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 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
1.3266
0.209
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
1.2655
0.19
Singularities of quadratic [1, 1, 0] approximant
2
2330.8819
8.15 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
1.5034
0.365
Singularities of quadratic [1, 1, 1] approximant
2
-8.0256
0.923
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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
1.4649
0.327
Singularities of quadratic [2, 1, 1] approximant
2
-4.8483
0.591
3
-10.0292
0.378 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
1.4511
0.303
Singularities of quadratic [2, 2, 1] approximant
2
-5.9117
1.23
3
-12.6584
0.551 i
4
401.2391
2.74 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
1.4862
0.397
Singularities of quadratic [2, 2, 2] approximant
2
4.1327
0.718 i
3
-5.6098
0.455
4
5.8961
2.5
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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
0.8405
0.0291
Singularities of quadratic [3, 2, 2] approximant
2
0.8492
0.0288 i
3
1.3986
0.191
4
-5.1962
0.441
5
-18.7404
0.365 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
1.5945 + 0.3265 i
0.313 - 0.153 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5945 - 0.3265 i
0.313 + 0.153 i
3
2.3204
0.853
4
-3.8461
0.119
5
-12.8023
0.179 i
6
18.08
0.358 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
1.5889 + 0.3254 i
0.305 - 0.16 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5889 - 0.3254 i
0.305 + 0.16 i
3
2.2826
0.764
4
-3.8341
0.119
5
-11.8272
0.176 i
6
21.3656
0.352 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
1.6162 + 0.3647 i
0.275 - 0.015 i
Singularities of quadratic [4, 3, 3] approximant
2
1.6162 - 0.3647 i
0.275 + 0.015 i
3
2.6218
5.56
4
-3.5058
0.0624
5
-1.5792 + 8.8541 i
0.0332 + 0.12 i
6
-1.5792 - 8.8541 i
0.0332 - 0.12 i
7
-78.4277
0.902 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
1.6058 + 0.344 i
0.307 - 0.0756 i
Singularities of quadratic [4, 4, 3] approximant
2
1.6058 - 0.344 i
0.307 + 0.0756 i
3
-1.8562
0.0112
4
-1.8742
0.0113 i
5
2.4196
1.38
6
-4.2947
0.363
7
-9.9979
0.178 i
8
22.4052
0.368 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
1.5966 + 0.3004 i
0.294 - 0.305 i
Singularities of quadratic [4, 4, 4] approximant
2
1.5966 - 0.3004 i
0.294 + 0.305 i
3
-2.1239 + 0.02 i
0.00735 + 0.00748 i
4
-2.1239 - 0.02 i
0.00735 - 0.00748 i
5
2.4106
0.774
6
-3.6714
0.0548
7
5.6591
0.879 i
8
25.651
2.58
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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
1.5948 + 0.2942 i
0.265 - 0.341 i
Singularities of quadratic [5, 4, 4] approximant
2
1.5948 - 0.2942 i
0.265 + 0.341 i
3
-1.9107 + 0.0117 i
0.00422 + 0.00425 i
4
-1.9107 - 0.0117 i
0.00422 - 0.00425 i
5
2.4393
0.775
6
-3.5602
0.0463
7
5.3328
0.928 i
8
16.3228 + 17.075 i
0.311 + 0.603 i
9
16.3228 - 17.075 i
0.311 - 0.603 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
1.051
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 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
1.1645
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 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
1.4189 + 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 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
1.3999 + 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 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
-0.6945 + 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 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
1.4038
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 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
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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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.