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

Molecule X 1^Sigma+ State of BH. Basis CC-PVDZ. 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

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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 [2, 2, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.6069 + 0.4681 i
0.216 - 0.00266 i
Singularities of quadratic [2, 2, 2] approximant
2
1.6069 - 0.4681 i
0.216 + 0.00266 i
3
4.0486
1.96
4
-20.5174
0.0435
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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
1.4687 + 0.3189 i
0.0184 - 0.306 i
Singularities of quadratic [2, 2, 3] approximant
2
1.4687 - 0.3189 i
0.0184 + 0.306 i
3
1.8894
0.217
4
4.2929
5.93 i
5
111.3005
0.48
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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
1.5334 + 0.4734 i
0.17 - 0.0256 i
Singularities of quadratic [2, 3, 3] approximant
2
1.5334 - 0.4734 i
0.17 + 0.0256 i
3
3.0055
8.89
4
-6.5835
0.042
5
-9.7035
0.0486 i
6
23.1296
0.219 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
1.5325 + 0.4517 i
0.183 - 0.0613 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5325 - 0.4517 i
0.183 + 0.0613 i
3
2.9297
3.45
4
-5.7768 + 0.494 i
0.0285 + 0.0378 i
5
-5.7768 - 0.494 i
0.0285 - 0.0378 i
6
-91.1162
0.0222
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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
1.5321 + 0.4334 i
0.183 - 0.103 i
Singularities of quadratic [3, 3, 4] approximant
2
1.5321 - 0.4334 i
0.183 + 0.103 i
3
3.0534
4.98
4
-5.3611 + 3.53 i
0.0089 + 0.0159 i
5
-5.3611 - 3.53 i
0.0089 - 0.0159 i
6
-3.9371 + 7.1938 i
0.0229 - 0.00593 i
7
-3.9371 - 7.1938 i
0.0229 + 0.00593 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
1.0263
0.0214
Singularities of quadratic [3, 4, 4] approximant
2
1.0285
0.0218 i
3
1.5321 + 0.4635 i
0.161 - 0.0444 i
4
1.5321 - 0.4635 i
0.161 + 0.0444 i
5
3.144
33.3
6
-5.8681
0.0317
7
-8.2612
0.0362 i
8
28.3385
0.205 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
1.5435 + 0.3442 i
0.0571 + 0.274 i
Singularities of quadratic [4, 4, 4] approximant
2
1.5435 - 0.3442 i
0.0571 - 0.274 i
3
2.2077
9.63
4
2.1605 + 0.7069 i
0.197 + 0.228 i
5
2.1605 - 0.7069 i
0.197 - 0.228 i
6
-5.0142 + 1.1336 i
0.00385 + 0.0053 i
7
-5.0142 - 1.1336 i
0.00385 - 0.0053 i
8
-11.1807
0.00767
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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
1.6154 + 0.4736 i
0.158 + 0.12 i
Singularities of quadratic [4, 4, 5] approximant
2
1.6154 - 0.4736 i
0.158 - 0.12 i
3
1.85 + 0.0706 i
0.234 - 0.211 i
4
1.85 - 0.0706 i
0.234 + 0.211 i
5
3.2684 + 1.8706 i
0.024 - 0.166 i
6
3.2684 - 1.8706 i
0.024 + 0.166 i
7
-4.8629
0.0109
8
-7.3588
0.0116 i
9
9.5639
0.0979
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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
1.6234 + 0.4544 i
0.223 + 0.141 i
Singularities of quadratic [4, 5, 5] approximant
2
1.6234 - 0.4544 i
0.223 - 0.141 i
3
1.8381 + 0.141 i
0.495 - 0.348 i
4
1.8381 - 0.141 i
0.495 + 0.348 i
5
3.7864 + 1.6624 i
0.129 - 0.252 i
6
3.7864 - 1.6624 i
0.129 + 0.252 i
