Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 1.0r_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
1.051
0.0159
Singularities of quadratic [5, 5, 4] approximant
2
1.0522
0.016 i
3
1.6045 + 0.3376 i
0.281 - 0.11 i
4
1.6045 - 0.3376 i
0.281 + 0.11 i
5
2.5115
1.97
6
-2.5469
0.0166
7
-2.7692
0.0173 i
8
-5.8361 + 1.9203 i
0.0867 - 0.163 i
9
-5.8361 - 1.9203 i
0.0867 + 0.163 i
10
25.0091
0.372 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
1.1645
0.0441
Singularities of quadratic [5, 5, 5] approximant
2
1.1675
0.0456 i
3
1.6116 + 0.3481 i
0.28 - 0.0621 i
4
1.6116 - 0.3481 i
0.28 + 0.0621 i
5
2.5427
2.75
6
-2.6106
0.0152
7
-2.9596
0.0159 i
8
-4.6812 + 2.6438 i
0.0595 - 0.0739 i
9
-4.6812 - 2.6438 i
0.0595 + 0.0739 i
10
148.3408
0.357 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
1.4189 + 0.0533 i
0.0359 - 0.028 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4189 - 0.0533 i
0.0359 + 0.028 i
3
1.7522 + 0.5114 i
0.133 - 0.148 i
4
1.7522 - 0.5114 i
0.133 + 0.148 i
5
1.9349
1.24
6
-2.5829 + 0.0868 i
0.0123 + 0.0119 i
7
-2.5829 - 0.0868 i
0.0123 - 0.0119 i
8
4.0478
3.46 i
9
-4.4238
0.111
10
-7.5528
1.56 i
11
10.4159
0.468
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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
1.3999 + 0.0427 i
0.0311 - 0.0258 i
Singularities of quadratic [6, 6, 5] approximant
2
1.3999 - 0.0427 i
0.0311 + 0.0258 i
3
1.7539 + 0.475 i
0.158 - 0.202 i
4
1.7539 - 0.475 i
0.158 + 0.202 i
5
1.9619
0.914
6
-2.5568 + 0.1027 i
0.00815 + 0.00815 i
7
-2.5568 - 0.1027 i
0.00815 - 0.00815 i
8
-4.0416
0.0481
9
5.1699
21.3 i
10
-7.656
17.7 i
11
9.5298 + 28.664 i
0.834 - 0.925 i
12
9.5298 - 28.664 i
0.834 + 0.925 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
-0.6945 + 0.e-5 i
2.97e-6 + 2.97e-6 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.6945 - 0.e-5 i
2.97e-6 - 2.97e-6 i
3
1.3855 + 0.0536 i
0.0165 - 0.0121 i
4
1.3855 - 0.0536 i
0.0165 + 0.0121 i
5
1.6969
0.211
6
1.7896 + 0.5585 i
0.131 - 0.021 i
7
1.7896 - 0.5585 i
0.131 + 0.021 i
8
-2.4527
0.00531
9
-2.8521
0.0073 i
10
5.388
2.28 i
11
-6.0456
0.291
12
-30.1049
0.15 i
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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
1.4038
0.0245
Singularities of quadratic [7, 6, 6] approximant
2
1.5027 + 0.5834 i
0.00647 + 0.00903 i
3
1.5027 - 0.5834 i
0.00647 - 0.00903 i
4
2.0262 + 0.5833 i
0.0232 + 0.0173 i
5
2.0262 - 0.5833 i
0.0232 - 0.0173 i
6
2.0003 + 1.2245 i
0.0148 + 0.00606 i
7
2.0003 - 1.2245 i
0.0148 - 0.00606 i
8
-2.3539
0.00187
9
-1.1263 + 2.1462 i
