Singularities of Møller-Plesset series: example "BH cc-pVQZ 2Re"

Molecule X 1^Sigma+ State of BH. Basis 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

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

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
1.0145
0.177
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
0.8522
0.126
Singularities of quadratic [1, 1, 0] approximant
2
122.2738
1.51 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
1.3306
0.894
Singularities of quadratic [1, 1, 1] approximant
2
-2.4169
0.223
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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
1.4106
1.4
Singularities of quadratic [2, 1, 1] approximant
2
-2.7006
0.239
3
11.347
0.275 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
-1.6474
0.0599
Singularities of quadratic [2, 2, 1] approximant
2
2.0247
0.974
3
3.8487
0.18 i
4
-5.0165
0.0933 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
1.3609 + 0.6111 i
0.336 - 0.0504 i
Singularities of quadratic [2, 2, 2] approximant
2
1.3609 - 0.6111 i
0.336 + 0.0504 i
3
-2.1331
0.129
4
2.4636
0.83
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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
0.9351 + 0.0601 i
0.0227 - 0.0184 i
Singularities of quadratic [3, 2, 2] approximant
2
0.9351 - 0.0601 i
0.0227 + 0.0184 i
3
-2.047 + 1.1674 i
0.0785 + 0.0201 i
4
-2.047 - 1.1674 i
0.0785 - 0.0201 i
5
3.2904
0.202
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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
1.3214 + 0.301 i
0.709 + 0.407 i
Singularities of quadratic [3, 3, 2] approximant
2
1.3214 - 0.301 i
0.709 - 0.407 i
3
1.792
0.439
4
-2.2679
0.234
5
-7.6017
0.204 i
6
184.3412
1.1 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
1.3129 + 0.3446 i
0.397 + 0.452 i
Singularities of quadratic [3, 3, 3] approximant
2
1.3129 - 0.3446 i
0.397 - 0.452 i
3
1.9386
0.393
4
-1.8922 + 0.5598 i
0.0202 + 0.0646 i
5
-1.8922 - 0.5598 i
0.0202 - 0.0646 i
6
-2.291
0.0509
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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
1.3017 + 0.4224 i
0.115 - 0.51 i
Singularities of quadratic [4, 3, 3] approximant
2
1.3017 - 0.4224 i
0.115 + 0.51 i
3
1.8045
0.385
4
-2.773
3.87
5
-3.1887
2.18 i
6
4.2736
2.13 i
7
30.2862
2.05
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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
-0.1975 + 0.e-4 i
5.58e-6 + 5.58e-6 i
Singularities of quadratic [4, 4, 3] approximant
2
-0.1975 - 0.e-4 i
5.58e-6 - 5.58e-6 i
3
1.3734
0.176
4
1.2934 + 0.5489 i
0.17 + 0.0574 i
5
1.2934 - 0.5489 i
0.17 - 0.0574 i
6
-2.897
2.6
7
-3.9913
0.166 i
8
20.2276
0.299 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
1.2293 + 0.3693 i
0.236 + 0.224 i
Singularities of quadratic [4, 4, 4] approximant
2
1.2293 - 0.3693 i
0.236 - 0.224 i
3
1.5348 + 0.2849 i
0.344 - 0.0904 i
4
1.5348 - 0.2849 i
0.344 + 0.0904 i
5
1.7967
0.893
6
-2.5131 + 0.642 i
0.201 + 0.184 i
7
-2.5131 - 0.642 i
0.201 - 0.184 i
8
-5.7011
0.356
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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
1.1941 + 0.4474 i
0.0664 - 0.111 i
Singularities of quadratic [5, 4, 4] approximant
2
1.1941 - 0.4474 i
0.0664 + 0.111 i
3
1.3904 + 0.0345 i
0.0617 - 0.046 i
4
1.3904 - 0.0345 i
0.0617 + 0.046 i
5
-2.5336 + 0.5539 i
0.0914 + 0.336 i
6
-2.5336 - 0.5539 i
0.0914 - 0.336 i
7
3.0201
0.778
