Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 2.0r_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

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
1.0447
0.185
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
0.125
Singularities of quadratic [1, 1, 0] approximant
2
90.9777
1.29 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
1.3109
0.767
Singularities of quadratic [1, 1, 1] approximant
2
-2.5028
0.248
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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
1.3959
1.21
Singularities of quadratic [2, 1, 1] approximant
2
-2.8235
0.266
3
10.5399
0.294 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
-1.654
0.06
Singularities of quadratic [2, 2, 1] approximant
2
2.047
0.859
3
3.5668
0.185 i
4
-4.8073
0.0926 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
1.4018 + 0.6443 i
0.341 - 0.00882 i
Singularities of quadratic [2, 2, 2] approximant
2
1.4018 - 0.6443 i
0.341 + 0.00882 i
3
-2.1448
0.128
4
2.9653
1.5
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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
0.821 + 0.0358 i
0.0105 - 0.00924 i
Singularities of quadratic [3, 2, 2] approximant
2
0.821 - 0.0358 i
0.0105 + 0.00924 i
3
-1.7309 + 1.125 i
0.0448 + 0.0123 i
4
-1.7309 - 1.125 i
0.0448 - 0.0123 i
5
4.7484
0.179
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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
1.3117 + 0.2627 i
0.602 + 0.0636 i
Singularities of quadratic [3, 3, 2] approximant
2
1.3117 - 0.2627 i
0.602 - 0.0636 i
3
1.8756
0.431
4
-2.2763
0.252
5
-6.4693
0.203 i
6
78.5239
0.754 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
1.3015 + 0.3001 i
0.4 + 0.153 i
Singularities of quadratic [3, 3, 3] approximant
2
1.3015 - 0.3001 i
0.4 - 0.153 i
3
-1.857 + 0.5952 i
0.0242 + 0.0516 i
4
-1.857 - 0.5952 i
0.0242 - 0.0516 i
5
2.1179
0.369
6
-2.3738
0.0468
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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
1.3094 + 0.4086 i
0.0759 - 0.543 i
Singularities of quadratic [4, 3, 3] approximant
2
1.3094 - 0.4086 i
0.0759 + 0.543 i
3
1.7687
0.392
4
-2.7382
3.34
5
-3.1932
1.75 i
6
3.8587
2.37 i
7
19.1135
1.49
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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
0.1627
4.65e-6
Singularities of quadratic [4, 4, 3] approximant
2
0.1627
4.65e-6 i
3
1.3177
0.135
4
1.3151 + 0.5601 i
0.135 + 0.0835 i
5
1.3151 - 0.5601 i
0.135 - 0.0835 i
6
-3.1737 + 0.2728 i
0.00819 + 0.331 i
7
-3.1737 - 0.2728 i
0.00819 - 0.331 i
8
16.8282
0.283 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
1.2249 + 0.374 i
0.176 + 0.218 i
Singularities of quadratic [4, 4, 4] approximant
2
1.2249 - 0.374 i
0.176 - 0.218 i
3
1.5309 + 0.2945 i
0.305 - 0.0676 i
4
1.5309 - 0.2945 i
0.305 + 0.0676 i
5
2.1372
0.414
6
-2.5534 + 0.6403 i
0.231 + 0.155 i
7
-2.5534 - 0.6403 i
0.231 - 0.155 i
8
-7.2945
0.61
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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
1.2092 + 0.4302 i
0.0655 - 0.154 i
Singularities of quadratic [5, 4, 4] approximant
2
1.2092 - 0.4302 i
0.0655 + 0.154 i
3
1.4485 + 0.1097 i
0.155 - 0.0581 i
4
1.4485 - 0.1097 i
0.155 + 0.0581 i
5
-2.5602 + 0.5721 i
0.186 + 0.29 i
6
-2.5602 - 0.5721 i
0.186 - 0.29 i
7
2.8718
0.514
8
-8.2734
0.39
9
10.8348