0.000158 + 0.000446 i
10
-1.1263 - 2.1462 i
0.000158 - 0.000446 i
11
-1.1538 + 2.1611 i
0.000454 - 0.000151 i
12
-1.1538 - 2.1611 i
0.000454 + 0.000151 i
13
-3.27
0.00449 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
0.9738
0.00016
Singularities of quadratic [7, 7, 6] approximant
2
0.9743
0.00016 i
3
1.3698
0.014
4
1.6695
0.828 i
5
1.5933 + 0.5514 i
0.0034 + 0.0321 i
6
1.5933 - 0.5514 i
0.0034 - 0.0321 i
7
-2.3862 + 0.2141 i
0.000918 + 0.00127 i
8
-2.3862 - 0.2141 i
0.000918 - 0.00127 i
9
-2.7941
0.00186
10
3.539 + 0.7772 i
0.315 - 0.203 i
11
3.539 - 0.7772 i
0.315 + 0.203 i
12
-4.5495
0.0269 i
13
5.755 + 19.5356 i
0.00739 - 0.347 i
14
5.755 - 19.5356 i
0.00739 + 0.347 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
1.4068
0.0213
Singularities of quadratic [7, 7, 7] approximant
2
1.3727 + 0.5657 i
0.00411 + 0.000866 i
3
1.3727 - 0.5657 i
0.00411 - 0.000866 i
4
1.4567 + 0.5685 i
0.00152 - 0.00484 i
5
1.4567 - 0.5685 i
0.00152 + 0.00484 i
6
1.8379 + 0.8767 i
0.00297 - 0.0223 i
7
1.8379 - 0.8767 i
0.00297 + 0.0223 i
8
-2.3499
0.00194
9
-3.326
0.00393 i
10
-2.6094 + 2.1789 i
0.00114 + 0.00183 i
11
-2.6094 - 2.1789 i
0.00114 - 0.00183 i
12
-2.5839 + 2.4166 i
0.00197 - 0.00152 i
13
-2.5839 - 2.4166 i
0.00197 + 0.00152 i
14
13.8277
0.228 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
1.438
0.0362
Singularities of quadratic [8, 7, 7] approximant
2
1.3818 + 0.4431 i
0.00319 - 0.00771 i
3
1.3818 - 0.4431 i
0.00319 + 0.00771 i
4
1.418 + 0.3909 i
0.00904 + 0.00302 i
5
1.418 - 0.3909 i
0.00904 - 0.00302 i
6
1.8418 + 0.7088 i
0.0249 + 0.0327 i
7
1.8418 - 0.7088 i
0.0249 - 0.0327 i
8
-2.0272
0.000184
9
-2.0684
0.000164 i
10
-2.2227
0.000364
11
-3.5935
0.00668 i
12
0.4916 + 4.0186 i
0.00101 - 0.00704 i
13
0.4916 - 4.0186 i
0.00101 + 0.00704 i
14
0.9112 + 3.9599 i
0.00801 + 0.000039 i
15
0.9112 - 3.9599 i
0.00801 - 0.000039 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
1.4407
0.039
Singularities of quadratic [8, 8, 7] approximant
2
1.3784 + 0.4401 i
0.00228 - 0.00776 i
3
1.3784 - 0.4401 i
0.00228 + 0.00776 i
4
1.4161 + 0.3905 i
0.00905 + 0.00222 i
5
1.4161 - 0.3905 i
0.00905 - 0.00222 i
6
1.8228 + 0.7175 i
0.0233 + 0.027 i
7
1.8228 - 0.7175 i
0.0233 - 0.027 i
8
-2.0033
0.000165
9
-2.0387
0.000152 i
10
-2.2255
0.000395
11
-3.6275
0.0069 i
12
1.1097 + 3.5235 i
0.006 - 0.00303 i
13
1.1097 - 3.5235 i
0.006 + 0.00303 i
14
0.8345 + 3.7227 i
0.00193 + 0.00607 i
15
0.8345 - 3.7227 i
0.00193 - 0.00607 i
16
9012.9463
51.7 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
1.4447 + 0.2677 i
0.0413 - 0.00328 i
