Singularities of Møller-Plesset series: example "BH cc-pVDZ Re"

Molecule X 1^Sigma+ State of BH. 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 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
0.8526
0.103
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
1.6023
0.455
Singularities of quadratic [1, 1, 0] approximant
2
11.6482
1.23 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
1.4438
0.263
Singularities of quadratic [1, 1, 1] approximant
2
6.4772
478. i
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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
1.4057
0.226
Singularities of quadratic [2, 1, 1] approximant
2
5.1821
15.6 i
3
176.1815
0.387
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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
-0.7165 + 0.0026 i
0.00457 + 0.00455 i
Singularities of quadratic [2, 2, 1] approximant
2
-0.7165 - 0.0026 i
0.00457 - 0.00455 i
3
1.3908
0.185
4
7.654
3.95 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
1.6069 + 0.4681 i
0.216 - 0.00266 i
Singularities of quadratic [2, 2, 2] approximant
2
1.6069 - 0.4681 i
0.216 + 0.00266 i
3
4.0486
1.96
4
-20.5174
0.0435
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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
1.4691 + 0.3201 i
0.0224 - 0.304 i
Singularities of quadratic [3, 2, 2] approximant
2
1.4691 - 0.3201 i
0.0224 + 0.304 i
3
1.8927
0.217
4
4.3112
6.31 i
5
117.5371
0.486
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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
1.5334 + 0.4735 i
0.17 - 0.0255 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5334 - 0.4735 i
0.17 + 0.0255 i
3
3.0058
8.92
4
-6.585
0.0419
5
-9.7211
0.0485 i
6
23.0372
0.221 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
1.5325 + 0.4517 i
0.183 - 0.0613 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5325 - 0.4517 i
0.183 + 0.0613 i
3
2.9297
3.45
4
-5.7768 + 0.494 i
0.0285 + 0.0378 i
5
-5.7768 - 0.494 i
0.0285 - 0.0378 i
6
-91.1162
0.0222
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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
1.5321 + 0.4334 i
0.183 - 0.103 i
Singularities of quadratic [4, 3, 3] approximant
2
1.5321 - 0.4334 i
0.183 + 0.103 i
3
3.0534
4.98
4
-5.3668 + 3.5321 i
0.00892 + 0.0159 i
5
-5.3668 - 3.5321 i
0.00892 - 0.0159 i
6
-3.9307 + 7.2054 i
0.0229 - 0.00595 i
7
-3.9307 - 7.2054 i
0.0229 + 0.00595 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
1.0255
0.0211
Singularities of quadratic [4, 4, 3] approximant
2
1.0277
0.0215 i
3
1.532 + 0.4634 i
0.161 - 0.0446 i
4
1.532 - 0.4634 i
0.161 + 0.0446 i
5
3.1449
33.7
6
-5.8669
0.0316
7
-8.2685
0.036 i
8
28.2434
0.207 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
1.5435 + 0.3442 i
0.0571 + 0.274 i
Singularities of quadratic [4, 4, 4] approximant
2
1.5435 - 0.3442 i
0.0571 - 0.274 i
3
2.2077
9.63
4
2.1605 + 0.7069 i
0.197 + 0.228 i
5
2.1605 - 0.7069 i
0.197 - 0.228 i
6
-5.0142 + 1.1336 i
0.00385 + 0.0053 i
7
-5.0142 - 1.1336 i
0.00385 - 0.0053 i
8
-11.1807
0.00767
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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
1.6156 + 0.4733 i
0.159 + 0.121 i
Singularities of quadratic [5, 4, 4] approximant
2
1.6156 - 0.4733 i
0.159 - 0.121 i
3
1.8497 + 0.0724 i
0.239 - 0.214 i
4
1.8497 - 0.0724 i
0.239 + 0.214 i
5
3.2753 + 1.8691 i
0.025 - 0.167 i
6
3.2753 - 1.8691 i
0.025 + 0.167 i
7
-4.863
0.0109
8
-7.3544
0.0116 i
9
9.6343
0.097