0.721 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
1.177 + 0.4453 i
0.0474 - 0.074 i
Singularities of quadratic [5, 5, 4] approximant
2
1.177 - 0.4453 i
0.0474 + 0.074 i
3
1.2659
0.0455
4
1.3617
0.0664 i
5
-2.4811 + 0.458 i
0.143 - 0.291 i
6
-2.4811 - 0.458 i
0.143 + 0.291 i
7
3.2111
1.29
8
-5.7441
0.15
9
7.0201
0.655 i
10
-50.6093
0.537 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
1.1759 + 0.4449 i
0.0457 - 0.0741 i
Singularities of quadratic [5, 5, 5] approximant
2
1.1759 - 0.4449 i
0.0457 + 0.0741 i
3
1.2633
0.0467
4
1.367
0.0703 i
5
-2.4952 + 0.4864 i
0.0704 - 0.328 i
6
-2.4952 - 0.4864 i
0.0704 + 0.328 i
7
3.7501
5.05
8
4.585
6.39 i
9
-5.9667
0.183
10
36.7277
78.2
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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
1.1878 + 0.4417 i
0.0484 - 0.103 i
Singularities of quadratic [6, 5, 5] approximant
2
1.1878 - 0.4417 i
0.0484 + 0.103 i
3
1.3579
0.0924
4
1.54
0.206 i
5
-2.5046 + 0.718 i
0.157 + 0.063 i
6
-2.5046 - 0.718 i
0.157 - 0.063 i
7
2.6626 + 1.6863 i
0.0351 + 0.243 i
8
2.6626 - 1.6863 i
0.0351 - 0.243 i
9
-4.6562 + 1.4236 i
0.117 + 0.204 i
10
-4.6562 - 1.4236 i
0.117 - 0.204 i
11
19.1322
0.478
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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
1.2044 + 0.4354 i
0.0326 - 0.17 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2044 - 0.4354 i
0.0326 + 0.17 i
3
1.5239
0.254
4
1.6074 + 0.5634 i
0.198 + 0.0962 i
5
1.6074 - 0.5634 i
0.198 - 0.0962 i
6
1.8092 + 0.9091 i
0.222 - 0.0718 i
7
1.8092 - 0.9091 i
0.222 + 0.0718 i
8
-2.5348 + 0.5802 i
0.197 + 0.272 i
9
-2.5348 - 0.5802 i
0.197 - 0.272 i
10
-5.3132
0.248
11
-22.1475
0.324 i
12
24.682
0.371 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
-0.5617 + 0.e-5 i
0.0000119 + 0.0000119 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.5617 - 0.e-5 i
0.0000119 - 0.0000119 i
3
1.1809 + 0.4111 i
0.0377 + 0.0723 i
4
1.1809 - 0.4111 i
0.0377 - 0.0723 i
5
1.3492 + 0.8382 i
0.0344 + 0.0266 i
6
1.3492 - 0.8382 i
0.0344 - 0.0266 i
7
1.6313
0.568
8
1.4334 + 0.9849 i
0.0408 - 0.028 i
9
1.4334 - 0.9849 i
0.0408 + 0.028 i
10
-2.4945 + 0.5266 i
0.00778 + 0.256 i
11
-2.4945 - 0.5266 i
0.00778 - 0.256 i
12
-8.0542
0.517
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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
1.2268 + 0.4411 i
0.0773 - 0.352 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2268 - 0.4411 i
0.0773 + 0.352 i
3
1.3629 + 0.4613 i
0.417 + 0.126 i
4
1.3629 - 0.4613 i
0.417 - 0.126 i
5
1.5336 + 0.4115 i
2.47 + 6.22 i
6
1.5336 - 0.4115 i
2.47 - 6.22 i
7
2.2445
0.442
8
-2.5318 + 0.6058 i
0.204 + 0.213 i
9
-2.5318 - 0.6058 i
0.204 - 0.213 i
10
-5.3587
0.412
11
6.3267
1.27 i
12
-9.1568
0.742 i
13
63.8252
4.85
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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
1.2073 + 0.4543 i
0.116 - 0.126 i
Singularities of quadratic [7, 7, 6] approximant
2
1.2073 - 0.4543 i
0.116 + 0.126 i
3
1.5533 + 0.3727 i
0.286 - 0.0182 i
4
1.5533 - 0.3727 i
0.286 + 0.0182 i
5
1.671
0.25
6
1.8542 + 0.5356 i
1.29 + 0.0335 i
7
1.8542 - 0.5356 i
1.29 - 0.0335 i
8
-1.9816
0.0208
9
-1.994
0.0209 i
10
-2.5867 + 0.5698 i
0.707 + 0.476 i
11
-2.5867 - 0.5698 i
0.707 - 0.476 i
12
-4.3293
0.162
13
12.9419
0.308 i
14
-16.9754
0.236 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.