Singularities of quadratic [8, 8, 8] approximant
2
1.4447 - 0.2677 i
0.0413 + 0.00328 i
3
1.5109 + 0.3813 i
0.0262 - 0.0503 i
4
1.5109 - 0.3813 i
0.0262 + 0.0503 i
5
1.5991
0.0666
6
1.6891
0.104 i
7
2.2552
0.666
8
-2.3674
0.00274
9
-3.2357 + 0.4162 i
0.000978 - 0.00183 i
10
-3.2357 - 0.4162 i
0.000978 + 0.00183 i
11
-3.3771 + 0.7904 i
0.00332 + 0.00111 i
12
-3.3771 - 0.7904 i
0.00332 - 0.00111 i
13
4.4899
1.17 i
14
-6.3527
3.22 i
15
6.8463 + 3.6002 i
0.115 - 0.206 i
16
6.8463 - 3.6002 i
0.115 + 0.206 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
1.4525 + 0.1394 i
0.0226 + 0.104 i
Singularities of quadratic [9, 8, 8] approximant
2
1.4525 - 0.1394 i
0.0226 - 0.104 i
3
1.4708 + 0.2289 i
0.0476 + 0.0308 i
4
1.4708 - 0.2289 i
0.0476 - 0.0308 i
5
1.5347 + 0.4523 i
0.0443 - 0.0016 i
6
1.5347 - 0.4523 i
0.0443 + 0.0016 i
7
-2.403 + 0.1372 i
0.000896 + 0.00238 i
8
-2.403 - 0.1372 i
0.000896 - 0.00238 i
9
2.358 + 0.9351 i
0.104 + 0.00551 i
10
2.358 - 0.9351 i
0.104 - 0.00551 i
11
-2.6224
0.002
12
3.3665
3.92
13
-3.4888
0.00785 i
14
-1.6005 + 5.0516 i
0.0112 + 0.00811 i
15
-1.6005 - 5.0516 i
0.0112 - 0.00811 i
16
-1.7752 + 6.4434 i
0.0114 - 0.0144 i
17
-1.7752 - 6.4434 i
0.0114 + 0.0144 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
-0.7696 + 0.6856 i
3.7e-7 - 1.19e-6 i
Singularities of quadratic [9, 9, 8] approximant
2
-0.7696 - 0.6856 i
3.7e-7 + 1.19e-6 i
3
-0.7696 + 0.6856 i
1.19e-6 + 3.7e-7 i
4
-0.7696 - 0.6856 i
1.19e-6 - 3.7e-7 i
5
1.4238 + 0.2598 i
0.0186 + 0.00122 i
6
1.4238 - 0.2598 i
0.0186 - 0.00122 i
7
1.5038 + 0.0698 i
0.0331 - 0.00306 i
8
1.5038 - 0.0698 i
0.0331 + 0.00306 i
9
1.5233 + 0.4278 i
0.0296 - 0.0111 i
10
1.5233 - 0.4278 i
0.0296 + 0.0111 i
11
-2.3581
0.002
12
-2.9318
0.00523 i
13
3.0174
0.711
14
3.5774
0.443 i
15
-3.8185
0.0758
16
-5.1703
0.0809 i
17
9.128 + 18.4846 i
0.108 + 0.343 i
18
9.128 - 18.4846 i
0.108 - 0.343 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
1.4353 + 0.2576 i
0.0283 + 0.00199 i
Singularities of quadratic [9, 9, 9] approximant
2
1.4353 - 0.2576 i
0.0283 - 0.00199 i
3
1.5224 + 0.0995 i
0.0626 + 0.011 i
4
1.5224 - 0.0995 i
0.0626 - 0.011 i
5
-1.4456 + 0.6118 i
0.0000125 - 0.0000211 i
6
-1.4456 - 0.6118 i
0.0000125 + 0.0000211 i
7
-1.4457 + 0.6115 i
0.0000211 + 0.0000125 i
8
-1.4457 - 0.6115 i
0.0000211 - 0.0000125 i
9
1.5297 + 0.4179 i
0.039 - 0.019 i
10
1.5297 - 0.4179 i
0.039 + 0.019 i
11
-2.4824 + 0.0382 i
0.0066 - 0.000891 i
12
-2.4824 - 0.0382 i
0.0066 + 0.000891 i
13
-3.0544
0.00379
14
3.1713 + 0.1167 i
0.218 - 0.319 i
15
3.1713 - 0.1167 i
0.218 + 0.319 i
16
