Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 1.9r_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
1.0653
0.186
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
0.896
0.133
Singularities of quadratic [1, 1, 0] approximant
2
130.3986
1.6 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
1.349
0.749
Singularities of quadratic [1, 1, 1] approximant
2
-2.7239
0.263
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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
1.4465
1.23
Singularities of quadratic [2, 1, 1] approximant
2
-3.1912
0.292
3
9.4009
0.319 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
-1.7468
0.0586
Singularities of quadratic [2, 2, 1] approximant
2
2.0967
0.959
3
3.8072
0.188 i
4
-4.5809
0.0863 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
1.4886 + 0.6684 i
0.377 + 0.0079 i
Singularities of quadratic [2, 2, 2] approximant
2
1.4886 - 0.6684 i
0.377 - 0.0079 i
3
-2.3407
0.135
4
3.3076
2.08
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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
0.9921 + 0.064 i
0.0244 - 0.0196 i
Singularities of quadratic [3, 2, 2] approximant
2
0.9921 - 0.064 i
0.0244 + 0.0196 i
3
-2.1984 + 1.2391 i
0.0764 + 0.0217 i
4
-2.1984 - 1.2391 i
0.0764 - 0.0217 i
5
3.6429
0.201
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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
1.3969 + 0.3097 i
0.803 + 0.458 i
Singularities of quadratic [3, 3, 2] approximant
2
1.3969 - 0.3097 i
0.803 - 0.458 i
3
1.924
0.448
4
-2.3992
0.21
5
-7.7254
0.198 i
6
57.6812
0.609 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
1.3634 + 0.3133 i
0.394 + 0.162 i
Singularities of quadratic [3, 3, 3] approximant
2
1.3634 - 0.3133 i
0.394 - 0.162 i
3
-1.8415 + 0.4993 i
0.0074 + 0.0344 i
4
-1.8415 - 0.4993 i
0.0074 - 0.0344 i
5
-1.9883
0.0252
6
2.3516
0.38
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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
1.39 + 0.4119 i
0.0392 - 0.706 i
Singularities of quadratic [4, 3, 3] approximant
2
1.39 - 0.4119 i
0.0392 + 0.706 i
3
1.9078
0.435
4
-2.7152
0.733
5
-3.8729
0.649 i
6
5.2542
1.08 i
7
43.0894
3.99
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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
-0.1553 + 0.e-5 i
2.23e-6 + 2.23e-6 i
Singularities of quadratic [4, 4, 3] approximant
2
-0.1553 - 0.e-5 i
2.23e-6 - 2.23e-6 i
3
1.4804
0.253
4
1.4113 + 0.5354 i
0.276 + 0.107 i
5
1.4113 - 0.5354 i
0.276 - 0.107 i
6
-2.8216
9.36
7
-4.5963
0.182 i
8
19.4187
0.314 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
1.2906 + 0.3377 i
0.252 + 0.0393 i
Singularities of quadratic [4, 4, 4] approximant
2
1.2906 - 0.3377 i
0.252 - 0.0393 i
3
1.6557
110.
4
1.695 + 0.3628 i
0.343 - 0.17 i
5
1.695 - 0.3628 i
0.343 + 0.17 i
6
-2.8094 + 0.6201 i
0.294 + 0.157 i
7
-2.8094 - 0.6201 i
0.294 - 0.157 i
8
-8.5097
0.972
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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
1.2984 + 0.4113 i
0.00906 - 0.267 i
Singularities of quadratic [5, 4, 4] approximant
2
1.2984 - 0.4113 i
0.00906 + 0.267 i
3
1.4728 + 0.1197 i
0.233 - 0.0907 i
4
1.4728 - 0.1197 i
0.233 + 0.0907 i
5
2.4456
0.428
6
-2.8228 + 0.5486 i
0.286 + 0.322 i
7
-2.8228 - 0.5486 i
0.286 - 0.322 i
8
-9.308
0.554
9
14.4771
0.578 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
1.1488
0.0138
Singularities of quadratic [5, 5, 4] approximant
2
1.1742
0.0147 i
3
1.2386 + 0.4334 i
0.0158 - 0.0754 i
4
1.2386 - 0.4334 i
0.0158 + 0.0754 i
5
-2.6173 + 0.3602 i
0.225 - 0.09 i
6
-2.6173 - 0.3602 i
0.225 + 0.09 i
7
3.1364
1.42
8
-5.0038
0.119
9
6.9352
0.549 i
10
-26.0318
0.296 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
1.1502
0.0151
Singularities of quadratic [5, 5, 5] approximant
2
1.1798
0.0162 i
3
1.2362 + 0.4321 i
0.0134 - 0.0748 i
4
1.2362 - 0.4321 i
0.0134 + 0.0748 i
5
-2.677 + 0.4295 i
0.193 - 0.275 i
6
-2.677 - 0.4295 i
0.193 + 0.275 i
7
3.7713 + 0.7619 i
0.973 - 1.46 i
8
3.7713 - 0.7619 i
0.973 + 1.46 i
9
-5.6022
0.162
10
26.55
516.
