Singularities of Møller-Plesset series: example "BH cc-pVQZ Re"

Molecule X 1^Sigma+ State of BH. Basis 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
1.2929
0.202
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
1.2875
0.2
Singularities of quadratic [1, 1, 0] approximant
2
289082.0616
94.9 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
1.5143
0.376
Singularities of quadratic [1, 1, 1] approximant
2
-8.5938
0.88
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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
1.4725
0.337
Singularities of quadratic [2, 1, 1] approximant
2
-4.1237
0.425
3
-6.9019
0.314 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
1.4463
0.293
Singularities of quadratic [2, 2, 1] approximant
2
-6.043
1.99
3
-10.0555
0.717 i
4
164.7778
2.17 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
1.5137
0.499
Singularities of quadratic [2, 2, 2] approximant
2
3.1207
0.616 i
3
4.4818
10.7
4
-5.443
0.36
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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
1.3387 + 0.2224 i
0.00552 - 0.144 i
Singularities of quadratic [3, 2, 2] approximant
2
1.3387 - 0.2224 i
0.00552 + 0.144 i
3
1.3631
0.1
4
-4.9941
0.328
5
-20.3627
0.323 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
1.5714 + 0.3138 i
0.279 - 0.223 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5714 - 0.3138 i
0.279 + 0.223 i
3
2.1439
0.503
4
-4.231
0.157
5
-17.6653
0.22 i
6
45.1976
0.472 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
1.599 + 0.3238 i
0.322 - 0.174 i
Singularities of quadratic [3, 3, 3] approximant
2
1.599 - 0.3238 i
0.322 + 0.174 i
3
2.3355
0.834
4
-4.2686
0.152
5
11.4329
0.49 i
6
-224.3151
0.111 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
1.6051 + 0.3334 i
0.32 - 0.129 i
Singularities of quadratic [4, 3, 3] approximant
2
1.6051 - 0.3334 i
0.32 + 0.129 i
3
2.4034
1.11
4
-4.163
0.127
5
13.7953
0.448 i
6
-0.5353 + 17.6038 i
0.0725 + 0.276 i
7
-0.5353 - 17.6038 i
0.0725 - 0.276 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
1.6046 + 0.3393 i
0.315 - 0.0989 i
Singularities of quadratic [4, 4, 3] approximant
2
1.6046 - 0.3393 i
0.315 + 0.0989 i
3
2.365
1.07
4
-3.083
0.0274
5
-3.3851
0.0287 i
6
-6.5814 + 2.1596 i
0.0661 - 0.214 i
7
-6.5814 - 2.1596 i
0.0661 + 0.214 i
8
63.6077
0.602 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
1.5999 + 0.3101 i
0.314 - 0.256 i
Singularities of quadratic [4, 4, 4] approximant
2
1.5999 - 0.3101 i
0.314 + 0.256 i
3
-1.8672 + 0.0011 i
0.00341 + 0.00342 i
4
-1.8672 - 0.0011 i
0.00341 - 0.00342 i
5
2.3937
0.811
6
-4.0805
0.0956
7
5.9291
0.818 i
8
13.8429
8.52
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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
-0.2399 + 0.e-4 i
2.39e-6 + 2.39e-6 i
Singularities of quadratic [5, 4, 4] approximant
2
-0.2399 - 0.e-4 i
2.39e-6 - 2.39e-6 i
3
1.5973 + 0.3064 i
0.286 - 0.278 i
4
1.5973 - 0.3064 i
0.286 + 0.278 i
5
2.4276
0.884
6
-4.0863
0.105
7
6.6158
0.566 i
8
11.4051 + 16.146 i
0.151 + 0.433 i
9
11.4051 - 16.146 i
0.151 - 0.433 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
1.2278 + 0.0049 i
0.0215 - 0.0217 i
Singularities of quadratic [5, 5, 4] approximant
2
1.2278 - 0.0049 i
0.0215 + 0.0217 i
3
1.6425 + 0.3744 i
0.321 + 0.121 i
4
1.6425 - 0.3744 i
0.321 - 0.121 i
5
2.3726
1.51
6
-3.1568
0.0429
7
-3.3453
0.0445 i
8
-5.5642
181.
