Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 2.0r_e"

Molecule X 1^Sigma+ State of BH. Basis AUG-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
1.177 + 0.4453 i
0.0474 - 0.074 i
Singularities of quadratic [5, 5, 4] approximant
2
1.177 - 0.4453 i
0.0474 + 0.074 i
3
1.2659
0.0455
4
1.3617
0.0664 i
5
-2.4811 + 0.458 i
0.143 - 0.291 i
6
-2.4811 - 0.458 i
0.143 + 0.291 i
7
3.2111
1.29
8
-5.7441
0.15
9
7.0201
0.655 i
10
-50.6093
0.537 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
1.1759 + 0.4449 i
0.0457 - 0.0741 i
Singularities of quadratic [5, 5, 5] approximant
2
1.1759 - 0.4449 i
0.0457 + 0.0741 i
3
1.2633
0.0467
4
1.367
0.0703 i
5
-2.4952 + 0.4864 i
0.0704 - 0.328 i
6
-2.4952 - 0.4864 i
0.0704 + 0.328 i
7
3.7501
5.05
8
4.585
6.39 i
9
-5.9667
0.183
10
36.7277
78.2
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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
1.1878 + 0.4417 i
0.0484 - 0.103 i
Singularities of quadratic [6, 5, 5] approximant
2
1.1878 - 0.4417 i
0.0484 + 0.103 i
3
1.3579
0.0924
4
1.54
0.206 i
5
-2.5046 + 0.718 i
0.157 + 0.063 i
6
-2.5046 - 0.718 i
0.157 - 0.063 i
7
2.6626 + 1.6863 i
0.0351 + 0.243 i
8
2.6626 - 1.6863 i
0.0351 - 0.243 i
9
-4.6562 + 1.4236 i
0.117 + 0.204 i
10
-4.6562 - 1.4236 i
0.117 - 0.204 i
11
19.1322
0.478
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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
1.2044 + 0.4354 i
0.0326 - 0.17 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2044 - 0.4354 i
0.0326 + 0.17 i
3
1.5239
0.254
4
1.6074 + 0.5634 i
0.198 + 0.0962 i
5
1.6074 - 0.5634 i
0.198 - 0.0962 i
6
1.8092 + 0.9091 i
0.222 - 0.0718 i
7
1.8092 - 0.9091 i
0.222 + 0.0718 i
8
-2.5348 + 0.5802 i
0.197 + 0.272 i
9
-2.5348 - 0.5802 i
0.197 - 0.272 i
10
-5.3132
0.248
11
-22.1475
0.324 i
12
24.682
0.371 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
-0.5617 + 0.e-5 i
0.0000119 + 0.0000119 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.5617 - 0.e-5 i
0.0000119 - 0.0000119 i
3
1.1809 + 0.4111 i
0.0377 + 0.0723 i
4
1.1809 - 0.4111 i
0.0377 - 0.0723 i
5
1.3492 + 0.8382 i
0.0344 + 0.0266 i
6
1.3492 - 0.8382 i
0.0344 - 0.0266 i
7
1.6313
0.568
8
1.4334 + 0.9849 i
0.0408 - 0.028 i
9
1.4334 - 0.9849 i
0.0408 + 0.028 i
10
-2.4945 + 0.5266 i
0.00778 + 0.256 i
11
-2.4945 - 0.5266 i
0.00778 - 0.256 i
12
-8.0542
0.517
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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
1.2268 + 0.4411 i
0.0773 - 0.352 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2268 - 0.4411 i
