Singularities of Møller-Plesset series: example "Ar cc-pVDZ"

Molecule Ar. 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

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
2.9464
0.827
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
5.6803 + 7.5385 i
3.99 - 1.33 i
Singularities of quadratic [1, 1, 0] approximant
2
5.6803 - 7.5385 i
3.99 + 1.33 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
-1.2269 + 0.1288 i
0.024 + 0.0221 i
Singularities of quadratic [1, 1, 1] approximant
2
-1.2269 - 0.1288 i
0.024 - 0.0221 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
1.9446
0.12
Singularities of quadratic [2, 1, 1] approximant
2
3.6984
0.199 i
3
-6.0186
0.367
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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
3.221 + 1.389 i
0.473 - 0.0219 i
Singularities of quadratic [2, 2, 1] approximant
2
3.221 - 1.389 i
0.473 + 0.0219 i
3
-0.7023 + 4.6923 i
0.419 - 0.0874 i
4
-0.7023 - 4.6923 i
0.419 + 0.0874 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
2.6541 + 1.3461 i
0.193 - 0.0126 i
Singularities of quadratic [2, 2, 2] approximant
2
2.6541 - 1.3461 i
0.193 + 0.0126 i
3
-1.1217 + 3.8981 i
0.181 - 0.0163 i
4
-1.1217 - 3.8981 i
0.181 + 0.0163 i
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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
2.5988
0.198
Singularities of quadratic [3, 2, 2] approximant
2
1.1208 + 3.7154 i
0.253 + 0.0315 i
3
1.1208 - 3.7154 i
0.253 - 0.0315 i
4
-6.4145 + 4.4305 i
0.224 + 0.0648 i
5
-6.4145 - 4.4305 i
0.224 - 0.0648 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
-2.1208 + 0.02 i
0.00612 + 0.00605 i
Singularities of quadratic [3, 3, 2] approximant
2
-2.1208 - 0.02 i
0.00612 - 0.00605 i
3
2.7265
0.254
4
0.2986 + 3.9097 i
0.0719 + 0.214 i
5
0.2986 - 3.9097 i
0.0719 - 0.214 i
6
11.4434
1.71 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
2.7449
0.301
Singularities of quadratic [3, 3, 3] approximant
2
0.7051 + 4.0041 i
0.278 + 0.188 i
3
0.7051 - 4.0041 i
0.278 - 0.188 i
4
-7.6586 + 2.3488 i
0.109 + 0.0769 i
5
-7.6586 - 2.3488 i
0.109 - 0.0769 i
6
11.5143
1.88 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
2.4733 + 0.4098 i
0.0169 - 0.114 i
Singularities of quadratic [4, 3, 3] approximant
2
2.4733 - 0.4098 i
0.0169 + 0.114 i
3
2.5714
0.0838
4
0.7769 + 4.3333 i
0.401 + 0.484 i
5
0.7769 - 4.3333 i
0.401 - 0.484 i
6
-5.6058 + 12.0383 i
0.667 + 0.241 i
7
-5.6058 - 12.0383 i
0.667 - 0.241 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
3.1778
2.33
Singularities of quadratic [4, 4, 3] approximant
2
3.4985
76.2 i
3
1.2775 + 4.2255 i
0.784 + 0.0464 i
4
1.2775 - 4.2255 i
0.784 - 0.0464 i
5
-1.1978 + 7.191 i
0.664 - 1.16 i
6
-1.1978 - 7.191 i
0.664 + 1.16 i
7
8.7095 + 2.5795 i
3.35 + 4.85 i
8
8.7095 - 2.5795 i
3.35 - 4.85 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
-1.847 + 0.0009 i
0.00107 + 0.00107 i
Singularities of quadratic [4, 4, 4] approximant
2
-1.847 - 0.0009 i
0.00107 - 0.00107 i
3
3.3444
28.
