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

Molecule X 1^Sigma+ State of HF. 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
-1.3764
0.016
Singularities of quadratic [5, 5, 4] approximant
2
0.2773 + 1.4523 i
0.00137 + 0.000175 i
3
0.2773 - 1.4523 i
0.00137 - 0.000175 i
4
0.2867 + 1.4633 i
0.000175 - 0.00139 i
5
0.2867 - 1.4633 i
0.000175 + 0.00139 i
6
-2.1232
0.116 i
7
-1.4268 + 2.396 i
0.0149 - 0.033 i
8
-1.4268 - 2.396 i
0.0149 + 0.033 i
9
3.6636 + 1.0528 i
0.153 - 0.181 i
10
3.6636 - 1.0528 i
0.153 + 0.181 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
-1.1546 + 0.0029 i
0.000583 + 0.000589 i
Singularities of quadratic [5, 5, 5] approximant
2
-1.1546 - 0.0029 i
0.000583 - 0.000589 i
3
-1.3336
0.00551
4
2.0992 + 0.0735 i
0.0362 - 0.0288 i
5
2.0992 - 0.0735 i
0.0362 + 0.0288 i
6
-2.6957
5.88 i
7
-1.5533 + 2.7765 i
0.0101 + 0.127 i
8
-1.5533 - 2.7765 i
0.0101 - 0.127 i
9
3.1926
0.653
10
111.4405
0.976 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
-1.3712
0.0174
Singularities of quadratic [6, 5, 5] approximant
2
-1.8463
0.0472 i
3
-1.5706 + 1.6235 i
0.0151 + 0.0184 i
4
-1.5706 - 1.6235 i
0.0151 - 0.0184 i
5
2.576 + 0.7034 i
0.227 + 0.0891 i
6
2.576 - 0.7034 i
0.227 - 0.0891 i
7
-2.4512 + 1.5245 i
0.0416 - 0.0187 i
8
-2.4512 - 1.5245 i
0.0416 + 0.0187 i
9
-0.2317 + 3.3195 i
0.0111 - 0.0648 i
10
-0.2317 - 3.3195 i
0.0111 + 0.0648 i
11
3.7334
3.84
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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
-1.2402 + 0.01 i
0.00113 + 0.00125 i
Singularities of quadratic [6, 6, 5] approximant
2
-1.2402 - 0.01 i
0.00113 - 0.00125 i
3
-1.3289
0.00378
4
2.509 + 0.3912 i
0.171 + 0.6 i
5
2.509 - 0.3912 i
0.171 - 0.6 i
6
-2.6747
2.68 i
7
3.0991
0.513
8
-1.8165 + 2.6524 i
0.0853 - 0.126 i
9
-1.8165 - 2.6524 i
0.0853 + 0.126 i
10
0.7904 + 5.7242 i
0.471 - 0.085 i
11
0.7904 - 5.7242 i
0.471 + 0.085 i
12
16.0796
1.29 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
-1.3049 + 0.0369 i
0.000366 + 0.00267 i
Singularities of quadratic [6, 6, 6] approximant
2
-1.3049 - 0.0369 i
0.000366 - 0.00267 i
3
-1.3135
0.00194
4
2.4861 + 0.3113 i
0.526 + 0.325 i
5
2.4861 - 0.3113 i
0.526 - 0.325 i
6
-2.742
3.2 i
7
2.9698
0.546
8
-2.0836 + 2.6771 i
0.19 - 0.131 i
9
-2.0836 - 2.6771 i
0.19 + 0.131 i
10
-1.1489 + 5.2214 i
0.754 + 0.594 i
11
-1.1489 - 5.2214 i
0.754 - 0.594 i
12
-13.7663
3.62
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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
0.369
