Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 1.8r_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
1.0882
0.187
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
0.94
0.141
Singularities of quadratic [1, 1, 0] approximant
2
188.5529
1.99 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
1.3865
0.729
Singularities of quadratic [1, 1, 1] approximant
2
-2.9647
0.281
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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
1.493
1.22
Singularities of quadratic [2, 1, 1] approximant
2
-3.6173
0.325
3
8.7359
0.346 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
-1.8387
0.0572
Singularities of quadratic [2, 2, 1] approximant
2
2.1138
1.24
3
4.1797
0.193 i
4
-4.3775
0.0807 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
1.5683 + 0.681 i
0.416 + 0.0146 i
Singularities of quadratic [2, 2, 2] approximant
2
1.5683 - 0.681 i
0.416 - 0.0146 i
3
-2.5614
0.145
4
3.5528
2.48
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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
1.1118 + 0.0868 i
0.0407 - 0.0303 i
Singularities of quadratic [3, 2, 2] approximant
2
1.1118 - 0.0868 i
0.0407 + 0.0303 i
3
-2.6467 + 1.3126 i
0.113 + 0.0321 i
4
-2.6467 - 1.3126 i
0.113 - 0.0321 i
5
3.249
0.23
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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
1.4753 + 0.3686 i
0.439 + 1.14 i
Singularities of quadratic [3, 3, 2] approximant
2
1.4753 - 0.3686 i
0.439 - 1.14 i
3
1.9619
0.467
4
-2.5365
0.181
5
-9.3132
0.197 i
6
43.4038
0.504 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
-0.8534
0.00211
Singularities of quadratic [3, 3, 3] approximant
2
-0.858
0.00211 i
3
1.404 + 0.3148 i
0.303 + 0.108 i
4
1.404 - 0.3148 i
0.303 - 0.108 i
5
-2.1834
0.0487
6
2.756
0.414
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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
1.4606 + 0.4318 i
0.118 - 0.78 i
Singularities of quadratic [4, 3, 3] approximant
2
1.4606 - 0.4318 i
0.118 + 0.78 i
3
2.0416
0.46
4
-2.8085
0.463
5
-4.4617
0.481 i
6
6.7633
0.8 i
7
867.1681
95.
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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
-0.6455 + 0.e-4 i
0.000375 + 0.000375 i
Singularities of quadratic [4, 4, 3] approximant
2
-0.6455 - 0.e-4 i
0.000375 - 0.000375 i
3
1.4827 + 0.516 i
0.502 + 0.0252 i
4
1.4827 - 0.516 i
0.502 - 0.0252 i
5
1.6734
0.386
6
-2.8126
0.904
7
-6.1315
0.167 i
8
21.1285
0.336 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
1.3483 + 0.3068 i
0.181 - 0.0613 i
Singularities of quadratic [4, 4, 4] approximant
2
1.3483 - 0.3068 i
0.181 + 0.0613 i
3
1.5279
0.382
4
1.738 + 0.5381 i
0.294 - 0.252 i
5
1.738 - 0.5381 i
0.294 + 0.252 i
6
-3.1271 + 0.5316 i
0.467 + 0.167 i
7
-3.1271 - 0.5316 i
0.467 - 0.167 i
8
-10.4911
2.09
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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
1.3979 + 0.3901 i
0.254 + 0.439 i
Singularities of quadratic [5, 4, 4] approximant
2
1.3979 - 0.3901 i
0.254 - 0.439 i
3
1.5647 + 0.0917 i
0.688 - 0.201 i
4
1.5647 - 0.0917 i
0.688 + 0.201 i
5
2.0888
0.422
6
-3.1524 + 0.4262 i
0.586 + 0.5 i
7
-3.1524 - 0.4262 i
0.586 - 0.5 i
8
-11.4288
0.923
9
16.7877
0.536 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
