Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 1.6r_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
0.8201
0.000464
Singularities of quadratic [5, 5, 4] approximant
2
0.8203
0.000464 i
3
1.4255 + 0.4367 i
0.0311 + 0.107 i
4
1.4255 - 0.4367 i
0.0311 - 0.107 i
5
-2.0037
0.00642
6
-2.04
0.00658 i
7
2.9583
1.34
8
-3.512
2.27
9
8.7742
0.333 i
10
-10.157
0.133 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
0.8062
0.000423
Singularities of quadratic [5, 5, 5] approximant
2
0.8064
0.000423 i
3
1.4253 + 0.4363 i
0.0321 + 0.106 i
4
1.4253 - 0.4363 i
0.0321 - 0.106 i
5
-1.9632
0.00576
6
-1.9946
0.00589 i
7
2.9676
1.37
8
-3.4933
2.85
9
8.6738
0.335 i
10
-10.2115
0.134 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
0.919
0.000989
Singularities of quadratic [6, 5, 5] approximant
2
0.9196
0.00099 i
3
1.4249 + 0.4403 i
0.0227 + 0.107 i
4
1.4249 - 0.4403 i
0.0227 - 0.107 i
5
-1.7475
0.00392
6
-1.7585
0.00395 i
7
2.969
1.26
8
-3.3111
11.5
9
7.7127
0.457 i
10
-8.2157
0.158 i
11
-6412.2289
856.
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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
0.7544 + 0.3204 i
0.000253 + 0.000477 i
Singularities of quadratic [6, 6, 5] approximant
2
0.7544 - 0.3204 i
0.000253 - 0.000477 i
3
0.7545 + 0.3204 i
0.000477 - 0.000253 i
4
0.7545 - 0.3204 i
0.000477 + 0.000253 i
5
1.4248 + 0.4329 i
0.0392 + 0.103 i
6
1.4248 - 0.4329 i
0.0392 - 0.103 i
7
-1.9083
0.00524
8
-1.9328
0.00533 i
9
2.9555
1.38
10
-3.4523
6.03
11
8.9436
0.324 i
12
-9.8932
0.134 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
1.4795
0.0695
Singularities of quadratic [6, 6, 6] approximant
2
1.4364 + 0.4612 i
0.0307 - 0.158 i
3
1.4364 - 0.4612 i
0.0307 + 0.158 i
4
1.5338
0.0827 i
5
-2.1091 + 0.0165 i
0.0108 + 0.0109 i
6
-2.1091 - 0.0165 i
0.0108 - 0.0109 i
7
2.7641 + 1.2451 i
0.163 + 0.331 i
8
2.7641 - 1.2451 i
0.163 - 0.331 i
9
-3.0734
0.121
10
-4.0579
769. i
11
5.9422
0.379
12
-9.5671
0.431
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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
1.1645 + 0.0017 i
0.00206 - 0.00204 i
Singularities of quadratic [7, 6, 6] approximant
2
1.1645 - 0.0017 i
0.00206 + 0.00204 i
3
1.4114 + 0.4746 i
0.0278 - 0.0719 i
4
1.4114 - 0.4746 i
0.0278 + 0.0719 i
5
-2.1683
0.00774
6
-2.2649
0.0083 i
7
2.3602 + 0.3197 i
0.434 - 0.729 i
8
2.3602 - 0.3197 i
0.434 + 0.729 i
9
-4.2734
0.128
10
4.711
0.329
11
-0.3816 + 8.7254 i
0.0408 + 0.0595 i
12
-0.3816 - 8.7254 i
0.0408 - 0.0595 i
13
12.8066