6.23e-7
Singularities of quadratic [7, 6, 6] approximant
2
0.369
6.23e-7 i
3
-1.2707
0.001
4
-1.287 + 0.0225 i
0.000368 - 0.00124 i
5
-1.287 - 0.0225 i
0.000368 + 0.00124 i
6
2.5219 + 0.3735 i
0.112 - 1.04 i
7
2.5219 - 0.3735 i
0.112 + 1.04 i
8
2.7942
0.499
9
-3.1476
31.6 i
10
-2.0203 + 3.2433 i
0.125 + 0.486 i
11
-2.0203 - 3.2433 i
0.125 - 0.486 i
12
-3.4761 + 5.0417 i
5.14 + 3.09 i
13
-3.4761 - 5.0417 i
5.14 - 3.09 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
-1.3006
0.00187
Singularities of quadratic [7, 7, 6] approximant
2
-1.3017 + 0.0435 i
0.0000807 + 0.00264 i
3
-1.3017 - 0.0435 i
0.0000807 - 0.00264 i
4
2.4477 + 0.3103 i
0.243 + 0.0562 i
5
2.4477 - 0.3103 i
0.243 - 0.0562 i
6
3.0906 + 0.8683 i
0.286 + 0.0247 i
7
3.0906 - 0.8683 i
0.286 - 0.0247 i
8
-1.6168 + 3.1027 i
0.0874 + 0.183 i
9
-1.6168 - 3.1027 i
0.0874 - 0.183 i
10
-3.7889 + 0.7136 i
2.09 - 1.83 i
11
-3.7889 - 0.7136 i
2.09 + 1.83 i
12
4.8135
0.508
13
-5.7375
146. i
14
12.5348
3.75 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
-1.3298 + 0.0536 i
0.0018 + 0.00528 i
Singularities of quadratic [7, 7, 7] approximant
2
-1.3298 - 0.0536 i
0.0018 - 0.00528 i
3
-1.3669
0.00443
4
2.495 + 0.4129 i
0.0103 + 0.566 i
5
2.495 - 0.4129 i
0.0103 - 0.566 i
6
-2.6034
0.689 i
7
3.0458
0.482
8
-2.0093 + 3.2174 i
0.152 - 0.677 i
9
-2.0093 - 3.2174 i
0.152 + 0.677 i
10
-3.8217
0.244
11
4.4727
105. i
12
-5.146 + 2.2161 i
0.134 - 0.341 i
13
-5.146 - 2.2161 i
0.134 + 0.341 i
14
6.8394
2.35
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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
-1.3083 + 0.0492 i
0.000407 + 0.00319 i
Singularities of quadratic [8, 7, 7] approximant
2
-1.3083 - 0.0492 i
0.000407 - 0.00319 i
3
-1.3162
0.00231
4
2.1686
0.0268
5
2.3129 + 0.0258 i
0.0127 + 0.0171 i
6
2.3129 - 0.0258 i
0.0127 - 0.0171 i
7
2.6064 + 0.5003 i
0.152 + 0.479 i
8
2.6064 - 0.5003 i
0.152 - 0.479 i
9
-2.739
0.508 i
10
-2.7666 + 0.4502 i
1.47 + 3.3 i
11
-2.7666 - 0.4502 i
1.47 - 3.3 i
12
-1.8245 + 3.0476 i
0.0266 + 0.275 i
13
-1.8245 - 3.0476 i
0.0266 - 0.275 i
14
-3.8841 + 7.1839 i
2.68 - 0.0487 i
15
-3.8841 - 7.1839 i
2.68 + 0.0487 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
0.2861 + 1.1069 i
0.000067 - 0.000012 i
Singularities of quadratic [8, 8, 7] approximant
2
0.2861 - 1.1069 i
0.000067 + 0.000012 i
3
0.2861 + 1.1069 i
0.000012 + 0.000067 i
4
0.2861 - 1.1069 i
0.000012 - 0.000067 i
5
-1.3416 + 0.0484 i
0.00269 + 0.0078 i
6
-1.3416 - 0.0484 i
0.00269 - 0.0078 i
7
-1.3918
