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

Molecule X 1^Sigma+ State of BH. Basis CC-PVTZ. 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
1.1103
0.163
Singularities of quadratic [1, 0, 0] approximant
Top of Page  Top of the page    

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
1.4075
0.269
Singularities of quadratic [1, 1, 0] approximant
2
88.8026
2.13 i
Top of Page  Top of the page    

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
1.5222
0.377
Singularities of quadratic [1, 1, 1] approximant
2
-23.6587
0.737
Top of Page  Top of the page    

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
1.227
0.112
Singularities of quadratic [2, 1, 1] approximant
2
1.9393
0.214 i
3
3.3867
0.683
Top of Page  Top of the page    

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
1.4388
0.271
Singularities of quadratic [2, 2, 1] approximant
2
-7.4877 + 1.5322 i
0.632 + 0.313 i
3
-7.4877 - 1.5322 i
0.632 - 0.313 i
4
27.8291
2.11 i
Top of Page  Top of the page    

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
1.6772
3.87
Singularities of quadratic [2, 2, 2] approximant
2
2.0432
1.24 i
3
3.3243
27.
4
-7.1167
0.215
Top of Page  Top of the page    

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
1.5962 + 0.3248 i
0.312 - 0.223 i
Singularities of quadratic [3, 2, 2] approximant
2
1.5962 - 0.3248 i
0.312 + 0.223 i
3
2.303
0.653
4
-5.8006
0.156
5
-20.7009
0.186 i
Top of Page  Top of the page    

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
1.5738 + 0.3228 i
0.271 - 0.238 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5738 - 0.3228 i
0.271 + 0.238 i
3
2.1899
0.498
4
-6.0845
0.182
5
-23.6012
0.216 i
6
1176.6925
1.88 i
Top of Page  Top of the page    

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
1.5735 + 0.3225 i
0.27 - 0.24 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5735 - 0.3225 i
0.27 + 0.24 i
3
2.1873
0.494
4
-6.0909
0.184
5
-22.1941
0.224 i
6
-533.8593
1.94
Top of Page  Top of the page    

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
0.5992 + 0.e-4 i
0.00104 - 0.00104 i
Singularities of quadratic [4, 3, 3] approximant
2
0.5992 - 0.e-4 i
0.00104 + 0.00104 i
3
1.5495 + 0.2941 i
0.119 - 0.335 i
4
1.5495 - 0.2941 i
0.119 + 0.335 i
5
2.1227
0.389
6
-5.8141
0.14
7
-28.6498
0.192 i
Top of Page  Top of the page    

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
1.5909 + 0.3638 i
0.275 - 0.0731 i
Singularities of quadratic [4, 4, 3] approximant
2
1.5909 - 0.3638 i
0.275 + 0.0731 i
3
2.3493
0.977
4
-3.7694
0.0253
5
-4.7931
0.0265 i
6
-4.8359 + 7.0011 i
0.0806 - 0.0865 i
7
-4.8359 - 7.0011 i
0.0806 + 0.0865 i
8
34.6813
5.01 i
Top of Page  Top of the page    

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
1.5921 + 0.372 i
0.272 - 0.027 i
Singularities of quadratic [4, 4, 4] approximant
2
1.5921 - 0.372 i
0.272 + 0.027 i
3
2.2475
0.773
4
-0.6286 + 2.3631 i
0.00435 + 0.00962 i
5
-0.6286 - 2.3631 i
0.00435 - 0.00962 i
6
-0.6435 + 2.4128 i
0.0099 - 0.00419 i
7
-0.6435 - 2.4128 i
0.0099 + 0.00419 i
8
-4.9966
0.0511
Top of Page  Top of the page    

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
1.5774 + 0.2644 i
0.104 + 0.364 i
Singularities of quadratic [5, 4, 4] approximant
2
1.5774 - 0.2644 i
0.104 - 0.364 i
3
2.1994 + 0.7274 i
0.225 + 0.201 i
4
2.1994 - 0.7274 i
0.225 - 0.201 i
5
-2.464 + 0.0267 i
0.00298 + 0.003 i
6
-2.464 - 0.0267 i
0.00298 - 0.003 i
7
3.1888
0.559
8
-4.9084
0.0322
9
16.2744
0.574 i
Top of Page  Top of the page    

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
1.3988 + 0.0332 i
0.0396 - 0.0368 i
Singularities of quadratic [5, 5, 4] approximant
2
1.3988 - 0.0332 i
0.0396 + 0.0368 i
3
1.6944 + 0.4471 i
0.0632 + 0.341 i
4
1.6944 - 0.4471 i
0.0632 - 0.341 i
5
2.193
1.23
6
-3.8032 + 0.0754 i
0.104 + 0.0985 i
7
-3.8032 - 0.0754 i
0.104 - 0.0985 i
8
-9.5739
1.18
9
-17.2736
1.07 i
10
33.7075
1.25 i
Top of Page  Top of the page    