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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
1.6234 + 0.4544 i
0.223 + 0.141 i
Singularities of quadratic [5, 5, 4] approximant
2
1.6234 - 0.4544 i
0.223 - 0.141 i
3
1.8381 + 0.141 i
0.495 - 0.348 i
4
1.8381 - 0.141 i
0.495 + 0.348 i
5
3.7863 + 1.6624 i
0.129 - 0.252 i
6
3.7863 - 1.6624 i
0.129 + 0.252 i
7
-4.8702
0.0119
8
-7.0615
0.0123 i
9
17.2497
0.0617
10
1175.9734
0.264 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
1.4305 + 0.0245 i
0.0328 - 0.0294 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4305 - 0.0245 i
0.0328 + 0.0294 i
3
1.616 + 0.3748 i
0.106 - 2.35 i
4
1.616 - 0.3748 i
0.106 + 2.35 i
5
2.7268 + 0.7745 i
0.0853 + 0.451 i
6
2.7268 - 0.7745 i
0.0853 - 0.451 i
7
4.2417
5.05
8
-4.4914 + 0.9966 i
0.00166 + 0.00286 i
9
-4.4914 - 0.9966 i
0.00166 - 0.00286 i
10
-6.7472
0.00325
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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
1.5419 + 0.0515 i
0.115 - 0.103 i
Singularities of quadratic [6, 5, 5] approximant
2
1.5419 - 0.0515 i
0.115 + 0.103 i
3
1.5966 + 0.3958 i
0.324 - 0.571 i
4
1.5966 - 0.3958 i
0.324 + 0.571 i
5
2.8341 + 0.9717 i
0.28 - 0.325 i
6
2.8341 - 0.9717 i
0.28 + 0.325 i
7
-4.3052 + 0.9079 i
0.000936 + 0.00239 i
8
-4.3052 - 0.9079 i
0.000936 - 0.00239 i
9
4.4592
72.9
10
-5.4452
0.00209
11
-36.0886
0.0134 i
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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
1.53 + 0.0536 i
0.0908 - 0.0723 i
Singularities of quadratic [6, 6, 5] approximant
2
1.53 - 0.0536 i
0.0908 + 0.0723 i
3
1.5973 + 0.3867 i
0.108 - 0.701 i
4
1.5973 - 0.3867 i
0.108 + 0.701 i
5
-2.7265
0.00031
6
-2.754
0.000307 i
7
2.9683 + 1.0723 i
0.339 - 0.13 i
8
2.9683 - 1.0723 i
0.339 + 0.13 i
9
-4.1884
0.0019
10
5.6462
1.06
11
-14.2045
0.00809 i
12
1669.5855
0.185 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
1.2109 + 0.1945 i
0.000195 - 0.00316 i
Singularities of quadratic [6, 6, 6] approximant
2
1.2109 - 0.1945 i
0.000195 + 0.00316 i
3
1.2179 + 0.1875 i
0.00316 + 0.0000928 i
4
1.2179 - 0.1875 i
0.00316 - 0.0000928 i
5
1.6223 + 0.3194 i
0.349 - 0.779 i
6
1.6223 - 0.3194 i
0.349 + 0.779 i
7
2.9723 + 0.8504 i
0.357 - 0.401 i
8
2.9723 - 0.8504 i
0.357 + 0.401 i
9
-4.9102 + 0.8494 i
0.00369 + 0.00594 i
10
-4.9102 - 0.8494 i
0.00369 - 0.00594 i
11
5.1338
8.26
12
-8.9892
0.0071
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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
1.4985 + 0.5466 i
0.0325 + 0.0136 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4985 - 0.5466 i
0.0325 - 0.0136 i
3
1.5979 + 0.5759 i
0.0244 - 0.0338 i
4
1.5979 - 0.5759 i
0.0244 + 0.0338 i
5
1.7554
0.162
6
2.234 + 0.5029 i
0.00208 - 0.171 i
7
2.234 - 0.5029 i
0.00208 + 0.171 i
8
-4.9089
0.0139
9
-6.6544
0.0157 i
10
7.0741
0.386 i
11
7.375 + 4.5985 i
0.219 + 0.42 i
12
7.375 - 4.5985 i
0.219 - 0.42 i
13
40.5827
0.157
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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
1.4761 + 0.5414 i
0.027 + 0.00921 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4761 - 0.5414 i
0.027 - 0.00921 i
3
1.5616 + 0.546 i
0.0161 - 0.0322 i
4
1.5616 - 0.546 i
0.0161 + 0.0322 i
5
1.7636
0.126
6
2.1261
0.141 i
7
2.5967
0.482
8
-4.6788
0.0065
9
7.2833
3.7 i
10
-6.9116 + 2.4758 i
0.00217 - 0.00905 i
11
-6.9116 - 2.4758 i
0.00217 + 0.00905 i
12
-9.966
0.0308 i
13
-10.4407 + 22.5971 i
0.0413 - 0.0044 i
14
-10.4407 - 22.5971 i
0.0413 + 0.0044 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.