Singularities of Møller-Plesset series: example "BH cc-pVTZ 1.5Re"

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
0.9993
0.155
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
1.1646
0.212
Singularities of quadratic [1, 1, 0] approximant
2
184.0096
2.67 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
1.5682
0.942
Singularities of quadratic [1, 1, 1] approximant
2
-4.639
0.261
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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
1.591
0.98
Singularities of quadratic [2, 1, 1] approximant
2
-6.1948
0.362
3
15.209
0.348 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
1.8793
847.
Singularities of quadratic [2, 2, 1] approximant
2
-1.9208
0.0377
3
-2.6873
0.0413 i
4
24.3434
0.328 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
1.6083 + 0.6144 i
0.374 - 0.0803 i
Singularities of quadratic [2, 2, 2] approximant
2
1.6083 - 0.6144 i
0.374 + 0.0803 i
3
2.5562
0.898
4
-3.7243
0.139
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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
1.5677 + 0.512 i
0.401 - 0.302 i
Singularities of quadratic [3, 2, 2] approximant
2
1.5677 - 0.512 i
0.401 + 0.302 i
3
2.0648
0.465
4
-3.7077
0.157
5
-23.9998
0.202 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
1.5697 + 0.4571 i
0.352 - 0.573 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5697 - 0.4571 i
0.352 + 0.573 i
3
2.0014
0.45
4
-3.8891
0.205
5
-17.3227
0.236 i
6
401.7676
1.34 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
1.5698 + 0.4577 i
0.362 - 0.565 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5698 - 0.4577 i
0.362 + 0.565 i
3
1.9945
0.45
4
-3.8627
0.195
5
-22.9793
0.199 i
6
62.1794
14. 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
1.57 + 0.4555 i
0.349 - 0.583 i
Singularities of quadratic [4, 3, 3] approximant
2
1.57 - 0.4555 i
0.349 + 0.583 i
3
2.001
0.451
4
-3.882
0.203
5
-17.9542
0.225 i
6
53.0717
2.31 i
7
122.3294
0.991
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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
0.007
1.96e-10 - 1.96e-10 i
Singularities of quadratic [4, 4, 3] approximant
2
0.007
1.96e-10 + 1.96e-10 i
3
1.569 + 0.4541 i
0.327 - 0.591 i
4
1.569 - 0.4541 i
0.327 + 0.591 i
5
2.0089
0.452
6
-3.8767
0.199
7
-17.8123
0.236 i
8
392.0337
1.31 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
0.9977 + 0.0015 i
0.0089 - 0.00887 i
Singularities of quadratic [4, 4, 4] approximant
2
0.9977 - 0.0015 i
0.0089 + 0.00887 i
3
1.5278 + 0.4186 i
0.0624 + 0.367 i
4
1.5278 - 0.4186 i
0.0624 - 0.367 i
5
2.2372
0.503
6
-4.1898
0.299
7
-5.532
83.7 i
8
-8.446
0.25
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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
0.9229 + 0.9967 i
0.00949 + 0.0022 i
Singularities of quadratic [5, 4, 4] approximant
2
0.9229 - 0.9967 i
0.00949 - 0.0022 i
3
0.9192 + 1.0054 i
0.00228 - 0.0095 i
4
0.9192 - 1.0054 i
0.00228 + 0.0095 i
5
1.4863 + 0.4346 i
0.0649 + 0.188 i
6
1.4863 - 0.4346 i
0.0649 - 0.188 i
7
2.3852
0.648
8
-4.0444
0.331
9
-14.0376
0.197 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