-4.8794
0.0422 i
17
11.2252 + 6.7659 i
0.197 - 0.0568 i
18
11.2252 - 6.7659 i
0.197 + 0.0568 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
-0.9009 + 0.5535 i
2.e-7 + 1.25e-6 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.9009 - 0.5535 i
2.e-7 - 1.25e-6 i
3
-0.9009 + 0.5535 i
1.25e-6 - 2.e-7 i
4
-0.9009 - 0.5535 i
1.25e-6 + 2.e-7 i
5
1.4264 + 0.2583 i
0.0202 + 0.00136 i
6
1.4264 - 0.2583 i
0.0202 - 0.00136 i
7
1.5029 + 0.0781 i
0.0373 - 0.000276 i
8
1.5029 - 0.0781 i
0.0373 + 0.000276 i
9
1.5247 + 0.4283 i
0.0311 - 0.0113 i
10
1.5247 - 0.4283 i
0.0311 + 0.0113 i
11
-2.3526
0.00183
12
-2.9622
0.00529 i
13
3.1818 + 0.3588 i
0.188 - 0.419 i
14
3.1818 - 0.3588 i
0.188 + 0.419 i
15
-3.9926
0.11
16
-5.8288
0.209 i
17
15.5765
0.258
18
-34.7579 + 25.4303 i
1.07 - 1.63 i
19
-34.7579 - 25.4303 i
1.07 + 1.63 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
0.2026
0
Singularities of quadratic [10, 10, 9] approximant
2
0.2026
0
3
-1.1086 + 0.6552 i
1.78e-6 - 7.88e-6 i
4
-1.1086 - 0.6552 i
1.78e-6 + 7.88e-6 i
5
-1.1086 + 0.6552 i
7.88e-6 + 1.78e-6 i
6
-1.1086 - 0.6552 i
7.88e-6 - 1.78e-6 i
7
1.4195 + 0.2603 i
0.0159 + 0.00134 i
8
1.4195 - 0.2603 i
0.0159 - 0.00134 i
9
1.491 + 0.0616 i
0.0245 - 0.00406 i
10
1.491 - 0.0616 i
0.0245 + 0.00406 i
11
1.5223 + 0.4333 i
0.0274 - 0.00788 i
12
1.5223 - 0.4333 i
0.0274 + 0.00788 i
13
-2.3679
0.00223
14
-2.8582
0.00606 i
15
3.1371
0.412
16
3.448
0.329 i
17
-3.6255
0.0329
18
-5.0289
0.0635 i
19
10.3457 + 18.8531 i
0.137 + 0.371 i
20
10.3457 - 18.8531 i
0.137 - 0.371 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
0.1467 + 1.0419 i
1.03e-6 + 3.07e-7 i
Singularities of quadratic [10, 10, 10] approximant
2
0.1467 - 1.0419 i
1.03e-6 - 3.07e-7 i
3
0.1467 + 1.0419 i
3.07e-7 - 1.03e-6 i
4
0.1467 - 1.0419 i
3.07e-7 + 1.03e-6 i
5
-1.2058 + 0.e-5 i
1.93e-6 + 1.93e-6 i
6
-1.2058 - 0.e-5 i
1.93e-6 - 1.93e-6 i
7
1.3343
0.000806
8
1.3475
0.000891 i
9
1.3807 + 0.2467 i
0.0041 - 0.00187 i
10
1.3807 - 0.2467 i
0.0041 + 0.00187 i
11
1.4894 + 0.4618 i
0.00984 - 0.00244 i
12
1.4894 - 0.4618 i
0.00984 + 0.00244 i
13
-2.3464
0.00209
14
3.5784 + 0.2203 i
0.283 - 0.191 i
15
3.5784 - 0.2203 i
0.283 + 0.191 i
16
-3.6122
0.00379 i
17
-3.2597 + 2.2496 i
0.0019 + 0.0022 i
18
-3.2597 - 2.2496 i
0.0019 - 0.0022 i
19
-3.7218 + 2.9246 i
0.00305 - 0.00449 i
20
-3.7218 - 2.9246 i
0.00305 + 0.00449 i
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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
0.2039 + 0.928 i
3.62e-8 + 2.11e-7 i
Singularities of quadratic [11, 10, 10] approximant
2
0.2039 - 0.928 i