0.0773 + 0.352 i
3
1.3629 + 0.4613 i
0.417 + 0.126 i
4
1.3629 - 0.4613 i
0.417 - 0.126 i
5
1.5336 + 0.4115 i
2.47 + 6.22 i
6
1.5336 - 0.4115 i
2.47 - 6.22 i
7
2.2445
0.442
8
-2.5318 + 0.6058 i
0.204 + 0.213 i
9
-2.5318 - 0.6058 i
0.204 - 0.213 i
10
-5.3587
0.412
11
6.3267
1.27 i
12
-9.1568
0.742 i
13
63.8252
4.85
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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
1.2073 + 0.4543 i
0.116 - 0.126 i
Singularities of quadratic [7, 7, 6] approximant
2
1.2073 - 0.4543 i
0.116 + 0.126 i
3
1.5533 + 0.3727 i
0.286 - 0.0182 i
4
1.5533 - 0.3727 i
0.286 + 0.0182 i
5
1.671
0.25
6
1.8542 + 0.5356 i
1.29 + 0.0335 i
7
1.8542 - 0.5356 i
1.29 - 0.0335 i
8
-1.9816
0.0208
9
-1.994
0.0209 i
10
-2.5867 + 0.5698 i
0.707 + 0.476 i
11
-2.5867 - 0.5698 i
0.707 - 0.476 i
12
-4.3293
0.162
13
12.9419
0.308 i
14
-16.9754
0.236 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
1.2067 + 0.4551 i
0.118 - 0.119 i
Singularities of quadratic [7, 7, 7] approximant
2
1.2067 - 0.4551 i
0.118 + 0.119 i
3
-1.2965
0.000922
4
-1.2966
0.000922 i
5
1.6082
0.209
6
1.5756 + 0.3597 i
0.276 - 0.0453 i
7
1.5756 - 0.3597 i
0.276 + 0.0453 i
8
1.8708 + 0.6091 i
0.872 - 0.328 i
9
1.8708 - 0.6091 i
0.872 + 0.328 i
10
-2.5727 + 0.6132 i
0.418 + 0.147 i
11
-2.5727 - 0.6132 i
0.418 - 0.147 i
12
-4.24
0.19
13
-11.1746
0.206 i
14
20.1242
0.293 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
1.2082 + 0.4535 i
0.116 - 0.136 i
Singularities of quadratic [8, 7, 7] approximant
2
1.2082 - 0.4535 i
0.116 + 0.136 i
3
1.526 + 0.3855 i
0.293 + 0.019 i
4
1.526 - 0.3855 i
0.293 - 0.019 i
5
1.8097
0.296
6
1.8064 + 0.4312 i
0.807 + 1.44 i
7
1.8064 - 0.4312 i
0.807 - 1.44 i
8
-2.51
0.691
9
-2.5098 + 0.5379 i
0.0224 - 0.411 i
10
-2.5098 - 0.5379 i
0.0224 + 0.411 i
11
-2.6291
0.359 i
12
-4.6709
0.156
13
8.6199
0.406 i
14
-29.7247
0.332 i
15
132.398
3.63
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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
1.2077 + 0.4537 i
0.115 - 0.132 i
Singularities of quadratic [8, 8, 7] approximant
2
1.2077 - 0.4537 i
0.115 + 0.132 i
3
1.5397 + 0.382 i
0.292 + 0.00104 i
4
1.5397 - 0.382 i
0.292 - 0.00104 i
5
1.7254
0.278
6
-1.5425 + 0.8263 i
0.00261 + 0.00429 i
7
-1.5425 - 0.8263 i
0.00261 - 0.00429 i
8
-1.5424 + 0.8276 i
0.00429 - 0.00261 i
9
-1.5424 - 0.8276 i
0.00429 + 0.00261 i
10
1.8302 + 0.4921 i
1.49 + 0.58 i
11
1.8302 - 0.4921 i
1.49 - 0.58 i
12
-2.5937 + 0.6151 i
0.523 + 0.0391 i
13
-2.5937 - 0.6151 i
0.523 - 0.0391 i
14
