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

[n1, n2, n3] 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.