Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 1.7r_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
1.1135
0.189
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
0.9841
0.148
Singularities of quadratic [1, 1, 0] approximant
2
274.355
2.48 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
1.4224
0.704
Singularities of quadratic [1, 1, 1] approximant
2
-3.2318
0.301
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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
1.5313
1.15
Singularities of quadratic [2, 1, 1] approximant
2
-4.0974
0.363
3
8.5416
0.372 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
-1.9337
0.0566
Singularities of quadratic [2, 2, 1] approximant
2
2.0876
2.07
3
-4.2277
0.0765 i
4
4.7862
0.2 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
1.6421 + 0.6788 i
0.464 + 0.00858 i
Singularities of quadratic [2, 2, 2] approximant
2
1.6421 - 0.6788 i
0.464 - 0.00858 i
3
-2.8094
0.157
4
3.6766
2.52
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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
1.1865 + 0.0973 i
0.0522 - 0.0378 i
Singularities of quadratic [3, 2, 2] approximant
2
1.1865 - 0.0973 i
0.0522 + 0.0378 i
3
2.9973
0.262
4
-3.087 + 1.3755 i
0.156 + 0.0412 i
5
-3.087 - 1.3755 i
0.156 - 0.0412 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
1.5347 + 0.417 i
0.252 - 1.13 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5347 - 0.417 i
0.252 + 1.13 i
3
1.9844
0.486
4
-2.6923
0.164
5
-10.9387
0.2 i
6
33.6489
0.433 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
1.1873 + 0.4429 i
0.0121 - 0.0383 i
Singularities of quadratic [3, 3, 3] approximant
2
1.1873 - 0.4429 i
0.0121 + 0.0383 i
3
1.2647 + 0.1971 i
0.0333 - 0.00873 i
4
1.2647 - 0.1971 i
0.0333 + 0.00873 i
5
-2.5386
0.0922
6
4.4505
1.06
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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
1.5188 + 0.456 i
0.285 - 0.746 i
Singularities of quadratic [4, 3, 3] approximant
2
1.5188 - 0.456 i
0.285 + 0.746 i
3
2.0963
0.483
4
-2.9024
0.308
5
-5.4061
0.357 i
6
7.616
0.697 i
7
743.7
115.
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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
-0.9545 + 0.0004 i
0.00148 + 0.00148 i
Singularities of quadratic [4, 4, 3] approximant
2
-0.9545 - 0.0004 i
0.00148 - 0.00148 i
3
1.5334 + 0.5152 i
0.585 - 0.105 i
4
1.5334 - 0.5152 i
0.585 + 0.105 i
5
1.814
0.443
6
-2.8878
0.427
7
-7.7823
0.171 i
8
21.8868
0.346 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
1.3854 + 0.2537 i
0.0876 - 0.0941 i
Singularities of quadratic [4, 4, 4] approximant
2
1.3854 - 0.2537 i
0.0876 + 0.0941 i
3
1.4259
0.114
4
1.7238 + 0.5984 i
0.199 - 0.343 i
5
1.7238 - 0.5984 i
0.199 + 0.343 i
6
-3.3524
29.3
7
-3.7733
0.973 i
8
-14.5475
15.4
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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
1.4658 + 0.4254 i
0.0304 + 0.504 i
Singularities of quadratic [5, 4, 4] approximant
2
1.4658 - 0.4254 i
0.0304 - 0.504 i
3
1.5272 + 0.0546 i
0.4 - 0.218 i
4
1.5272 - 0.0546 i
0.4 + 0.218 i
5
2.239
0.465
6
-3.1062
0.743
7
-4.1451
0.852 i
8
11.5771
0.614 i
9
-17.9436
1.68
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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
0.9333 + 0.0002 i
0.000994 - 0.000993 i
Singularities of quadratic [5, 5, 4] approximant
2
0.9333 - 0.0002 i
0.000994 + 0.000993 i
3
1.4013 + 0.4414 i
0.0257 + 0.136 i
4
1.4013 - 0.4414 i
0.0257 - 0.136 i
5
2.8782
1.02
6
-2.9013
0.051
7
-2.9999
0.0619 i
8
-4.6587
0.121
9
8.0288
0.413 i
10
-16.1005
0.187 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
0.5797 + 1.0685 i
0.00164 - 0.000274 i
Singularities of quadratic [5, 5, 5] approximant
2
0.5797 - 1.0685 i
0.00164 + 0.000274 i
3
0.5808 + 1.0696 i
0.000274 + 0.00164 i
4
0.5808 - 1.0696 i
0.000274 - 0.00164 i
5
1.4041 + 0.4326 i
0.0624 + 0.132 i
6
1.4041 - 0.4326 i
0.0624 - 0.132 i
7
2.6065
0.857
8
-3.265
65.4
9
-4.7302
0.193 i
10
81.3671
0.214 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
0.3168 + 1.0472 i
0.000572 + 0.000328 i
Singularities of quadratic [6, 5, 5] approximant
2
0.3168 - 1.0472 i
0.000572 - 0.000328 i
3
0.3165 + 1.0477 i
0.000328 - 0.000572 i
4
0.3165 - 1.0477 i
0.000328 + 0.000572 i
5
1.4031 + 0.4315 i
0.0627 + 0.131 i
6
1.4031 - 0.4315 i
0.0627 - 0.131 i
7
2.671
0.934
8
-3.3162
24.