7
-4.8701
0.0119
8
-7.0618
0.0123 i
9
17.2578
0.0617
10
1143.4555
0.266 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
1.4305 + 0.0245 i
0.0328 - 0.0294 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4305 - 0.0245 i
0.0328 + 0.0294 i
3
1.616 + 0.3748 i
0.106 - 2.35 i
4
1.616 - 0.3748 i
0.106 + 2.35 i
5
2.7268 + 0.7745 i
0.0853 + 0.451 i
6
2.7268 - 0.7745 i
0.0853 - 0.451 i
7
4.2417
5.05
8
-4.4914 + 0.9966 i
0.00166 + 0.00286 i
9
-4.4914 - 0.9966 i
0.00166 - 0.00286 i
10
-6.7472
0.00325
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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
1.5419 + 0.0515 i
0.115 - 0.104 i
Singularities of quadratic [5, 5, 6] approximant
2
1.5419 - 0.0515 i
0.115 + 0.104 i
3
1.5966 + 0.3959 i
0.324 - 0.571 i
4
1.5966 - 0.3959 i
0.324 + 0.571 i
5
2.8338 + 0.9714 i
0.279 - 0.325 i
6
2.8338 - 0.9714 i
0.279 + 0.325 i
7
-4.3075 + 0.9087 i
0.000943 + 0.0024 i
8
-4.3075 - 0.9087 i
0.000943 - 0.0024 i
9
4.4564
69.8
10
-5.4555
0.0021
11
-36.2786
0.0134 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
1.53 + 0.0536 i
0.0908 - 0.0724 i
Singularities of quadratic [5, 6, 6] approximant
2
1.53 - 0.0536 i
0.0908 + 0.0724 i
3
1.5973 + 0.3867 i
0.108 - 0.701 i
4
1.5973 - 0.3867 i
0.108 + 0.701 i
5
-2.7267
0.000311
6
-2.7543
0.000307 i
7
2.9683 + 1.0723 i
0.339 - 0.13 i
8
2.9683 - 1.0723 i
0.339 + 0.13 i
9
-4.1883
0.0019
10
5.6462
1.06
11
-14.2067
0.00809 i
12
1642.2542
0.186 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
1.2109 + 0.1945 i
0.000195 - 0.00316 i
Singularities of quadratic [6, 6, 6] approximant
2
1.2109 - 0.1945 i
0.000195 + 0.00316 i
3
1.2179 + 0.1875 i
0.00316 + 0.0000928 i
4
1.2179 - 0.1875 i
0.00316 - 0.0000928 i
5
1.6223 + 0.3194 i
0.349 - 0.779 i
6
1.6223 - 0.3194 i
0.349 + 0.779 i
7
2.9723 + 0.8504 i
0.357 - 0.401 i
8
2.9723 - 0.8504 i
0.357 + 0.401 i
9
-4.9102 + 0.8494 i
0.00369 + 0.00594 i
10
-4.9102 - 0.8494 i
0.00369 - 0.00594 i
11
5.1338
8.26
12
-8.9892
0.0071
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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
1.4984 + 0.5465 i
0.0325 + 0.0135 i
Singularities of quadratic [6, 6, 7] approximant
2
1.4984 - 0.5465 i
0.0325 - 0.0135 i
3
1.5977 + 0.5758 i
0.0244 - 0.0338 i
4
1.5977 - 0.5758 i
0.0244 + 0.0338 i
5
1.7554
0.162
6
2.2346 + 0.5019 i
0.00206 - 0.172 i
7
2.2346 - 0.5019 i
0.00206 + 0.172 i
8
-4.9086
0.0139
9
-6.6556
0.0157 i
10
7.097
0.387 i
11
7.395 + 4.6239 i
0.209 + 0.417 i
12
7.395 - 4.6239 i
0.209 - 0.417 i
13
40.3692
0.158
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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
1.4761 + 0.5414 i
0.027 + 0.00921 i
Singularities of quadratic [6, 7, 7] approximant
2
1.4761 - 0.5414 i
0.027 - 0.00921 i
3
1.5616 + 0.546 i
0.0161 - 0.0322 i
4
1.5616 - 0.546 i
0.0161 + 0.0322 i
5
1.7636
0.126
6
2.1261
0.141 i
7
2.5968
0.483
8
-4.6787
0.00649
9
7.2846
3.71 i
10
-6.9106 + 2.4749 i
0.00217 - 0.00905 i
11
-6.9106 - 2.4749 i
0.00217 + 0.00905 i
12
-9.9534
0.0308 i
13
-10.3897 + 22.5762 i
0.0412 - 0.00436 i
14
-10.3897 - 22.5762 i
0.0412 + 0.00436 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.