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
1.4094 + 0.037 i
0.0419 - 0.0382 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4094 - 0.037 i
0.0419 + 0.0382 i
3
1.7019 + 0.452 i
0.0277 + 0.345 i
4
1.7019 - 0.452 i
0.0277 - 0.345 i
5
2.1754
1.23
6
-3.8418 + 0.0998 i
0.0778 + 0.0725 i
7
-3.8418 - 0.0998 i
0.0778 - 0.0725 i
8
-10.5165 + 2.8855 i
0.378 + 0.91 i
9
-10.5165 - 2.8855 i
0.378 - 0.91 i
10
71.5882
0.386 i
Top of Page  Top of the page    

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
1.4256 + 0.051 i
0.0384 - 0.0308 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4256 - 0.051 i
0.0384 + 0.0308 i
3
1.743 + 0.4829 i
0.177 - 0.256 i
4
1.743 - 0.4829 i
0.177 + 0.256 i
5
1.9998
0.784
6
-3.3459 + 0.2289 i
0.00301 + 0.00388 i
7
-3.3459 - 0.2289 i
0.00301 - 0.00388 i
8
-4.201
0.00687
9
-1.0487 + 10.4445 i
0.14 + 0.0835 i
10
-1.0487 - 10.4445 i
0.14 - 0.0835 i
11
-13.0021
0.111 i
Top of Page  Top of the page    

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
1.4451 + 0.0724 i
0.0397 - 0.0284 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4451 - 0.0724 i
0.0397 + 0.0284 i
3
1.7223 + 0.5549 i
0.103 - 0.116 i
4
1.7223 - 0.5549 i
0.103 + 0.116 i
5
1.8199
0.574
6
2.7438
0.589 i
7
3.6133
1.39
8
-3.6954 + 0.2236 i
0.015 + 0.0146 i
9
-3.6954 - 0.2236 i
0.015 - 0.0146 i
10
-6.9129
0.0876
11
18.0988
3.02 i
12
-27.2941
1.31 i
Top of Page  Top of the page    

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
0.3947 + 0.e-4 i
2.03e-7 - 2.03e-7 i
Singularities of quadratic [6, 6, 6] approximant
2
0.3947 - 0.e-4 i
2.03e-7 + 2.03e-7 i
3
1.1884 + 0.0074 i
0.000656 - 0.000634 i
4
1.1884 - 0.0074 i
0.000656 + 0.000634 i
5
1.4094
0.0111
6
1.6954 + 0.6836 i
0.0401 - 0.00458 i
7
1.6954 - 0.6836 i
0.0401 + 0.00458 i
8
2.8647
0.486 i
9
-3.4469
0.00857
10
-4.4119
0.0123 i
11
5.0293
1.13
12
-14.548
0.217
Top of Page  Top of the page    

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
1.352 + 0.1442 i
0.0395 + 0.0209 i
Singularities of quadratic [7, 6, 6] approximant
2
1.352 - 0.1442 i
0.0395 - 0.0209 i
3
1.3698 + 0.1201 i
0.0222 - 0.0366 i
4
1.3698 - 0.1201 i
0.0222 + 0.0366 i
5
1.7021 + 0.4562 i
0.0394 - 0.36 i
6
1.7021 - 0.4562 i
0.0394 + 0.36 i
7
2.0811
0.765
8
-3.6231 + 0.2205 i
0.0111 + 0.0122 i
9
-3.6231 - 0.2205 i
0.0111 - 0.0122 i
10
-5.7083
0.0365
11
0.2127 + 13.7937 i
0.236 + 0.213 i
12
0.2127 - 13.7937 i
0.236 - 0.213 i
13
-42.5007
1.75 i
Top of Page  Top of the page    

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
1.4598
0.0372
Singularities of quadratic [7, 7, 6] approximant
2
1.4202 + 0.3677 i
0.0121 + 0.00398 i
3
1.4202 - 0.3677 i
0.0121 - 0.00398 i
4
1.4087 + 0.4323 i
0.00605 - 0.0106 i
5
1.4087 - 0.4323 i
0.00605 + 0.0106 i
6
1.9186 + 0.6392 i
0.0494 + 0.101 i
7
1.9186 - 0.6392 i
0.0494 - 0.101 i
8
-3.3971
0.00718
9
-4.5308
0.00876 i
10
-5.8864 + 4.9359 i
0.00094 - 0.0268 i
11
-5.8864 - 4.9359 i
0.00094 + 0.0268 i
12
-3.9501 + 7.5184 i
0.0317 - 0.021 i
13
-3.9501 - 7.5184 i
0.0317 + 0.021 i
14
14.6777
11.1 i
Top of Page  Top of the page    


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.