8
-6.8996
0.266
9
7.7455
0.932 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
1.1783 + 0.4516 i
0.0521 - 0.0814 i
Singularities of quadratic [5, 5, 4] approximant
2
1.1783 - 0.4516 i
0.0521 + 0.0814 i
3
1.2731
0.0499
4
1.3621
0.0714 i
5
-2.4979 + 0.4998 i
0.0695 - 0.33 i
6
-2.4979 - 0.4998 i
0.0695 + 0.33 i
7
3.2274
1.35
8
-5.9464
0.181
9
6.5923
0.906 i
10
-261.9871
1.6 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
1.1796 + 0.4513 i
0.0527 - 0.086 i
Singularities of quadratic [5, 5, 5] approximant
2
1.1796 - 0.4513 i
0.0527 + 0.086 i
3
1.2905
0.0589
4
1.3986
0.0918 i
5
-2.5154 + 0.5455 i
0.0576 + 0.331 i
6
-2.5154 - 0.5455 i
0.0576 - 0.331 i
7
3.4429 + 1.1421 i
0.0167 - 0.876 i
8
3.4429 - 1.1421 i
0.0167 + 0.876 i
9
-6.0682
0.244
10
11.5789
0.923
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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
1.1898 + 0.4487 i
0.0552 - 0.114 i
Singularities of quadratic [6, 5, 5] approximant
2
1.1898 - 0.4487 i
0.0552 + 0.114 i
3
1.3824
0.108
4
1.5681
0.255 i
5
-2.5265 + 0.696 i
0.188 + 0.0992 i
6
-2.5265 - 0.696 i
0.188 - 0.0992 i
7
2.5433 + 1.6185 i
0.0761 + 0.245 i
8
2.5433 - 1.6185 i
0.0761 - 0.245 i
9
-5.9915 + 1.7529 i
0.299 + 0.394 i
10
-5.9915 - 1.7529 i
0.299 - 0.394 i
11
10.9231
0.321
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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
1.2053 + 0.4441 i
0.0463 - 0.182 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2053 - 0.4441 i
0.0463 + 0.182 i
3
1.5671
0.281
4
1.6059 + 0.573 i
0.221 + 0.107 i
5
1.6059 - 0.573 i
0.221 - 0.107 i
6
1.7982 + 0.8911 i
0.265 - 0.0843 i
7
1.7982 - 0.8911 i
0.265 + 0.0843 i
8
-2.5376 + 0.6034 i
0.196 + 0.256 i
9
-2.5376 - 0.6034 i
0.196 - 0.256 i
10
-5.7653
0.287
11
29.2217
0.353 i
12
-110.0327
0.65 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
1.2491 + 0.0271 i
0.0626 - 0.0427 i
Singularities of quadratic [6, 6, 6] approximant
2
1.2491 - 0.0271 i
0.0626 + 0.0427 i
3
1.1829 + 0.4562 i
0.0516 - 0.0885 i
4
1.1829 - 0.4562 i
0.0516 + 0.0885 i
5
1.4361
0.506
6
2.1816 + 0.3841 i
0.427 - 0.33 i
7
2.1816 - 0.3841 i
0.427 + 0.33 i
8
2.0549 + 1.3166 i
0.12 + 0.145 i
9
2.0549 - 1.3166 i
0.12 - 0.145 i
10
-2.5339 + 0.6026 i
0.177 + 0.253 i
11
-2.5339 - 0.6026 i
0.177 - 0.253 i
12
-6.3062
0.362
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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
1.2177 + 0.4507 i
0.0994 - 0.254 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2177 - 0.4507 i
0.0994 + 0.254 i
3
1.416 + 0.4735 i
0.338 + 0.109 i
4
1.416 - 0.4735 i
0.338 - 0.109 i
5
1.5987 + 0.4403 i
31.3 + 253. i
6
1.5987 - 0.4403 i
31.3 - 253. i
7
2.1788
0.419
8
-2.5358 + 0.617 i
0.199 + 0.226 i
9
-2.5358 - 0.617 i
0.199 - 0.226 i
10
5.6584
2.36 i
11
-5.9326
0.387
12
-18.2606
0.612 i
13
19.3361
1.31
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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
-1.0817
0.000465
Singularities of quadratic [7, 7, 6] approximant
2
-1.0817
0.000465 i
3
1.2057 + 0.4603 i
0.119 - 0.13 i
4
1.2057 - 0.4603 i
0.119 + 0.13 i
5
1.625
0.215
6
1.618 + 0.3748 i
0.311 - 0.0556 i
7
1.618 - 0.3748 i
0.311 + 0.0556 i
8
1.8834 + 0.6603 i
0.855 - 0.257 i
9
1.8834 - 0.6603 i
0.855 + 0.257 i
10
-2.5556 + 0.6183 i
0.294 + 0.231 i
11
-2.5556 - 0.6183 i
0.294 - 0.231 i
12
-5.0697
0.227
13
16.6234
0.309 i
14
-46.9239
0.425 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.