-4.2311
0.168
15
12.2916
0.308 i
16
-16.1565
0.224 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
1.2841
0.0308
Singularities of quadratic [8, 8, 8] approximant
2
1.2033 + 0.451 i
0.0817 - 0.115 i
3
1.2033 - 0.451 i
0.0817 + 0.115 i
4
1.2934
0.0322 i
5
1.4778 + 0.4742 i
1.1 + 0.134 i
6
1.4778 - 0.4742 i
1.1 - 0.134 i
7
1.5162 + 0.5356 i
0.1 + 0.853 i
8
1.5162 - 0.5356 i
0.1 - 0.853 i
9
-2.4807 + 0.585 i
0.061 + 0.232 i
10
-2.4807 - 0.585 i
0.061 - 0.232 i
11
2.6587
0.812
12
-3.116 + 0.109 i
0.0234 + 0.324 i
13
-3.116 - 0.109 i
0.0234 - 0.324 i
14
-4.9747
0.134
15
5.3431
0.947 i
16
30.1138
9.71
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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
1.2057 + 0.4513 i
0.0943 - 0.129 i
Singularities of quadratic [9, 8, 8] approximant
2
1.2057 - 0.4513 i
0.0943 + 0.129 i
3
1.4374
0.0606
4
1.4515
0.066 i
5
1.5109 + 0.4944 i
0.615 + 0.073 i
6
1.5109 - 0.4944 i
0.615 - 0.073 i
7
1.5623 + 0.5336 i
1.36 + 4.12 i
8
1.5623 - 0.5336 i
1.36 - 4.12 i
9
-2.4847 + 0.5917 i
0.093 + 0.227 i
10
-2.4847 - 0.5917 i
0.093 - 0.227 i
11
2.6103
0.694
12
-2.9787 + 0.1009 i
0.173 - 0.496 i
13
-2.9787 - 0.1009 i
0.173 + 0.496 i
14
5.2118
1.36 i
15
-5.3092
0.177
16
20.7279
9.21
17
-39.0835
0.494 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
1.2073 + 0.4492 i
0.0829 - 0.154 i
Singularities of quadratic [9, 9, 8] approximant
2
1.2073 - 0.4492 i
0.0829 + 0.154 i
3
1.5426 + 0.3825 i
0.321 + 0.195 i
4
1.5426 - 0.3825 i
0.321 - 0.195 i
5
1.5743 + 0.4444 i
0.618 - 0.0521 i
6
1.5743 - 0.4444 i
0.618 + 0.0521 i
7
-2.1398 + 0.0057 i
0.0142 + 0.0137 i
8
-2.1398 - 0.0057 i
0.0142 - 0.0137 i
9
2.2964
0.666
10
-2.4685 + 0.6211 i
0.0883 + 0.108 i
11
-2.4685 - 0.6211 i
0.0883 - 0.108 i
12
0.9499 + 2.9195 i
0.0139 + 0.0114 i
13
0.9499 - 2.9195 i
0.0139 - 0.0114 i
14
0.9995 + 2.9031 i
0.0115 - 0.0141 i
15
0.9995 - 2.9031 i
0.0115 + 0.0141 i
16
-6.4163
1.56
17
-10.7312
0.408 i
18
20.1582
0.273 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
-0.7532 + 0.e-5 i
3.76e-6 + 3.76e-6 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.7532 - 0.e-5 i
3.76e-6 - 3.76e-6 i
3
1.2071 + 0.4496 i
0.0856 - 0.15 i
4
1.2071 - 0.4496 i
0.0856 + 0.15 i
5
1.5585 + 0.3935 i
0.335 + 0.124 i
6
1.5585 - 0.3935 i
0.335 - 0.124 i
7
1.6008 + 0.4532 i
0.806 - 0.334 i
8
1.6008 - 0.4532 i
0.806 + 0.334 i
9
2.1232
0.6
10
-2.4638 + 0.5883 i
0.0261 + 0.174 i
11
-2.4638 - 0.5883 i
0.0261 - 0.174 i
12
3.3728 + 2.0554 i
0.186 - 0.195 i
13
3.3728 - 2.0554 i
0.186 + 0.195 i
14
-4.0364
0.059