0.9568
0.00204
Singularities of quadratic [5, 5, 4] approximant
2
0.958
0.00204 i
3
1.326 + 0.4266 i
0.0204 + 0.101 i
4
1.326 - 0.4266 i
0.0204 - 0.101 i
5
-2.7235 + 0.2419 i
0.125 + 0.0302 i
6
-2.7235 - 0.2419 i
0.125 - 0.0302 i
7
3.0285
1.29
8
-4.5166
0.11
9
7.2155
0.472 i
10
-18.0001
0.207 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
1.0039
0.00398
Singularities of quadratic [5, 5, 5] approximant
2
1.0072
0.004 i
3
1.3214 + 0.4241 i
0.0228 + 0.0972 i
4
1.3214 - 0.4241 i
0.0228 - 0.0972 i
5
-2.9455 + 0.3856 i
0.254 - 0.357 i
6
-2.9455 - 0.3856 i
0.254 + 0.357 i
7
3.2732 + 1.0771 i
0.131 - 0.699 i
8
3.2732 - 1.0771 i
0.131 + 0.699 i
9
-6.1624
0.202
10
11.939
1.97
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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
1.3672
0.0607
Singularities of quadratic [6, 5, 5] approximant
2
1.3334 + 0.4431 i
0.0156 - 0.144 i
3
1.3334 - 0.4431 i
0.0156 + 0.144 i
4
1.4244
0.0719 i
5
2.4475 + 1.2658 i
0.175 + 0.206 i
6
2.4475 - 1.2658 i
0.175 - 0.206 i
7
-3.0914 + 0.5362 i
0.408 + 0.213 i
8
-3.0914 - 0.5362 i
0.408 - 0.213 i
9
4.7882
0.262
10
-10.4992
68.7
11
-11.6902
2.74 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
1.2955
0.0359
Singularities of quadratic [6, 6, 5] approximant
2
1.3295
0.039 i
3
1.3293 + 0.44 i
0.00849 - 0.128 i
4
1.3293 - 0.44 i
0.00849 + 0.128 i
5
2.7119 + 1.3442 i
0.107 + 0.301 i
6
2.7119 - 1.3442 i
0.107 - 0.301 i
7
-3.1103 + 0.5609 i
0.385 + 0.126 i
8
-3.1103 - 0.5609 i
0.385 - 0.126 i
9
-7.2251 + 4.6815 i
0.291 + 0.212 i
10
-7.2251 - 4.6815 i
0.291 - 0.212 i
11
10.5616
0.445
12
52.7312
112. 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
-1.2044 + 0.e-4 i
0.00045 + 0.00045 i
Singularities of quadratic [6, 6, 6] approximant
2
-1.2044 - 0.e-4 i
0.00045 - 0.00045 i
3
1.3344 + 0.4383 i
0.013 + 0.155 i
4
1.3344 - 0.4383 i
0.013 - 0.155 i
5
1.4516
0.14
6
1.5749
0.216 i
7
2.2698 + 1.2789 i
0.129 + 0.147 i
8
2.2698 - 1.2789 i
0.129 - 0.147 i
9
-2.8954 + 0.3587 i
0.207 - 0.158 i
10
-2.8954 - 0.3587 i
0.207 + 0.158 i
11
3.705
0.266
12
-7.4259
0.293
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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
1.3269 + 0.4253 i
0.0639 + 0.0889 i
Singularities of quadratic [7, 6, 6] approximant
2
1.3269 - 0.4253 i
0.0639 - 0.0889 i
3
1.5198 + 0.8033 i
0.0483 + 0.0344 i
4
1.5198 - 0.8033 i
0.0483 - 0.0344 i
5
1.5882 + 0.9294 i
0.0515 - 0.0357 i
6
1.5882 - 0.9294 i
0.0515 + 0.0357 i
7
1.9861
0.623
8
-2.9236 + 1.1453 i
0.0439 - 0.0208 i
9
-2.9236 - 1.1453 i
0.0439 + 0.0208 i
10
-3.4221 + 2.0121 i
0.0315 + 0.0334 i
11
-3.4221 - 2.0121 i
0.0315 - 0.0334 i
12
6.2878
22.1 i
13
-16.9368
0.226
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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
1.3289 + 0.4715 i
0.0777 - 0.0876 i
Singularities of quadratic [7, 7, 6] approximant
2
1.3289 - 0.4715 i
0.0777 + 0.0876 i
3
1.4834 + 0.0348 i
0.0384 - 0.0309 i
4
1.4834 - 0.0348 i
0.0384 + 0.0309 i
5
-1.8257
0.00382
6
-1.8319
0.00383 i
7
1.9951
0.756
8
2.0405 + 0.4113 i
1.52 + 0.932 i
9
2.0405 - 0.4113 i
1.52 - 0.932 i
10
-3.1797 + 0.7535 i
0.121 - 0.231 i
11
-3.1797 - 0.7535 i
0.121 + 0.231 i
12
-4.5201
0.462
13
-11.3576
0.193 i
14
13.4377
0.286 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.