Singularities of Møller-Plesset series: example "BH cc-pVTZ 2Re"

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

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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
0.9063
0.15
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
0.8933
0.146
Singularities of quadratic [1, 1, 0] approximant
2
17125.8517
20.2 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
1.3614
1.18
Singularities of quadratic [1, 1, 1] approximant
2
-2.5983
0.188
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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
1.4261
1.7
Singularities of quadratic [2, 1, 1] approximant
2
-3.0202
0.218
3
11.4819
0.255 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
-1.5505
0.0407
Singularities of quadratic [2, 2, 1] approximant
2
2.0577
0.782
3
-3.2361
0.0534 i
4
4.8511
0.154 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
1.2929 + 0.6041 i
0.266 - 0.0418 i
Singularities of quadratic [2, 2, 2] approximant
2
1.2929 - 0.6041 i
0.266 + 0.0418 i
3
2.1451
0.618
4
-2.2454
0.107
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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
1.3094 + 0.5151 i
0.367 - 0.211 i
Singularities of quadratic [3, 2, 2] approximant
2
1.3094 - 0.5151 i
0.367 + 0.211 i
3
1.8671
0.412
4
-2.3031
0.132
5
-17.3272
0.185 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
1.3099 + 0.3336 i
0.523 + 0.487 i
Singularities of quadratic [3, 3, 2] approximant
2
1.3099 - 0.3336 i
0.523 - 0.487 i
3
1.9077
0.385
4
-2.6534
0.392
5
-5.7112
0.286 i
6
227.0767
1.84 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
1.3072 + 0.3911 i
0.124 + 0.632 i
Singularities of quadratic [3, 3, 3] approximant
2
1.3072 - 0.3911 i
0.124 - 0.632 i
3
1.8911
0.39
4
-2.3157 + 0.8012 i
0.0544 + 0.114 i
5
-2.3157 - 0.8012 i
0.0544 - 0.114 i
6
-3.9396
0.102
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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
1.1774 + 0.3033 i
0.099 - 0.0211 i
Singularities of quadratic [4, 3, 3] approximant
2
1.1774 - 0.3033 i
0.099 + 0.0211 i
3
1.5175
0.554
4
1.4971 + 0.6872 i
0.116 - 0.126 i
5
1.4971 - 0.6872 i
0.116 + 0.126 i
6
-3.0968 + 0.8551 i
0.311 - 0.000173 i
7
-3.0968 - 0.8551 i
0.311 + 0.000173 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
0.7569
0.00337
Singularities of quadratic [4, 4, 3] approximant
2
0.7641
0.00339 i
3
1.2362
0.0759
4
1.357 + 0.6142 i
0.055 + 0.163 i
5
1.357 - 0.6142 i
0.055 - 0.163 i
6
-3.0687 + 0.9469 i
0.244 - 0.0407 i
7
-3.0687 - 0.9469 i
0.244 + 0.0407 i
8
1296.2668
3.6 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
1.2101 + 0.4277 i
0.0565 - 0.208 i
Singularities of quadratic [4, 4, 4] approximant
2
1.2101 - 0.4277 i
0.0565 + 0.208 i
3
1.4088 + 0.1202 i
0.201 - 0.0658 i
4
1.4088 - 0.1202 i
0.201 + 0.0658 i
5
2.3508
0.435
6
-2.6865 + 0.7713 i
0.111 + 0.231 i
7
-2.6865 - 0.7713 i
0.111 - 0.231 i
8
-6.489
0.189
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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
1.1883 + 0.4542 i
0.0692 - 0.121 i
Singularities of quadratic [5, 4, 4] approximant
2
1.1883 - 0.4542 i
0.0692 + 0.121 i
3
1.4089
0.0546
4
1.4363
0.0615 i
5
-2.7504 + 0.8199 i
0.154 + 0.197 i
6
-2.7504 - 0.8199 i
0.154 - 0.197 i
7
4.1852 + 0.9977 i
0.379 + 1.64 i
8
4.1852 - 0.9977 i
0.379 - 1.64 i
9
-25.1589
0.668
