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

Molecule X 1^Sigma+ State of BH. Basis CC-PVTZ. Structure ""

Content


ExamplesBH-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-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 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 O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-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 [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
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Table 2. Singularities with their weights for the quadratic approximant [2, 2, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5945 + 0.3247 i
0.309 - 0.224 i
Singularities of quadratic [2, 2, 3] approximant
2
1.5945 - 0.3247 i
0.309 + 0.224 i
3
2.2941
0.639
4
-5.8212
0.158
5
-20.9267
0.188 i
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Table 3. Singularities with their weights for the quadratic approximant [2, 3, 3]
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 [2, 3, 3] approximant
2
1.5738 - 0.3228 i
0.271 + 0.238 i
3
2.1898
0.498
4
-6.0847
0.182
5
-23.5412
0.216 i
6
1351.2209
1.73 i
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Table 4. 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
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Table 5. Singularities with their weights for the quadratic approximant [3, 3, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.5621 + 0.e-4 i
0.000838 - 0.000838 i
Singularities of quadratic [3, 3, 4] approximant
2
0.5621 - 0.e-4 i
0.000838 + 0.000838 i
3
1.552 + 0.2965 i
0.137 - 0.333 i
4
1.552 - 0.2965 i
0.137 + 0.333 i
5
2.1276
0.396
6
-5.8267
0.141
7
-28.3618
0.193 i
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Table 6. Singularities with their weights for the quadratic approximant [3, 4, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5909 + 0.3638 i
0.275 - 0.073 i
Singularities of quadratic [3, 4, 4] approximant
2
1.5909 - 0.3638 i
0.275 + 0.073 i
3
2.3491
0.976
4
-3.7737
0.0253
5
-4.8133
0.0266 i
6
-4.7932 + 6.9725 i
0.0799 - 0.0858 i
7
-4.7932 - 6.9725 i
0.0799 + 0.0858 i
8
35.8289
4.36 i
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Table 7. 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
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Table 8. Singularities with their weights for the quadratic approximant [4, 4, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5774 + 0.2656 i
0.0968 + 0.365 i
Singularities of quadratic [4, 4, 5] approximant
2
1.5774 - 0.2656 i
0.0968 - 0.365 i
3
2.2086 + 0.7322 i
0.221 + 0.208 i
4
2.2086 - 0.7322 i
0.221 - 0.208 i
5
-2.4426 + 0.0254 i
0.00289 + 0.0029 i
6
-2.4426 - 0.0254 i
0.00289 - 0.0029 i
7
3.2368
0.558
8
-4.8956
0.032
9
15.9009
0.583 i
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Table 9. Singularities with their weights for the quadratic approximant [4, 5, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.3992 + 0.0333 i
0.0397 - 0.0369 i
Singularities of quadratic [4, 5, 5] approximant
2
1.3992 - 0.0333 i
0.0397 + 0.0369 i
3
1.6947 + 0.4473 i
0.0619 + 0.341 i
4
1.6947 - 0.4473 i
0.0619 - 0.341 i
5
2.1923
1.23
6
-3.8046 + 0.0764 i
0.102 + 0.0971 i
7
-3.8046 - 0.0764 i
0.102 - 0.0971 i
8
-9.639
1.24
9
-16.9053
1.16 i
10
34.4087
1.19 i
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Table 10. 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
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Table 11. Singularities with their weights for the quadratic approximant [5, 5, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4255 + 0.0509 i
0.0384 - 0.0308 i
Singularities of quadratic [5, 5, 6] approximant
2
1.4255 - 0.0509 i
0.0384 + 0.0308 i
3
1.7429 + 0.4826 i
0.177 - 0.257 i
4
1.7429 - 0.4826 i
0.177 + 0.257 i
5
2.0007
0.785
6
-3.3365 + 0.2251 i
0.00292 + 0.00378 i
7
-3.3365 - 0.2251 i
0.00292 - 0.00378 i
8
-4.1699
0.00664
9
-1.1906 + 10.4479 i
0.137 + 0.0862 i
10
-1.1906 - 10.4479 i
0.137 - 0.0862 i
11
-12.5294
0.102 i
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Table 12. Singularities with their weights for the quadratic approximant [5, 6, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.445 + 0.0724 i
0.0395 - 0.0283 i
Singularities of quadratic [5, 6, 6] approximant
2
1.445 - 0.0724 i
0.0395 + 0.0283 i
3
1.7224 + 0.5552 i
0.103 - 0.115 i
4
1.7224 - 0.5552 i
0.103 + 0.115 i
5
1.8183
0.566
6
2.7447
0.589 i
7
3.6164
1.38
8
-3.6945 + 0.2252 i
0.0148 + 0.0145 i
9
-3.6945 - 0.2252 i
0.0148 - 0.0145 i
10
-6.8971
0.0859
11
18.2734
2.84 i
12
-26.8394
1.41 i
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Table 13. 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
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Table 14. Singularities with their weights for the quadratic approximant [6, 6, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.3528 + 0.1468 i
0.0372 + 0.0234 i
Singularities of quadratic [6, 6, 7] approximant
2
1.3528 - 0.1468 i
0.0372 - 0.0234 i
3
1.3709 + 0.1221 i
0.0239 - 0.0341 i
4
1.3709 - 0.1221 i
0.0239 + 0.0341 i
5
1.7035 + 0.455 i
0.0469 - 0.371 i
6
1.7035 - 0.455 i
0.0469 + 0.371 i
7
2.0744
0.741
8
-3.6249 + 0.2174 i
0.0114 + 0.0125 i
9
-3.6249 - 0.2174 i
0.0114 - 0.0125 i
10
-5.7252
0.0375
11
0.0997 + 13.814 i
0.231 + 0.219 i
12
0.0997 - 13.814 i
0.231 - 0.219 i
13
-43.2235
1.64 i
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Table 15. Singularities with their weights for the quadratic approximant [6, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4602
0.0373
Singularities of quadratic [6, 7, 7] approximant
2
1.4198 + 0.366 i
0.0122 + 0.00384 i
3
1.4198 - 0.366 i
0.0122 - 0.00384 i
4
1.4093 + 0.4309 i
0.00597 - 0.0108 i
5
1.4093 - 0.4309 i
0.00597 + 0.0108 i
6
1.9188 + 0.6367 i
0.0506 + 0.102 i
7
1.9188 - 0.6367 i
0.0506 - 0.102 i
8
-3.3983
0.00724
9
-4.521
0.00882 i
10
-5.9174 + 4.9686 i
0.00077 - 0.0274 i
11
-5.9174 - 4.9686 i
0.00077 + 0.0274 i
12
-3.9049 + 7.5292 i
0.0317 - 0.0215 i
13
-3.9049 - 7.5292 i
0.0317 + 0.0215 i
14
14.9153
13.4 i
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ExamplesBH-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-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 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 O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-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.