0.118 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
1.4267 + 0.0096 i
0.0155 - 0.0145 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4267 - 0.0096 i
0.0155 + 0.0145 i
3
1.4287 + 0.4813 i
0.0676 - 0.0954 i
4
1.4287 - 0.4813 i
0.0676 + 0.0954 i
5
-2.2019
0.0108
6
-2.2961
0.0114 i
7
2.3919 + 0.5698 i
1.01 - 0.493 i
8
2.3919 - 0.5698 i
1.01 + 0.493 i
9
2.8619
13.5
10
-4.3398 + 0.9171 i
0.0332 + 0.0851 i
11
-4.3398 - 0.9171 i
0.0332 - 0.0851 i
12
-6.4233 + 3.2725 i
0.0728 - 0.126 i
13
-6.4233 - 3.2725 i
0.0728 + 0.126 i
14
16.768
0.274 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
1.4341 + 0.4355 i
0.0825 + 0.0808 i
Singularities of quadratic [7, 7, 7] approximant
2
1.4341 - 0.4355 i
0.0825 - 0.0808 i
3
1.4858 + 0.6089 i
0.0868 - 0.0919 i
4
1.4858 - 0.6089 i
0.0868 + 0.0919 i
5
1.5402 + 0.5667 i
0.152 + 0.0245 i
6
1.5402 - 0.5667 i
0.152 - 0.0245 i
7
-2.0847 + 0.1301 i
0.0000711 - 0.00138 i
8
-2.0847 - 0.1301 i
0.0000711 + 0.00138 i
9
-2.1211
0.000862
10
-2.3031
0.00183 i
11
3.1013
0.82
12
4.0998
1.71e3 i
13
-4.8832
0.104
14
28.0812
108.
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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
1.4488 + 0.479 i
0.125 - 0.189 i
Singularities of quadratic [8, 7, 7] approximant
2
1.4488 - 0.479 i
0.125 + 0.189 i
3
1.6915 + 0.3661 i
0.331 + 0.0264 i
4
1.6915 - 0.3661 i
0.331 - 0.0264 i
5
1.8383 + 0.3175 i
1.26 + 0.268 i
6
1.8383 - 0.3175 i
1.26 - 0.268 i
7
-2.2409 + 0.0131 i
0.0505 + 0.0518 i
8
-2.2409 - 0.0131 i
0.0505 - 0.0518 i
9
2.4187
0.499
10
-3.4923 + 0.2088 i
0.67 - 0.342 i
11
-3.4923 - 0.2088 i
0.67 + 0.342 i
12
5.5873
1.63 i
13
-5.8591
0.282
14
-14.3575
0.438 i
15
25.2931
3.59
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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
1.4451 + 0.4767 i
0.0922 - 0.18 i
Singularities of quadratic [8, 8, 7] approximant
2
1.4451 - 0.4767 i
0.0922 + 0.18 i
3
1.7506 + 0.3492 i
0.351 - 0.0566 i
4
1.7506 - 0.3492 i
0.351 + 0.0566 i
5
1.8631 + 0.2848 i
0.638 + 0.0728 i
6
1.8631 - 0.2848 i
0.638 - 0.0728 i
7
-2.0965
0.00092
8
-2.0967 + 0.0996 i
0.000191 - 0.00133 i
9
-2.0967 - 0.0996 i
0.000191 + 0.00133 i
10
-2.3549
0.00289 i
11
2.425
0.555
12
-5.2239
0.0858
13
8.2061
0.335 i
14
-4.6565 + 9.6764 i
0.129 + 0.093 i
15
-4.6565 - 9.6764 i
0.129 - 0.093 i
16
-14.2617
0.693 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
1.4423 + 0.4785 i
0.095 - 0.153 i
Singularities of quadratic [8, 8, 8] approximant
2
1.4423 - 0.4785 i
0.095 + 0.153 i
3
1.7001
0.128
4
1.8497 + 0.1819 i