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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
1.321
0.0561
Singularities of quadratic [6, 5, 5] approximant
2
1.2519 + 0.4405 i
0.0309 - 0.106 i
3
1.2519 - 0.4405 i
0.0309 + 0.106 i
4
1.409
0.076 i
5
-2.7667 + 0.6178 i
0.242 + 0.175 i
6
-2.7667 - 0.6178 i
0.242 - 0.175 i
7
2.6114 + 1.4364 i
0.0984 + 0.261 i
8
2.6114 - 1.4364 i
0.0984 - 0.261 i
9
7.6035
0.291
10
-7.6092 + 1.0287 i
1.25 + 1.62 i
11
-7.6092 - 1.0287 i
1.25 - 1.62 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
1.2654 + 0.4427 i
0.0399 - 0.151 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2654 - 0.4427 i
0.0399 + 0.151 i
3
1.4651
0.147
4
1.892 + 0.2121 i
0.907 - 0.136 i
5
1.892 - 0.2121 i
0.907 + 0.136 i
6
2.0311 + 1.0217 i
0.251 + 0.0339 i
7
2.0311 - 1.0217 i
0.251 - 0.0339 i
8
-2.7511 + 0.5455 i
0.196 + 0.348 i
9
-2.7511 - 0.5455 i
0.196 - 0.348 i
10
-5.4343
0.255
11
-21.1425
0.322 i
12
28.2362
0.398 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
-0.6353 + 0.e-5 i
0.0000184 + 0.0000184 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.6353 - 0.e-5 i
0.0000184 - 0.0000184 i
3
1.2582 + 0.4266 i
0.0324 + 0.12 i
4
1.2582 - 0.4266 i
0.0324 - 0.12 i
5
1.5445
0.348
6
1.9205 + 0.6533 i
0.0169 + 0.204 i
7
1.9205 - 0.6533 i
0.0169 - 0.204 i
8
1.842 + 1.2411 i
0.091 + 0.0434 i
9
1.842 - 1.2411 i
0.091 - 0.0434 i
10
-2.6852 + 0.4583 i
0.109 - 0.255 i
11
-2.6852 - 0.4583 i
0.109 + 0.255 i
12
-7.4833
0.344
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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
1.2912 + 0.4285 i
0.158 + 0.264 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2912 - 0.4285 i
0.158 - 0.264 i
3
1.3971 + 0.5274 i
0.291 - 0.133 i
4
1.3971 - 0.5274 i
0.291 + 0.133 i
5
1.5743 + 0.5148 i
1.26 + 0.731 i
6
1.5743 - 0.5148 i
1.26 - 0.731 i
7
2.1493
0.461
8
-2.7593 + 0.6125 i
0.249 + 0.182 i
9
-2.7593 - 0.6125 i
0.249 - 0.182 i
10
-5.6658
0.869
11
6.8537
1.16 i
12
-7.4889
1.69 i
13
119.8042
7.79
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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
1.2677 + 0.4647 i
0.107 - 0.0996 i
Singularities of quadratic [7, 7, 6] approximant
2
1.2677 - 0.4647 i
0.107 + 0.0996 i
3
-1.4907
0.00162
4
-1.4911
0.00162 i
5
1.6188 + 0.2522 i
0.173 - 0.109 i
6
1.6188 - 0.2522 i
0.173 + 0.109 i
7
1.6509
0.146
8
1.9205 + 0.4932 i
1.62 + 0.452 i
9
1.9205 - 0.4932 i
1.62 - 0.452 i
10
-2.802 + 0.5953 i
0.524 + 0.125 i
11
-2.802 - 0.5953 i
0.524 - 0.125 i
12
-4.4502
0.202
13
13.4357
0.3 i
14
-14.7748
0.22 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.