Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 1.4r_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 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 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-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 [1, 0, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2012
0.196
Singularities of quadratic [1, 0, 0] approximant
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Table 2. Singularities with their weights for the quadratic approximant [1, 1, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.1155
0.17
Singularities of quadratic [1, 1, 0] approximant
2
846.1994
4.67 i
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Table 3. Singularities with their weights for the quadratic approximant [1, 1, 1]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5047
0.582
Singularities of quadratic [1, 1, 1] approximant
2
-4.3348
0.401
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Table 4. Singularities with their weights for the quadratic approximant [2, 1, 1]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5658
0.725
Singularities of quadratic [2, 1, 1] approximant
2
-5.5523
0.499
3
12.9771
0.411 i
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Table 5. Singularities with their weights for the quadratic approximant [2, 2, 1]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.8227
13.
Singularities of quadratic [2, 2, 1] approximant
2
-2.4124
0.0723
3
-4.7512
0.0884 i
4
10.3213
0.266 i
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Table 6. Singularities with their weights for the quadratic approximant [2, 2, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.8851 + 0.522 i
0.873 - 0.0903 i
Singularities of quadratic [2, 2, 2] approximant
2
1.8851 - 0.522 i
0.873 + 0.0903 i
3
3.6744
2.26
4
-3.7148
0.215
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Table 7. Singularities with their weights for the quadratic approximant [3, 2, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.0358 + 0.029 i
0.0186 - 0.0173 i
Singularities of quadratic [3, 2, 2] approximant
2
1.0358 - 0.029 i
0.0186 + 0.0173 i
3
2.2369
0.722
4
-4.3549 + 1.6762 i
0.274 + 0.0334 i
5
-4.3549 - 1.6762 i
0.274 - 0.0334 i
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Table 8. Singularities with their weights for the quadratic approximant [3, 3, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5877 + 0.3929 i
0.341 - 0.613 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5877 - 0.3929 i
0.341 + 0.613 i
3
1.804
0.419
4
-3.2322
0.148
5
-12.8818
0.203 i
6
23.3409
0.371 i
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Table 9. Singularities with their weights for the quadratic approximant [3, 3, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5872 + 0.3966 i
0.35 - 0.585 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5872 - 0.3966 i
0.35 + 0.585 i
3
1.8045
0.415
4
-3.2304
0.147
5
-13.3828
0.204 i
6
21.4697
0.371 i
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Table 10. Singularities with their weights for the quadratic approximant [4, 3, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5742 + 0.4406 i
0.358 - 0.262 i
Singularities of quadratic [4, 3, 3] approximant
2
1.5742 - 0.4406 i
0.358 + 0.262 i
3
1.7702
0.348
4
-3.1269
0.111
5
15.3547
0.353 i
6
-2.5484 + 15.7983 i
0.061 + 0.238 i
7
-2.5484 - 15.7983 i
0.061 - 0.238 i
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Table 11. Singularities with their weights for the quadratic approximant [4, 4, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5595 + 0.4531 i
0.297 - 0.209 i
Singularities of quadratic [4, 4, 3] approximant
2
1.5595 - 0.4531 i
0.297 + 0.209 i
3
1.7623
0.321
4
-3.1626
0.122
5
4.1099
0.791 i
6
5.483
477.