0.112 - 0.277 i
5
1.8497 - 0.1819 i
0.112 + 0.277 i
6
2.178 + 0.49 i
1.21 + 0.609 i
7
2.178 - 0.49 i
1.21 - 0.609 i
8
-2.2393 + 0.0607 i
0.00498 + 0.00587 i
9
-2.2393 - 0.0607 i
0.00498 - 0.00587 i
10
-2.7995 + 0.0958 i
0.0114 + 0.00682 i
11
-2.7995 - 0.0958 i
0.0114 - 0.00682 i
12
-5.0631
0.116
13
4.4713 + 2.9541 i
0.336 + 0.115 i
14
4.4713 - 2.9541 i
0.336 - 0.115 i
15
7.7631
0.444 i
16
16.6673
4.38
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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
1.4437 + 0.4748 i
0.0746 - 0.18 i
Singularities of quadratic [9, 8, 8] approximant
2
1.4437 - 0.4748 i
0.0746 + 0.18 i
3
1.8069 + 0.3684 i
0.471 - 0.217 i
4
1.8069 - 0.3684 i
0.471 + 0.217 i
5
1.8386 + 0.2632 i
0.381 - 0.000196 i
6
1.8386 - 0.2632 i
0.381 + 0.000196 i
7
-2.2278 + 0.0852 i
0.00273 + 0.00352 i
8
-2.2278 - 0.0852 i
0.00273 - 0.00352 i
9
2.5553
0.866
10
-2.6749 + 0.0854 i
0.00547 + 0.00316 i
11
-2.6749 - 0.0854 i
0.00547 - 0.00316 i
12
3.8764 + 3.0664 i
0.14 - 0.0793 i
13
3.8764 - 3.0664 i
0.14 + 0.0793 i
14
-5.4294
0.125
15
5.8291 + 4.5725 i
0.0557 + 0.152 i
16
5.8291 - 4.5725 i
0.0557 - 0.152 i
17
-18.0796
0.691 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
1.4425 + 0.4767 i
0.0851 - 0.163 i
Singularities of quadratic [9, 9, 8] approximant
2
1.4425 - 0.4767 i
0.0851 + 0.163 i
3
1.7543
0.14
4
1.9305 + 0.2007 i
0.0712 - 0.327 i
5
1.9305 - 0.2007 i
0.0712 + 0.327 i
6
2.133 + 0.4287 i
0.0913 + 1.82 i
7
2.133 - 0.4287 i
0.0913 - 1.82 i
8
-2.23 + 0.0824 i
0.00286 + 0.00387 i
9
-2.23 - 0.0824 i
0.00286 - 0.00387 i
10
-2.6399 + 0.0815 i
0.00531 + 0.00314 i
11
-2.6399 - 0.0815 i
0.00531 - 0.00314 i
12
2.8306
8.07 i
13
4.3625 + 0.8183 i
1.81 - 0.458 i
14
4.3625 - 0.8183 i
1.81 + 0.458 i
15
-5.2062
0.11
16
-2.465 + 19.0334 i
0.401 + 0.144 i
17
-2.465 - 19.0334 i
0.401 - 0.144 i
18
-34.7842
5.65 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
1.4434 + 0.4751 i
0.075 - 0.176 i
Singularities of quadratic [9, 9, 9] approximant
2
1.4434 - 0.4751 i
0.075 + 0.176 i
3
1.8146 + 0.351 i
0.379 - 0.23 i
4
1.8146 - 0.351 i
0.379 + 0.23 i
5
1.8657 + 0.267 i
0.381 - 0.000341 i
6
1.8657 - 0.267 i
0.381 + 0.000341 i
7
-2.0549
0.000617
8
-2.0825 + 0.0734 i
0.000208 - 0.000803 i
9
-2.0825 - 0.0734 i
0.000208 + 0.000803 i
10
2.414
0.629
11
-2.4418
0.00332 i
12
-2.9848
0.0357
13
-3.1787
0.504 i
14
-4.6058
0.1
15
4.3822 + 3.8285 i
0.172 + 0.0446 i
16
4.3822 - 3.8285 i
0.172 - 0.0446 i
17
5.4707 + 7.4915 i
0.139 - 0.173 i
18
5.4707 - 7.4915 i