9
-5.0643
0.142 i
10
13.1736 + 32.2699 i
0.053 + 0.329 i
11
13.1736 - 32.2699 i
0.053 - 0.329 i
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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
1.0812
0.00581
Singularities of quadratic [6, 6, 5] approximant
2
1.0838
0.00583 i
3
1.3969 + 0.4403 i
0.0262 + 0.134 i
4
1.3969 - 0.4403 i
0.0262 - 0.134 i
5
-1.5471 + 1.8361 i
0.000768 + 0.00855 i
6
-1.5471 - 1.8361 i
0.000768 - 0.00855 i
7
-1.594 + 1.8313 i
0.00856 - 0.000721 i
8
-1.594 - 1.8313 i
0.00856 + 0.000721 i
9
3.2403
2.13
10
-3.3954
1.39
11
6.1518
0.561 i
12
-9.1811
0.103 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
1.4116
0.0692
Singularities of quadratic [6, 6, 6] approximant
2
1.4539
0.0776 i
3
1.4014 + 0.452 i
0.00524 - 0.171 i
4
1.4014 - 0.452 i
0.00524 + 0.171 i
5
-1.8366 + 0.0046 i
0.00406 + 0.00406 i
6
-1.8366 - 0.0046 i
0.00406 - 0.00406 i
7
2.6407 + 1.236 i
0.153 + 0.283 i
8
2.6407 - 1.236 i
0.153 - 0.283 i
9
-3.1329 + 0.0758 i
0.109 + 0.0587 i
10
-3.1329 - 0.0758 i
0.109 - 0.0587 i
11
5.4895
0.345
12
-7.7585
0.284
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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
0.0309
0
Singularities of quadratic [7, 6, 6] approximant
2
0.0309
0
3
1.3781 + 0.447 i
0.0241 + 0.0852 i
4
1.3781 - 0.447 i
0.0241 - 0.0852 i
5
-1.7615
0.00118
6
-1.778
0.00121 i
7
2.0667
0.736
8
2.3104
0.529 i
9
2.6707 + 2.7179 i
0.0496 + 0.0269 i
10
2.6707 - 2.7179 i
0.0496 - 0.0269 i
11
-5.0504
0.0659
12
1.7264 + 4.8203 i
0.0394 - 0.0123 i
13
1.7264 - 4.8203 i
0.0394 + 0.0123 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
1.3435 + 0.0058 i
0.0099 - 0.00956 i
Singularities of quadratic [7, 7, 6] approximant
2
1.3435 - 0.0058 i
0.0099 + 0.00956 i
3
1.3889 + 0.4755 i
0.0563 - 0.0961 i
4
1.3889 - 0.4755 i
0.0563 + 0.0961 i
5
-2.1133
0.00819
6
-2.1623
0.00841 i
7
2.227 + 0.4432 i
1.62 - 0.25 i
8
2.227 - 0.4432 i
1.62 + 0.25 i
9
2.462
10.9
10
-3.699 + 1.0706 i
0.0155 + 0.102 i
11
-3.699 - 1.0706 i
0.0155 - 0.102 i
12
-6.6498 + 1.6772 i
0.0722 - 0.227 i
13
-6.6498 - 1.6772 i
0.0722 + 0.227 i
14
14.4066
0.271 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

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Designed by A. Sergeev.