15
-4.1702 + 0.6013 i
0.0294 - 0.0553 i
16
-4.1702 - 0.6013 i
0.0294 + 0.0553 i
17
4.3495
0.248 i
18
7.9025
0.315
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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
1.1299 + 0.0003 i
0.00425 - 0.00424 i
Singularities of quadratic [10, 9, 9] approximant
2
1.1299 - 0.0003 i
0.00425 + 0.00424 i
3
1.2047 + 0.4511 i
0.0852 - 0.119 i
4
1.2047 - 0.4511 i
0.0852 + 0.119 i
5
1.4771 + 0.4498 i
0.492 + 0.158 i
6
1.4771 - 0.4498 i
0.492 - 0.158 i
7
1.577 + 0.4819 i
2.05 + 3.65 i
8
1.577 - 0.4819 i
2.05 - 3.65 i
9
-1.7407 + 0.5892 i
0.000373 + 0.00174 i
10
-1.7407 - 0.5892 i
0.000373 - 0.00174 i
11
-1.7422 + 0.5882 i
0.00174 - 0.000371 i
12
-1.7422 - 0.5882 i
0.00174 + 0.000371 i
13
2.3176
0.54
14
-2.4343 + 0.6304 i
0.0506 + 0.0714 i
15
-2.4343 - 0.6304 i
0.0506 - 0.0714 i
16
5.8249
1.3 i
17
-8.3135 + 1.6412 i
1.25 + 0.261 i
18
-8.3135 - 1.6412 i
1.25 - 0.261 i
19
21.2671
1.59
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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
1.2274 + 0.001 i
0.0122 - 0.012 i
Singularities of quadratic [10, 10, 9] approximant
2
1.2274 - 0.001 i
0.0122 + 0.012 i
3
1.2054 + 0.4509 i
0.0888 - 0.126 i
4
1.2054 - 0.4509 i
0.0888 + 0.126 i
5
1.4871 + 0.4534 i
0.478 + 0.165 i
6
1.4871 - 0.4534 i
0.478 - 0.165 i
7
1.5747 + 0.4806 i
3.24 + 2.42 i
8
1.5747 - 0.4806 i
3.24 - 2.42 i
9
-1.6529
0.00181
10
-1.6534
0.00181 i
11
2.3484
0.57
12
-2.5217 + 0.0258 i
0.0704 + 0.0502 i
13
-2.5217 - 0.0258 i
0.0704 - 0.0502 i
14
-2.4878 + 0.6495 i
0.16 + 0.0611 i
15
-2.4878 - 0.6495 i
0.16 - 0.0611 i
16
6.7916
0.571 i
17
-7.3302
0.627
18
-11.1239
42.3 i
19
-6.766 + 22.2808 i
0.649 + 0.192 i
20
-6.766 - 22.2808 i
0.649 - 0.192 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
1.2065 + 0.4495 i
0.0806 - 0.145 i
Singularities of quadratic [10, 10, 10] approximant
2
1.2065 - 0.4495 i
0.0806 + 0.145 i
3
-1.0172 + 1.0399 i
0.0000172 + 0.000116 i
4
-1.0172 - 1.0399 i
0.0000172 - 0.000116 i
5
-1.0172 + 1.04 i
0.000116 - 0.0000172 i
6
-1.0172 - 1.04 i
0.000116 + 0.0000172 i
7
1.5364 + 0.4042 i
0.382 + 0.0925 i
8
1.5364 - 0.4042 i
0.382 - 0.0925 i
9
1.6148 + 0.4844 i
2.43 + 0.504 i
10
1.6148 - 0.4844 i
2.43 - 0.504 i
11
-1.7477 + 0.0009 i
0.000756 + 0.000754 i
12
-1.7477 - 0.0009 i
0.000756 - 0.000754 i
13
1.9267
0.518
14
-2.4575 + 0.6376 i
0.0776 + 0.0707 i
15
-2.4575 - 0.6376 i
0.0776 - 0.0707 i
16
2.5735
2.25 i
17
3.7064
2.4e4
18
4.9406
0.838 i
19
-5.6379
0.312
20
80.1293
0.652