0.00664
8
2.525 + 0.4957 i
0.403 + 0.00797 i
9
2.525 - 0.4957 i
0.403 - 0.00797 i
10
2.6547
0.316
11
-2.8765
5.31 i
12
-1.7365 + 3.0372 i
0.023 + 0.176 i
13
-1.7365 - 3.0372 i
0.023 - 0.176 i
14
-4.6598 + 3.8189 i
5.8 + 2.97 i
15
-4.6598 - 3.8189 i
5.8 - 2.97 i
16
62.9561
87.1 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
-0.8735 + 0.e-5 i
0.0000181 + 0.0000181 i
Singularities of quadratic [8, 8, 8] approximant
2
-0.8735 - 0.e-5 i
0.0000181 - 0.0000181 i
3
-1.3477
0.016
4
-1.4181
0.0823 i
5
-1.4854
0.0359
6
2.2294
0.0232
7
2.2893 + 0.1585 i
0.0073 - 0.0345 i
8
2.2893 - 0.1585 i
0.0073 + 0.0345 i
9
2.6101 + 0.5974 i
0.00788 - 0.236 i
10
2.6101 - 0.5974 i
0.00788 + 0.236 i
11
-2.7135
1.53 i
12
-1.8742 + 2.9993 i
0.049 - 0.222 i
13
-1.8742 - 2.9993 i
0.049 + 0.222 i
14
-4.6176 + 4.0064 i
1.34 + 1.18 i
15
-4.6176 - 4.0064 i
1.34 - 1.18 i
16
-16.9456
0.956
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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
-0.8245 + 0.e-5 i
9.34e-6 + 9.34e-6 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.8245 - 0.e-5 i
9.34e-6 - 9.34e-6 i
3
-1.3448
0.0141
4
-1.4296
0.0562 i
5
-1.4955
0.0453
6
1.8937
0.00373
7
1.9018
0.00375 i
8
2.4425
0.0946
9
2.5649 + 0.5815 i
0.0936 + 0.205 i
10
2.5649 - 0.5815 i
0.0936 - 0.205 i
11
-2.7242
1.74 i
12
-1.8414 + 2.9981 i
0.0203 - 0.203 i
13
-1.8414 - 2.9981 i
0.0203 + 0.203 i
14
-4.0326 + 4.4812 i
5.4 + 2.96 i
15
-4.0326 - 4.4812 i
5.4 - 2.96 i
16
18.3953
392. i
17
1022.8773
81.7
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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
-1.3026
0.0253
Singularities of quadratic [9, 9, 8] approximant
2
-1.3267
0.00349 i
3
-1.3388 + 0.069 i
0.00209 + 0.005 i
4
-1.3388 - 0.069 i
0.00209 - 0.005 i
5
-1.3537
0.00279
6
-1.993
0.564 i
7
-2.0891
0.373
8
2.4153 + 0.312 i
0.183 - 0.0495 i
9
2.4153 - 0.312 i
0.183 + 0.0495 i
10
2.6427
0.476
11
2.7015 + 0.5433 i
0.241 - 0.305 i
12
2.7015 - 0.5433 i
0.241 + 0.305 i
13
-3.0267
19.4 i
14
-1.8732 + 3.122 i
0.0537 + 0.348 i
15
-1.8732 - 3.122 i
0.0537 - 0.348 i
16
-4.8005 + 6.0872 i
2.86 - 0.142 i
17
-4.8005 - 6.0872 i
2.86 + 0.142 i
18
725.6465
26.8 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
-1.181 + 0.388 i
0.000203 - 0.000549 i
Singularities of quadratic [9, 9, 9] approximant
2
-1.181 - 0.388 i
0.000203 + 0.000549 i
3
-1.1809 + 0.3883 i
0.000549 + 0.000203 i
4
-1.1809 - 0.3883 i
0.000549 - 0.000203 i
5
-1.343
0.0142
6
-1.4467
0.0339 i
7
-1.5137
0.085
8
2.3724 + 0.2645 i