3.62e-8 - 2.11e-7 i
3
0.2039 + 0.928 i
2.11e-7 - 3.62e-8 i
4
0.2039 - 0.928 i
2.11e-7 + 3.62e-8 i
5
1.0692
0.000016
6
1.0697
0.000016 i
7
-1.3492 + 0.0002 i
5.75e-7 + 5.75e-7 i
8
-1.3492 - 0.0002 i
5.75e-7 - 5.75e-7 i
9
1.3669 + 0.2188 i
0.00067 - 0.00285 i
10
1.3669 - 0.2188 i
0.00067 + 0.00285 i
11
1.4637 + 0.4663 i
0.00505 - 0.00256 i
12
1.4637 - 0.4663 i
0.00505 + 0.00256 i
13
-2.0453 + 0.5888 i
0.0000332 + 3.75e-6 i
14
-2.0453 - 0.5888 i
0.0000332 - 3.75e-6 i
15
-2.0767 + 0.5552 i
7.68e-6 - 0.0000339 i
16
-2.0767 - 0.5552 i
7.68e-6 + 0.0000339 i
17
-2.6193
0.00141
18
3.1701
0.538
19
5.0864
5.39 i
20
-9.0113 + 3.3221 i
0.057 - 0.0279 i
21
-9.0113 - 3.3221 i
0.057 + 0.0279 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
0.1548 + 0.5411 i
1.09e-9 + 1.3e-9 i
Singularities of quadratic [11, 11, 10] approximant
2
0.1548 - 0.5411 i
1.09e-9 - 1.3e-9 i
3
0.1548 + 0.5411 i
1.3e-9 - 1.09e-9 i
4
0.1548 - 0.5411 i
1.3e-9 + 1.09e-9 i
5
-1.3359
1.12e-6
6
-1.3361
1.12e-6 i
7
1.3837 + 0.2 i
0.00192 + 0.0046 i
8
1.3837 - 0.2 i
0.00192 - 0.0046 i
9
1.4398 + 0.4392 i
0.00121 - 0.00455 i
10
1.4398 - 0.4392 i
0.00121 + 0.00455 i
11
1.2144 + 1.7668 i
0.0000329 + 0.000186 i
12
1.2144 - 1.7668 i
0.0000329 - 0.000186 i
13
1.234 + 1.7903 i
0.000197 - 0.0000278 i
14
1.234 - 1.7903 i
0.000197 + 0.0000278 i
15
-2.2368
0.000301
16
-2.6352
0.00515 i
17
3.4981
0.779
18
-3.8913
0.0051
19
-3.3996 + 3.1899 i
0.00253 + 0.00182 i
20
-3.3996 - 3.1899 i
0.00253 - 0.00182 i
21
-9.1489
0.0324 i
22
13.6137
0.0884 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
0.0533 + 0.8764 i
2.15e-7 - 6.36e-8 i
Singularities of quadratic [11, 11, 11] approximant
2
0.0533 - 0.8764 i
2.15e-7 + 6.36e-8 i
3
0.0533 + 0.8764 i
6.36e-8 + 2.15e-7 i
4
0.0533 - 0.8764 i
6.36e-8 - 2.15e-7 i
5
-0.9278 + 0.088 i
3.72e-8 + 3.41e-8 i
6
-0.9278 - 0.088 i
3.72e-8 - 3.41e-8 i
7
-0.9278 + 0.088 i
3.41e-8 - 3.72e-8 i
8
-0.9278 - 0.088 i
3.41e-8 + 3.72e-8 i
9
1.4048 + 0.2532 i
0.00962 - 0.00159 i
10
1.4048 - 0.2532 i
0.00962 + 0.00159 i
11
1.4425 + 0.0324 i
0.00747 - 0.0039 i
12
1.4425 - 0.0324 i
0.00747 + 0.0039 i
13
1.5051 + 0.447 i
0.0161 - 0.00535 i
14
1.5051 - 0.447 i
0.0161 + 0.00535 i
15
-2.3599
0.00282
16
3.4354 + 0.3861 i
0.293 - 0.226 i
17
3.4354 - 0.3861 i
0.293 + 0.226 i
18
-3.6257
0.00345 i
19
-3.5358 + 2.261 i
0.0028 + 0.00223 i
20
-3.5358 - 2.261 i
0.0028 - 0.00223 i
21
-4.3389 + 3.3832 i
0.00129 - 0.00901 i
22
-4.3389 - 3.3832 i
0.00129 + 0.00901 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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