1.0105
0.00187
Singularities of quadratic [5, 5, 4] approximant
2
1.0134
0.00188 i
3
1.409 + 0.4356 i
0.0124 + 0.0693 i
4
1.409 - 0.4356 i
0.0124 - 0.0693 i
5
-2.9035
0.0165
6
-3.257
0.0195 i
7
3.2788
2.8
8
-7.0103 + 3.1517 i
0.0464 + 0.0757 i
9
-7.0103 - 3.1517 i
0.0464 - 0.0757 i
10
24.7247
0.241 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
1.0634
0.0027
Singularities of quadratic [5, 5, 5] approximant
2
1.0678
0.00272 i
3
1.4107 + 0.4391 i
0.00806 + 0.0716 i
4
1.4107 - 0.4391 i
0.00806 - 0.0716 i
5
-3.1512
0.0272
6
3.2161
2.22
7
-3.9459
0.0409 i
8
-5.3866 + 4.1494 i
0.0525 + 0.0763 i
9
-5.3866 - 4.1494 i
0.0525 - 0.0763 i
10
91.0823
0.156 i
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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
1.4238
0.0337
Singularities of quadratic [6, 5, 5] approximant
2
1.4795
0.0404 i
3
1.4275 + 0.4709 i
0.0446 - 0.0918 i
4
1.4275 - 0.4709 i
0.0446 + 0.0918 i
5
-2.4742
0.0159
6
-2.5239
0.0162 i
7
3.2271 + 1.0378 i
0.596 + 0.806 i
8
3.2271 - 1.0378 i
0.596 - 0.806 i
9
-4.5799
7.8
10
5.7274
0.601
11
-9.7376
0.2 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
1.4611 + 0.5165 i
0.147 - 0.0364 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4611 - 0.5165 i
0.147 + 0.0364 i
3
1.6715 + 0.284 i
0.281 + 0.054 i
4
1.6715 - 0.284 i
0.281 - 0.054 i
5
1.8507 + 0.558 i
0.573 - 0.554 i
6
1.8507 - 0.558 i
0.573 + 0.554 i
7
-2.6798
0.0149
8
-2.8138
0.0155 i
9
2.9104
2.68
10
-5.7181
0.296
11
-8.987
0.104 i
12
83.933
0.441 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
1.4582 + 0.4875 i
0.129 - 0.128 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4582 - 0.4875 i
0.129 + 0.128 i
3
1.8178 + 0.0952 i
0.144 - 0.0767 i
4
1.8178 - 0.0952 i
0.144 + 0.0767 i
5
2.3614
2.68
6
2.2598 + 0.7262 i
1.09 - 0.407 i
7
2.2598 - 0.7262 i
1.09 + 0.407 i
8
-2.7458
0.0221
9
-2.8788
0.0228 i
10
-5.8522 + 0.9418 i
0.0107 + 0.281 i
11
-5.8522 - 0.9418 i
0.0107 - 0.281 i
12
-25.4217
8.56
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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
1.4589 + 0.4851 i
0.127 - 0.141 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4589 - 0.4851 i
0.127 + 0.141 i
3
1.8799 + 0.0225 i
0.0591 - 0.0527 i
4
1.8799 - 0.0225 i
0.0591 + 0.0527 i
5
2.186
0.794
6
2.2641 + 0.7658 i
0.946 - 0.212 i
7
2.2641 - 0.7658 i
0.946 + 0.212 i
8
-2.7464
0.0253
9
-2.8654
0.026 i
10
-5.7637 + 0.725 i
0.00254 + 0.38 i
11
-5.7637 - 0.725 i
0.00254 - 0.38 i
12
-31.9013
3.24
13
56.2779
0.405 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
1.4609 + 0.4811 i
0.119 - 0.167 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4609 - 0.4811 i
0.119 + 0.167 i
3
1.8483
0.21
4
1.9912 + 0.3296 i
0.437 - 0.218 i
5
1.9912 - 0.3296 i
0.437 + 0.218 i
6
2.2352 + 0.7579 i
0.925 + 0.0074 i
7
2.2352 - 0.7579 i
0.925 - 0.0074 i
8
-2.8111 + 0.0458 i
0.0277 + 0.0298 i
9
-2.8111 - 0.0458 i
0.0277 - 0.0298 i
10
-4.4382 + 0.3556 i
0.156 + 0.0344 i
11
-4.4382 - 0.3556 i
0.156 - 0.0344 i
12
-10.0515
0.118
13
-26.5844
0.151 i
14
47.5992
0.325 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.