0.0813 - 0.0623 i
9
2.3724 - 0.2645 i
0.0813 + 0.0623 i
10
2.4765
0.119
11
2.657 + 0.5735 i
0.108 - 0.295 i
12
2.657 - 0.5735 i
0.108 + 0.295 i
13
-2.794
3.71 i
14
-1.8458 + 3.0603 i
0.0147 + 0.258 i
15
-1.8458 - 3.0603 i
0.0147 - 0.258 i
16
-4.5408 + 4.8541 i
0.371 - 4.93 i
17
-4.5408 - 4.8541 i
0.371 + 4.93 i
18
-32.7449
2.37
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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
-1.2082 + 0.5605 i
0.000114 - 0.000479 i
Singularities of quadratic [10, 9, 9] approximant
2
-1.2082 - 0.5605 i
0.000114 + 0.000479 i
3
-1.2084 + 0.5607 i
0.000479 + 0.000114 i
4
-1.2084 - 0.5607 i
0.000479 - 0.000114 i
5
-1.3367
0.0104
6
-1.5011
0.0247 i
7
-1.5739
1.25
8
1.8803
0.012
9
1.8818
0.012 i
10
2.5159 + 0.4489 i
0.556 - 0.477 i
11
2.5159 - 0.4489 i
0.556 + 0.477 i
12
2.8226
0.387
13
-2.8247
8.26 i
14
3.6223
9.86 i
15
-1.8461 + 3.1341 i
0.117 + 0.316 i
16
-1.8461 - 3.1341 i
0.117 - 0.316 i
17
4.0703
1.17
18
-3.9006 + 6.3743 i
2.66 + 0.889 i
19
-3.9006 - 6.3743 i
2.66 - 0.889 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
-0.2197
0
Singularities of quadratic [10, 10, 9] approximant
2
-0.2197
0
3
-1.335
0.00941
4
-1.5198
0.0249 i
5
-1.5992
14.6
6
-1.2468 + 1.3165 i
0.00135 + 0.000545 i
7
-1.2468 - 1.3165 i
0.00135 - 0.000545 i
8
-1.249 + 1.3163 i
0.000551 - 0.00135 i
9
-1.249 - 1.3163 i
0.000551 + 0.00135 i
10
2.3848 + 0.3462 i
0.119 + 0.0239 i
11
2.3848 - 0.3462 i
0.119 - 0.0239 i
12
-2.7632
5.39 i
13
2.8011 + 0.6825 i
0.205 - 0.0567 i
14
2.8011 - 0.6825 i
0.205 + 0.0567 i
15
2.9508
96.7
16
-1.999 + 3.1987 i
0.191 + 1.03 i
17
-1.999 - 3.1987 i
0.191 - 1.03 i
18
-2.63 + 8.3198 i
0.999 + 0.0858 i
19
-2.63 - 8.3198 i
0.999 - 0.0858 i
20
156.9253
5.25 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
-0.0025
0
Singularities of quadratic [10, 10, 10] approximant
2
-0.0025
0
3
0.0923
0
4
0.0923
0
5
-1.3341
0.00901
6
-1.5463
0.0244 i
7
-1.6473
0.931
8
2.0353
0.0602
9
2.0393
0.0563 i
10
-2.2896
0.296 i
11
2.5833
0.246
12
2.536 + 0.5079 i
0.345 + 0.123 i
13
2.536 - 0.5079 i
0.345 - 0.123 i
14
-2.6936 + 0.3547 i
0.274 - 0.00704 i
15
-2.6936 - 0.3547 i
0.274 + 0.00704 i
16
-1.7949 + 2.9237 i
0.0371 - 0.127 i
17
-1.7949 - 2.9237 i
0.0371 + 0.127 i
18
-3.6547 + 2.7587 i
0.438 - 0.273 i
19
-3.6547 - 2.7587 i
0.438 + 0.273 i
20
-32.4777
1.21
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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
-0.7883 + 0.e-5 i
1.23e-6 + 1.23e-6 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.7883 - 0.e-5 i