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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
-1.1739 + 0.2694 i
9.03e-6 - 1.68e-7 i
Singularities of quadratic [11, 10, 10] approximant
2
-1.1739 - 0.2694 i
9.03e-6 + 1.68e-7 i
3
-1.1739 + 0.2694 i
1.67e-7 + 9.03e-6 i
4
-1.1739 - 0.2694 i
1.67e-7 - 9.03e-6 i
5
-1.2403 + 0.e-4 i
4.89e-6 + 4.89e-6 i
6
-1.2403 - 0.e-4 i
4.89e-6 - 4.89e-6 i
7
1.2065 + 0.4497 i
0.0835 - 0.144 i
8
1.2065 - 0.4497 i
0.0835 + 0.144 i
9
1.5516 + 0.4216 i
0.402 + 0.068 i
10
1.5516 - 0.4216 i
0.402 - 0.068 i
11
1.6086 + 0.4901 i
2.29 - 0.329 i
12
1.6086 - 0.4901 i
2.29 + 0.329 i
13
1.8114
0.428
14
2.0047
3.95 i
15
-2.4497 + 0.636 i
0.0695 + 0.0707 i
16
-2.4497 - 0.636 i
0.0695 - 0.0707 i
17
2.7834
0.955
18
5.5218
1. i
19
-6.2356
0.538
20
-18.2673
0.46 i
21
23.5849
7.82
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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
0.2905
7.76e-10 - 7.76e-10 i
Singularities of quadratic [11, 11, 10] approximant
2
0.2905
7.76e-10 + 7.76e-10 i
3
1.2062 + 0.4496 i
0.0796 - 0.141 i
4
1.2062 - 0.4496 i
0.0796 + 0.141 i
5
-1.3471 + 0.5472 i
0.0000613 + 0.000163 i
6
-1.3471 - 0.5472 i
0.0000613 - 0.000163 i
7
-1.3472 + 0.5472 i
0.000163 - 0.0000612 i
8
-1.3472 - 0.5472 i
0.000163 + 0.0000612 i
9
1.5303 + 0.4132 i
0.354 + 0.12 i
10
1.5303 - 0.4132 i
0.354 - 0.12 i
11
1.6062 + 0.4528 i
1.37 - 1.1 i
12
1.6062 - 0.4528 i
1.37 + 1.1 i
13
2.163
0.604
14
-2.444 + 0.621 i
0.0508 + 0.0891 i
15
-2.444 - 0.621 i
0.0508 - 0.0891 i
16
3.1411 + 1.3937 i
0.263 + 0.39 i
17
3.1411 - 1.3937 i
0.263 - 0.39 i
18
3.7513
0.251 i
19
4.2974
0.173
20
-7.8619
50.7
21
-9.2039
0.909 i
22
55.5899
0.585 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
0.8183
0.000166
Singularities of quadratic [11, 11, 11] approximant
2
0.8183
0.000166 i
3
-0.7235 + 0.482 i
4.91e-8 - 1.16e-6 i
4
-0.7235 - 0.482 i
4.91e-8 + 1.16e-6 i
5
-0.7235 + 0.482 i
1.16e-6 + 4.91e-8 i
6
-0.7235 - 0.482 i
1.16e-6 - 4.91e-8 i
7
1.2063 + 0.4491 i
0.0756 - 0.146 i
8
1.2063 - 0.4491 i
0.0756 + 0.146 i
9
-1.4233 + 0.e-4 i
0.0000614 + 0.0000614 i
10
-1.4233 - 0.e-4 i
0.0000614 - 0.0000614 i
11
1.5222 + 0.3996 i
0.385 + 0.092 i
12
1.5222 - 0.3996 i
0.385 - 0.092 i
13
1.6211 + 0.4921 i
2.27 + 2.47 i
14
1.6211 - 0.4921 i
2.27 - 2.47 i
15
1.9122
0.505
16
-2.4501 + 0.6327 i
0.0662 + 0.0759 i
17
-2.4501 - 0.6327 i
0.0662 - 0.0759 i
18
2.746
1.04 i
19
3.8471
9.01
20
5.5978
0.433 i
21
-5.8784
0.411
22
-383.0715
0.147 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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