9
-9.8315
0.22 i
10
82.9303
0.695 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
1.2942 + 0.0094 i
0.0303 - 0.0307 i
Singularities of quadratic [5, 5, 5] approximant
2
1.2942 - 0.0094 i
0.0303 + 0.0307 i
3
1.6568 + 0.3847 i
0.293 + 0.182 i
4
1.6568 - 0.3847 i
0.293 - 0.182 i
5
2.3818
1.85
6
-3.5478
0.0492
7
-4.7808
0.0541 i
8
-4.9641 + 3.2827 i
0.0704 - 0.111 i
9
-4.9641 - 3.2827 i
0.0704 + 0.111 i
10
-22.0044
4.01
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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
1.3942 + 0.0369 i
0.034 - 0.0299 i
Singularities of quadratic [6, 5, 5] approximant
2
1.3942 - 0.0369 i
0.034 + 0.0299 i
3
1.7339 + 0.4595 i
0.0819 - 0.276 i
4
1.7339 - 0.4595 i
0.0819 + 0.276 i
5
2.081
1.33
6
-3.0611 + 0.0724 i
0.017 + 0.0172 i
7
-3.0611 - 0.0724 i
0.017 - 0.0172 i
8
-4.3966
0.0962
9
4.7811
30. i
10
7.2777
0.625
11
-11.1261
0.482 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
1.4412 + 0.0658 i
0.0497 - 0.0376 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4412 - 0.0658 i
0.0497 + 0.0376 i
3
1.6888 + 0.5347 i
0.0323 - 0.146 i
4
1.6888 - 0.5347 i
0.0323 + 0.146 i
5
2.0551 + 0.2311 i
0.675 + 0.0237 i
6
2.0551 - 0.2311 i
0.675 - 0.0237 i
7
3.0301
180.
8
-3.2458
0.201
9
-3.3189
0.197 i
10
-5.1778
0.956
11
-9.9524
0.29 i
12
156.374
1.06 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
1.5739 + 0.1599 i
1.42 - 3.9 i
Singularities of quadratic [6, 6, 6] approximant
2
1.5739 - 0.1599 i
1.42 + 3.9 i
3
1.577 + 0.436 i
0.159 - 0.0536 i
4
1.577 - 0.436 i
0.159 + 0.0536 i
5
1.6681 + 0.1793 i
0.0138 - 0.205 i
6
1.6681 - 0.1793 i
0.0138 + 0.205 i
7
1.9698
0.184
8
-3.1442
0.0333
9
-3.3514
0.0359 i
10
-5.2287
5.81
11
17.7283
0.469 i
12
-17.7717
0.176 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
1.4637
0.0518
Singularities of quadratic [7, 6, 6] approximant
2
1.4787 + 0.3166 i
0.0286 + 0.00635 i
3
1.4787 - 0.3166 i
0.0286 - 0.00635 i
4
1.4699 + 0.4284 i
0.0145 - 0.0223 i
5
1.4699 - 0.4284 i
0.0145 + 0.0223 i
6
1.945 + 0.5207 i
0.0749 + 0.122 i
7
1.945 - 0.5207 i
0.0749 - 0.122 i
8
-3.1085
0.0136
9
-3.5649
0.0164 i
10
-9.1147
0.0587
11
-4.308 + 8.2387 i
0.000402 - 0.0676 i
12
-4.308 - 8.2387 i
0.000402 + 0.0676 i
13
-15.6356
0.0712 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
1.3974 + 0.1935 i
0.0621 + 0.0671 i
Singularities of quadratic [7, 7, 6] approximant
2
1.3974 - 0.1935 i
0.0621 - 0.0671 i
3
1.4374 + 0.2004 i
0.0639 - 0.055 i
4
1.4374 - 0.2004 i
0.0639 + 0.055 i
5
1.675 + 0.4223 i
0.108 + 0.359 i
6
1.675 - 0.4223 i
0.108 - 0.359 i
7
2.0809
0.672
8
-3.2214
0.388
9
-3.2618
0.412 i
10
4.3581
11.7 i
11
-4.9857
0.519
12
5.3763
0.82
13
-10.6449
0.302 i
14
279.2109
1.55 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.