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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
1.1716 + 0.4577 i
0.0543 - 0.0857 i
Singularities of quadratic [5, 5, 4] approximant
2
1.1716 - 0.4577 i
0.0543 + 0.0857 i
3
1.271
0.0559
4
1.3686
0.0831 i
5
-2.7287 + 0.7388 i
0.0616 + 0.268 i
6
-2.7287 - 0.7388 i
0.0616 - 0.268 i
7
3.8908
3.99
8
5.6525
2.29 i
9
-15.5579
0.213
10
-81.7609
0.584 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
1.18 + 0.3935 i
0.0606 + 0.0502 i
Singularities of quadratic [5, 5, 5] approximant
2
1.18 - 0.3935 i
0.0606 - 0.0502 i
3
1.1159 + 0.6584 i
0.0138 - 0.0352 i
4
1.1159 - 0.6584 i
0.0138 + 0.0352 i
5
1.1756 + 0.642 i
0.0398 + 0.00838 i
6
1.1756 - 0.642 i
0.0398 - 0.00838 i
7
2.2068
0.546
8
-2.7409 + 0.8731 i
0.19 + 0.128 i
9
-2.7409 - 0.8731 i
0.19 - 0.128 i
10
-8.0514
0.312
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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
1.1915 + 0.4535 i
0.06 - 0.148 i
Singularities of quadratic [6, 5, 5] approximant
2
1.1915 - 0.4535 i
0.06 + 0.148 i
3
1.4693
0.184
4
2.043 + 0.2704 i
0.531 + 1.24 i
5
2.043 - 0.2704 i
0.531 - 1.24 i
6
2.0459 + 1.2303 i
0.212 + 0.0939 i
7
2.0459 - 1.2303 i
0.212 - 0.0939 i
8
-2.7321 + 0.8353 i
0.171 + 0.169 i
9
-2.7321 - 0.8353 i
0.171 - 0.169 i
10
-7.1887
0.278
11
-25.5878
0.324 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
1.2011 + 0.4557 i
0.0811 - 0.186 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2011 - 0.4557 i
0.0811 + 0.186 i
3
1.6346
0.306
4
1.574 + 0.5098 i
0.298 + 0.0923 i
5
1.574 - 0.5098 i
0.298 - 0.0923 i
6
1.876 + 0.7363 i
0.507 - 0.0495 i
7
1.876 - 0.7363 i
0.507 + 0.0495 i
8
-2.7369 + 0.7936 i
0.146 + 0.225 i
9
-2.7369 - 0.7936 i
0.146 - 0.225 i
10
-8.8372
0.22
11
32.0625
0.347 i
12
-136.8165
0.591 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
1.1917 + 0.4688 i
0.102 - 0.117 i
Singularities of quadratic [6, 6, 6] approximant
2
1.1917 - 0.4688 i
0.102 + 0.117 i
3
1.4166 + 0.2348 i
0.225 + 0.16 i
4
1.4166 - 0.2348 i
0.225 - 0.16 i
5
1.5351 + 0.3158 i
0.421 + 0.0896 i
6
1.5351 - 0.3158 i
0.421 - 0.0896 i
7
2.4354 + 1.2131 i
0.221 + 0.28 i
8
2.4354 - 1.2131 i
0.221 - 0.28 i
9
-2.7329 + 0.8036 i
0.147 + 0.21 i
10
-2.7329 - 0.8036 i
0.147 - 0.21 i
11
3.4541
0.431
12
-8.6519
0.265
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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
1.2196 + 0.4597 i
0.157 - 0.361 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2196 - 0.4597 i
0.157 + 0.361 i
3
1.3527 + 0.4498 i
0.384 + 0.322 i
4
1.3527 - 0.4498 i
0.384 - 0.322 i
5
1.4781 + 0.4041 i
1.33 + 0.982 i
6
1.4781 - 0.4041 i
1.33 - 0.982 i
7
2.6865
0.485
8
-2.7311 + 0.8248 i
0.169 + 0.179 i
9
-2.7311 - 0.8248 i
0.169 - 0.179 i
10
4.9604
248. i
11
-5.8976
0.272
12
-9.3075
0.39 i
13
15.6645
0.741
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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
1.2004 + 0.4655 i
0.12 - 0.149 i
Singularities of quadratic [7, 7, 6] approximant
2
1.2004 - 0.4655 i
0.12 + 0.149 i
3
1.5527 + 0.399 i
0.335 + 0.0226 i
4
1.5527 - 0.399 i
0.335 - 0.0226 i
5
1.7907 + 0.4042 i
0.556 - 1.31 i
6
1.7907 - 0.4042 i
0.556 + 1.31 i
7
2.0022
0.324
8
-2.6893 + 0.804 i
0.0937 + 0.191 i
9
-2.6893 - 0.804 i
0.0937 - 0.191 i
10
-3.8279 + 0.2264 i
0.0399 - 0.337 i
11
-3.8279 - 0.2264 i
0.0399 + 0.337 i
12
-8.5367
0.124
13
16.5753
0.328 i
14
-38.1117
0.267 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.