0.139 + 0.173 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
0.6016
1.39e-6
Singularities of quadratic [10, 9, 9] approximant
2
0.6016
1.39e-6 i
3
1.4448 + 0.477 i
0.104 - 0.181 i
4
1.4448 - 0.477 i
0.104 + 0.181 i
5
1.7858 + 0.1003 i
0.136 - 0.0712 i
6
1.7858 - 0.1003 i
0.136 + 0.0712 i
7
1.8732 + 0.3048 i
0.273 - 0.666 i
8
1.8732 - 0.3048 i
0.273 + 0.666 i
9
-2.2174 + 0.0995 i
0.00203 + 0.00263 i
10
-2.2174 - 0.0995 i
0.00203 - 0.00263 i
11
-2.6503 + 0.0793 i
0.00395 + 0.00228 i
12
-2.6503 - 0.0793 i
0.00395 - 0.00228 i
13
3.0851 + 0.7604 i
0.383 - 0.217 i
14
3.0851 - 0.7604 i
0.383 + 0.217 i
15
3.202 + 2.0208 i
0.036 + 0.137 i
16
3.202 - 2.0208 i
0.036 - 0.137 i
17
-5.8938
0.157
18
8.4744
0.187
19
-12.5196
1.33 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
-0.5859
6.e-8
Singularities of quadratic [10, 10, 9] approximant
2
-0.5859
6.e-8 i
3
1.4454 + 0.4741 i
0.0779 - 0.2 i
4
1.4454 - 0.4741 i
0.0779 + 0.2 i
5
1.7616 + 0.3933 i
0.483 - 0.0173 i
6
1.7616 - 0.3933 i
0.483 + 0.0173 i
7
1.7842 + 0.2756 i
0.436 + 0.0784 i
8
1.7842 - 0.2756 i
0.436 - 0.0784 i
9
-2.1965 + 0.1246 i
0.00136 + 0.00148 i
10
-2.1965 - 0.1246 i
0.00136 - 0.00148 i
11
-2.7527 + 0.0392 i
0.00213 + 0.00162 i
12
-2.7527 - 0.0392 i
0.00213 - 0.00162 i
13
2.8482
1.91
14
1.6193 + 3.4009 i
0.00879 - 0.0127 i
15
1.6193 - 3.4009 i
0.00879 + 0.0127 i
16
1.4757 + 3.5332 i
0.0116 + 0.00882 i
17
1.4757 - 3.5332 i
0.0116 - 0.00882 i
18
-6.0147 + 2.8093 i
0.0651 + 0.09 i
19
-6.0147 - 2.8093 i
0.0651 - 0.09 i
20
51.6754
0.46 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
-0.1026 + 0.8226 i
1.59e-6 + 2.06e-6 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.1026 - 0.8226 i
1.59e-6 - 2.06e-6 i
3
-0.1026 + 0.8226 i
2.06e-6 - 1.59e-6 i
4
-0.1026 - 0.8226 i
2.06e-6 + 1.59e-6 i
5
1.4426 + 0.4747 i
0.0679 - 0.17 i
6
1.4426 - 0.4747 i
0.0679 + 0.17 i
7
1.8044 + 0.3551 i
0.388 - 0.133 i
8
1.8044 - 0.3551 i
0.388 + 0.133 i
9
1.8945 + 0.3188 i
0.65 + 0.085 i
10
1.8945 - 0.3188 i
0.65 - 0.085 i
11
-2.228 + 0.086 i
0.00281 + 0.00332 i
12
-2.228 - 0.086 i
0.00281 - 0.00332 i
13
2.2982
0.496
14
-2.7167 + 0.0907 i
0.00647 + 0.00357 i
15
-2.7167 - 0.0907 i
0.00647 - 0.00357 i
16
-5.2252
0.121
17
5.6882 + 3.8464 i
0.253 + 0.248 i
18
5.6882 - 3.8464 i
0.253 - 0.248 i
19
9.564 + 9.5224 i
0.889 - 0.247 i
20
9.564 - 9.5224 i
0.889 + 0.247 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
-0.1104 + 0.7906 i
1.49e-6 + 2.24e-6 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.1104 - 0.7906 i
1.49e-6 - 2.24e-6 i
3