7
-18.3768
0.228 i
8
20.5655
0.365 i
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Table 12. Singularities with their weights for the quadratic approximant [4, 4, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.6006 + 0.e-4 i
0.000361 - 0.000361 i
Singularities of quadratic [4, 4, 4] approximant
2
0.6006 - 0.e-4 i
0.000361 + 0.000361 i
3
1.5302 + 0.3728 i
0.122 + 0.266 i
4
1.5302 - 0.3728 i
0.122 - 0.266 i
5
2.1075
0.494
6
-3.0907
0.0947
7
5.6392
0.633 i
8
28.4852
1.19
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Table 13. Singularities with their weights for the quadratic approximant [5, 4, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5017
0.0771
Singularities of quadratic [5, 4, 4] approximant
2
1.4725 + 0.5959 i
0.0576 + 0.0216 i
3
1.4725 - 0.5959 i
0.0576 - 0.0216 i
4
0.6715 + 1.7405 i
0.00769 - 0.00395 i
5
0.6715 - 1.7405 i
0.00769 + 0.00395 i
6
0.7408 + 1.7747 i
0.00441 + 0.00793 i
7
0.7408 - 1.7747 i
0.00441 - 0.00793 i
8
-2.9822
0.0615
9
-17.596
0.437 i
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Table 14. 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
1.5007
0.0535
Singularities of quadratic [5, 5, 4] approximant
2
1.4295 + 0.4749 i
0.0562 - 0.0517 i
3
1.4295 - 0.4749 i
0.0562 + 0.0517 i
4
1.6995
0.131 i
5
-2.3741
0.0183
6
-2.568
0.0201 i
7
3.007
1.62
8
-4.262
1.39
9
-8.999
0.13 i
10
11.1316
0.305 i
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Table 15. 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
1.4935
0.0522
Singularities of quadratic [5, 5, 5] approximant
2
1.4267 + 0.477 i
0.0543 - 0.049 i
3
1.4267 - 0.477 i
0.0543 + 0.049 i
4
1.7067
0.138 i
5
-2.3349
0.0171
6
-2.4984
0.0185 i
7
3.115
2.14
8
-4.063
5.27
9
9.5164
0.322 i
10
-10.4906
0.139 i
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Table 16. 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
1.4537 + 0.4703 i
0.0827 - 0.0812 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4537 - 0.4703 i
0.0827 + 0.0812 i
3
1.6178
0.106
4
1.8912
0.422 i
5
-2.2583
0.0649
6
-2.2941
0.0708 i
7
-3.4485
0.235
8
3.9819 + 0.8356 i
0.869 - 1.84 i
9
3.9819 - 0.8356 i
0.869 + 1.84 i
10
-8.3667
0.309 i
11
30.8806
3.55
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Table 17. 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
1.475 + 0.4637 i
0.118 - 0.129 i
Singularities of quadratic [6, 6, 5] approximant
2
1.475 - 0.4637 i
0.118 + 0.129 i
3
1.7808
0.176
4
2.142
1.02 i
5
-2.2944
0.031
6
-2.3724
0.0324 i
7
2.526 + 1.0785 i
0.494 + 0.0535 i
8
2.526 - 1.0785 i
0.494 - 0.0535 i
9
3.0314
1.39
10
-3.6748
0.924
11
-8.9382
0.181 i
12
22.061
0.35 i
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Table 18. 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
1.4828 + 0.4691 i
0.153 - 0.118 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4828 - 0.4691 i
0.153 + 0.118 i
3
1.8893 + 0.1771 i
0.239 - 0.0557 i
4
1.8893 - 0.1771 i
0.239 + 0.0557 i
5
-2.2857
0.0228
6
-2.3815
0.0239 i
7
2.335 + 0.7474 i
0.52 - 0.759 i
8
2.335 - 0.7474 i
0.52 + 0.759 i
9
2.7825
49.3
10
-3.7264
2.
11
-10.5214
0.162 i
12
12.158
0.298 i
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Table 19. 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
1.4834 + 0.4711 i
0.157 - 0.109 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4834 - 0.4711 i
0.157 + 0.109 i
3
1.8575 + 0.1959 i
0.246 - 0.0429 i
4
1.8575 - 0.1959 i
0.246 + 0.0429 i
5
-2.2846
0.0211
6
-2.3859
0.0223 i
7
2.3123 + 0.7075 i
0.351 - 0.892 i
8
2.3123 - 0.7075 i
0.351 + 0.892 i
9
2.9155
143.
10
-3.7515
2.99
11
-11.2175
0.154 i
12
11.9218
0.283 i
13
-501.2415
1.7
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Table 20. 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
1.4834 + 0.4711 i
0.157 - 0.109 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4834 - 0.4711 i
0.157 + 0.109 i
3
1.8562 + 0.199 i
0.248 - 0.0417 i
4
1.8562 - 0.199 i
0.248 + 0.0417 i
5
-2.2851
0.0217
6
-2.3847
0.0228 i
7
2.307 + 0.6957 i
0.344 - 0.95 i
8
2.307 - 0.6957 i
0.344 + 0.95 i
9
2.9137
71.2
10
-3.7425
2.55
11
-10.6947
0.16 i
12
10.817
0.299 i
13
76.9952
0.904
14
88.0075
0.745 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 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 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-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

Plot of singularities Blank Molecule - icon for Allen-dataList of examples Blank Mathematica programs Blank Work in UMassD Blank Waste iconUnpublished reports

Designed by A. Sergeev.