1.23e-6 - 1.23e-6 i
3
0.2939 + 0.8531 i
2.24e-6 + 1.47e-6 i
4
0.2939 - 0.8531 i
2.24e-6 - 1.47e-6 i
5
0.2939 + 0.8531 i
1.47e-6 - 2.24e-6 i
6
0.2939 - 0.8531 i
1.47e-6 + 2.24e-6 i
7
-1.3321
0.00789
8
-1.5662 + 0.0753 i
0.00871 - 0.0364 i
9
-1.5662 - 0.0753 i
0.00871 + 0.0364 i
10
-1.5886 + 0.1063 i
0.301 + 0.249 i
11
-1.5886 - 0.1063 i
0.301 - 0.249 i
12
2.4148 + 0.373 i
0.155 + 0.0949 i
13
2.4148 - 0.373 i
0.155 - 0.0949 i
14
-2.859
12.8 i
15
2.8973 + 0.6154 i
0.301 + 0.000706 i
16
2.8973 - 0.6154 i
0.301 - 0.000706 i
17
3.1593
3.57
18
-1.8292 + 3.1528 i
0.153 + 0.287 i
19
-1.8292 - 3.1528 i
0.153 - 0.287 i
20
-3.8271 + 6.3848 i
2.39 + 1.07 i
21
-3.8271 - 6.3848 i
2.39 - 1.07 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
0.7708
1.76e-7
Singularities of quadratic [11, 11, 10] approximant
2
0.7708
1.76e-7 i
3
0.1427 + 1.0227 i
2.72e-7 - 3.36e-6 i
4
0.1427 - 1.0227 i
2.72e-7 + 3.36e-6 i
5
0.1427 + 1.0227 i
3.36e-6 + 2.72e-7 i
6
0.1427 - 1.0227 i
3.36e-6 - 2.72e-7 i
7
-1.3287
0.0075
8
-1.4377 + 0.1128 i
0.0055 - 0.0144 i
9
-1.4377 - 0.1128 i
0.0055 + 0.0144 i
10
-1.4641 + 0.1024 i
0.0105 + 0.0162 i
11
-1.4641 - 0.1024 i
0.0105 - 0.0162 i
12
2.421 + 0.4221 i
0.0408 + 0.157 i
13
2.421 - 0.4221 i
0.0408 - 0.157 i
14
-2.7346
2.4 i
15
3.1878
0.719
16
-1.7185 + 3.2153 i
0.185 + 0.0763 i
17
-1.7185 - 3.2153 i
0.185 - 0.0763 i
18
-1.49 + 5.241 i
0.201 - 0.353 i
19
-1.49 - 5.241 i
0.201 + 0.353 i
20
6.7442
0.895 i
21
3.6044 + 10.8525 i
0.406 - 0.381 i
22
3.6044 - 10.8525 i
0.406 + 0.381 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
0.1083 + 1.1362 i
7.89e-6 - 8.37e-6 i
Singularities of quadratic [11, 11, 11] approximant
2
0.1083 - 1.1362 i
7.89e-6 + 8.37e-6 i
3
0.1083 + 1.1362 i
8.37e-6 + 7.89e-6 i
4
0.1083 - 1.1362 i
8.37e-6 - 7.89e-6 i
5
-1.3316
0.00844
6
1.4267
0.0000767
7
1.4267
0.0000767 i
8
-1.4866 + 0.1623 i
0.000436 + 0.0126 i
9
-1.4866 - 0.1623 i
0.000436 - 0.0126 i
10
-1.5077 + 0.1772 i
0.0184 + 0.00031 i
11
-1.5077 - 0.1772 i
0.0184 - 0.00031 i
12
2.4105 + 0.4237 i
0.0297 + 0.132 i
13
2.4105 - 0.4237 i
0.0297 - 0.132 i
14
-2.6608
1.06 i
15
3.2665
0.779
16
-1.7923 + 3.0452 i
0.0438 + 0.159 i
17
-1.7923 - 3.0452 i
0.0438 - 0.159 i
18
-2.9945 + 4.5342 i
90. - 7.88 i
19
-2.9945 - 4.5342 i
90. + 7.88 i
20
5.5384
1.48 i
21
10.5159
22.3
22
-11.5378
1.73
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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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