076 i
16
-2.6906 + 0.8278 i
0.116 + 0.152 i
17
-2.6906 - 0.8278 i
0.116 - 0.152 i
18
-3.9129 + 0.1378 i
0.423 - 0.701 i
19
-3.9129 - 0.1378 i
0.423 + 0.701 i
20
11.6386
0.929 i
21
-21.7389
0.595
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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
-0.844 + 0.408 i
2.23e-6 + 5.64e-6 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.844 - 0.408 i
2.23e-6 - 5.64e-6 i
3
-0.844 + 0.408 i
5.64e-6 - 2.23e-6 i
4
-0.844 - 0.408 i
5.64e-6 + 2.23e-6 i
5
1.2536 + 0.0005 i
0.00976 - 0.00971 i
6
1.2536 - 0.0005 i
0.00976 + 0.00971 i
7
1.1991 + 0.4637 i
0.105 - 0.144 i
8
1.1991 - 0.4637 i
0.105 + 0.144 i
9
1.4952 + 0.4759 i
0.398 + 0.242 i
10
1.4952 - 0.4759 i
0.398 - 0.242 i
11
1.534 + 0.4555 i
0.801 - 1.39 i
12
1.534 - 0.4555 i
0.801 + 1.39 i
13
-2.6773 + 0.824 i
0.0841 + 0.133 i
14
-2.6773 - 0.824 i
0.0841 - 0.133 i
15
3.0557 + 0.9499 i
0.152 + 0.523 i
16
3.0557 - 0.9499 i
0.152 - 0.523 i
17
-4.5295
0.607
18
-4.9569
1.45 i
19
4.33 + 3.0678 i
0.162 + 0.2 i
20
4.33 - 3.0678 i
0.162 - 0.2 i
21
8.3492 + 17.9168 i
0.265 - 0.0371 i
22
8.3492 - 17.9168 i
0.265 + 0.0371 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
-0.7697 + 0.5362 i
1.33e-6 - 0.0000171 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.7697 - 0.5362 i
1.33e-6 + 0.0000171 i
3
-0.7697 + 0.5362 i
0.0000171 + 1.33e-6 i
4
-0.7697 - 0.5362 i
0.0000171 - 1.33e-6 i
5
1.1998 + 0.4635 i
0.107 - 0.156 i
6
1.1998 - 0.4635 i
0.107 + 0.156 i
7
1.5409 + 0.5561 i
0.597 + 0.353 i
8
1.5409 - 0.5561 i
0.597 - 0.353 i
9
1.6619
0.222
10
1.6019 + 0.5198 i
0.868 - 0.971 i
11
1.6019 - 0.5198 i
0.868 + 0.971 i
12
1.8923
0.806 i
13
2.231
33.2
14
2.2761 + 0.9061 i
0.384 + 0.111 i
15
2.2761 - 0.9061 i
0.384 - 0.111 i
16
-2.6882 + 0.8177 i
0.0957 + 0.162 i
17
-2.6882 - 0.8177 i
0.0957 - 0.162 i
18
-4.7764 + 0.4795 i
0.0261 + 0.328 i
19
-4.7764 - 0.4795 i
0.0261 - 0.328 i
20
-8.5768 + 7.069 i
0.283 - 0.0338 i
21
-8.5768 - 7.069 i
0.283 + 0.0338 i
22
406.1411
0.0721 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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