4
3.6981
1.19 i
5
1.7167 + 4.2418 i
0.093 - 0.692 i
6
1.7167 - 4.2418 i
0.093 + 0.692 i
7
-4.8473 + 8.5426 i
0.184 + 0.0281 i
8
-4.8473 - 8.5426 i
0.184 - 0.0281 i
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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
2.935 + 0.3103 i
0.511 + 0.375 i
Singularities of quadratic [5, 4, 4] approximant
2
2.935 - 0.3103 i
0.511 - 0.375 i
3
3.6066
0.42
4
1.1874 + 4.0136 i
0.413 - 0.00688 i
5
1.1874 - 4.0136 i
0.413 + 0.00688 i
6
-2.4279 + 7.6307 i
0.69 - 0.112 i
7
-2.4279 - 7.6307 i
0.69 + 0.112 i
8
20.2565
25.3 i
9
-41.2271
1.11
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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
2.1264 + 1.7812 i
0.0168 - 0.0107 i
Singularities of quadratic [5, 5, 4] approximant
2
2.1264 - 1.7812 i
0.0168 + 0.0107 i
3
2.2579 + 1.7959 i
0.0114 + 0.0174 i
4
2.2579 - 1.7959 i
0.0114 - 0.0174 i
5
0.8483 + 3.855 i
0.071 + 0.155 i
6
0.8483 - 3.855 i
0.071 - 0.155 i
7
4.0946
0.172
8
4.8346
0.161 i
9
0.0363 + 6.4471 i
1.99 - 20. i
10
0.0363 - 6.4471 i
1.99 + 20. 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
-2.8009 + 0.0043 i
0.00154 + 0.00154 i
Singularities of quadratic [5, 5, 5] approximant
2
-2.8009 - 0.0043 i
0.00154 - 0.00154 i
3
3.0741 + 0.2839 i
0.594 + 0.465 i
4
3.0741 - 0.2839 i
0.594 - 0.465 i
5
0.5812 + 3.967 i
0.00681 + 0.162 i
6
0.5812 - 3.967 i
0.00681 - 0.162 i
7
-0.3576 + 5.0388 i
0.0813 + 0.239 i
8
-0.3576 - 5.0388 i
0.0813 - 0.239 i
9
6.531
1.48
10
25.8325
0.612 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
2.6021 + 1.9359 i
0.0236 + 0.0112 i
Singularities of quadratic [6, 5, 5] approximant
2
2.6021 - 1.9359 i
0.0236 - 0.0112 i
3
3.0481 + 1.1819 i
0.00509 + 0.0574 i
4
3.0481 - 1.1819 i
0.00509 - 0.0574 i
5
0.077 + 3.4315 i
0.0217 - 0.0165 i
6
0.077 - 3.4315 i
0.0217 + 0.0165 i
7
2.3772 + 2.6327 i
0.026 - 0.0195 i
8
2.3772 - 2.6327 i
0.026 + 0.0195 i
9
-0.0177 + 3.8677 i
0.0215 + 0.0317 i
10
-0.0177 - 3.8677 i
0.0215 - 0.0317 i
11
-62.8263
0.703
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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
0.4684 + 0.e-5 i
1.73e-7 - 1.73e-7 i
Singularities of quadratic [6, 6, 5] approximant
2
0.4684 - 0.e-5 i
1.73e-7 + 1.73e-7 i
3
2.3551 + 0.038 i
0.00754 - 0.00654 i
4
2.3551 - 0.038 i
0.00754 + 0.00654 i
5
0.2402 + 3.782 i
0.0352 - 0.042 i
6
0.2402 - 3.782 i
0.0352 + 0.042 i
7
-0.4689 + 4.475 i
0.000693 - 0.0807 i
8
-0.4689 - 4.475 i
0.000693 + 0.0807 i
9
4.884 + 1.917 i
0.278 + 0.0836 i
10
4.884 - 1.917 i
0.278 - 0.0836 i
11
-8.8119
0.0615
12
-11.9535
0.104 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
1.39 + 0.0001 i
0.0000867 - 0.0000867 i
Singularities of quadratic [6, 6, 6] approximant
2
1.39 - 0.0001 i
0.0000867 + 0.0000867 i
3
2.3276 + 0.0439 i
0.00536 - 0.00433 i
4
2.3276 - 0.0439 i
0.00536 + 0.00433 i
5
0.1929 + 3.7944 i
0.0461 - 0.0412 i
6
0.1929 - 3.7944 i
0.0461 + 0.0412 i
7
-0.3974 + 4.4065 i
0.00787 + 0.0882 i
8
-0.3974 - 4.4065 i
0.00787 - 0.0882 i
9
5.0787 + 2.626 i
0.228 + 0.257 i
10
5.0787 - 2.626 i
0.228 - 0.257 i
11
-10.9042
0.367
12
-12.2254
1.49 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
2.824 + 0.4434 i
0.076 - 0.12 i
Singularities of quadratic [7, 6, 6] approximant
2
2.824 - 0.4434 i
0.076 + 0.12 i
3
3.1512 + 0.2868 i
0.208 + 0.0695 i
4
3.1512 - 0.2868 i
0.208 - 0.0695 i
5
-3.4222 + 0.0066 i
0.00157 + 0.00157 i
6
-3.4222 - 0.0066 i
0.00157 - 0.00157 i
7
0.179 + 3.728 i
0.0288 - 0.0555 i
8
0.179 - 3.728 i
0.0288 + 0.0555 i
9
-0.256 + 4.1197 i
0.0419 + 0.0517 i
10
-0.256 - 4.1197 i
0.0419 - 0.0517 i
11
4.0676 + 4.2549 i
0.258 - 0.406 i
12
4.0676 - 4.2549 i
0.258 + 0.406 i
13
-27.2584
0.2
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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
-1.4971 + 0.e-5 i
0.0000324 + 0.0000324 i
Singularities of quadratic [7, 7, 6] approximant
2
-1.4971 - 0.e-5 i
0.0000324 - 0.0000324 i
3
2.493 + 0.5695 i
0.0121 - 0.0193 i
4
2.493 - 0.5695 i
0.0121 + 0.0193 i
5
2.584 + 0.5722 i
0.0208 + 0.0129 i
6
2.584 - 0.5722 i
0.0208 - 0.0129 i
7
0.1989 + 3.7565 i
0.0321 - 0.0441 i
8
0.1989 - 3.7565 i
0.0321 + 0.0441 i
9
-0.4014 + 4.2849 i
0.0176 + 0.0634 i
10
-0.4014 - 4.2849 i
0.0176 - 0.0634 i
11
4.7666 + 2.7405 i
0.191 + 0.279 i
12
4.7666 - 2.7405 i
0.191 - 0.279 i
13
-11.1231
0.0849
14
-21.4196
0.226 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.