-0.1104 + 0.7906 i
2.24e-6 - 1.49e-6 i
4
-0.1104 - 0.7906 i
2.24e-6 + 1.49e-6 i
5
1.443 + 0.4748 i
0.0704 - 0.174 i
6
1.443 - 0.4748 i
0.0704 + 0.174 i
7
1.8085 + 0.3587 i
0.391 - 0.182 i
8
1.8085 - 0.3587 i
0.391 + 0.182 i
9
1.8708 + 0.2954 i
0.467 + 0.0522 i
10
1.8708 - 0.2954 i
0.467 - 0.0522 i
11
-2.2273 + 0.0867 i
0.00272 + 0.00333 i
12
-2.2273 - 0.0867 i
0.00272 - 0.00333 i
13
2.3845
0.586
14
-2.6954 + 0.088 i
0.00587 + 0.0033 i
15
-2.6954 - 0.088 i
0.00587 - 0.0033 i
16
-5.3211
0.123
17
4.6756 + 3.4663 i
0.249 + 0.0326 i
18
4.6756 - 3.4663 i
0.249 - 0.0326 i
19
6.7587 + 6.4363 i
0.0482 - 0.305 i
20
6.7587 - 6.4363 i
0.0482 + 0.305 i
21
-27.6438
0.544 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
-0.0163 + 0.7982 i
5.29e-7 + 5.49e-7 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.0163 - 0.7982 i
5.29e-7 - 5.49e-7 i
3
-0.0163 + 0.7982 i
5.49e-7 - 5.29e-7 i
4
-0.0163 - 0.7982 i
5.49e-7 + 5.29e-7 i
5
1.4185 + 0.0031 i
0.00757 - 0.00737 i
6
1.4185 - 0.0031 i
0.00757 + 0.00737 i
7
1.4441 + 0.4816 i
0.138 - 0.127 i
8
1.4441 - 0.4816 i
0.138 + 0.127 i
9
1.8688 + 0.5088 i
0.472 + 0.192 i
10
1.8688 - 0.5088 i
0.472 - 0.192 i
11
2.0514 + 0.6848 i
0.353 + 0.0525 i
12
2.0514 - 0.6848 i
0.353 - 0.0525 i
13
-2.2089
0.00682
14
2.3127
0.522
15
-2.3748
0.0194 i
16
-2.4386 + 0.0526 i
0.00414 + 0.0127 i
17
-2.4386 - 0.0526 i
0.00414 - 0.0127 i
18
-4.9397
0.0902
19
5.3763
2.64 i
20
-2.4494 + 14.127 i
0.244 + 0.013 i
21
-2.4494 - 14.127 i
0.244 - 0.013 i
22
-22.5129
35.3 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
-0.4127
6.48e-10
Singularities of quadratic [11, 11, 11] approximant
2
-0.4127
6.48e-10 i
3
-0.1007 + 0.7448 i
3.57e-7 - 1.01e-7 i
4
-0.1007 - 0.7448 i
3.57e-7 + 1.01e-7 i
5
-0.1007 + 0.7448 i
1.01e-7 + 3.57e-7 i
6
-0.1007 - 0.7448 i
1.01e-7 - 3.57e-7 i
7
1.4439 + 0.4749 i
0.0767 - 0.184 i
8
1.4439 - 0.4749 i
0.0767 + 0.184 i
9
1.8333 + 0.3463 i
0.369 - 0.353 i
10
1.8333 - 0.3463 i
0.369 + 0.353 i
11
1.8548 + 0.2364 i
0.292 - 0.0434 i
12
1.8548 - 0.2364 i
0.292 + 0.0434 i
13
-2.2202 + 0.1 i
0.00233 + 0.00221 i
14
-2.2202 - 0.1 i
0.00233 - 0.00221 i
15
2.3947
0.648
16
-2.8423 + 0.1036 i
0.00872 + 0.00409 i
17
-2.8423 - 0.1036 i
0.00872 - 0.00409 i
18
-5.3576
0.144
19
4.644 + 3.2702 i
0.226 + 0.117 i
20
4.644 - 3.2702 i
0.226 - 0.117 i
21
9.4973
0.544 i
22
21.245
74.5
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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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Designed by A. Sergeev.