Singularities of Møller-Plesset series: example "O2- aug-cc-pVDZ"

Molecule X 1^Sigma+ State of O2-. Basis AUG-CC-PVDZ. 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
-1.3489
0.814
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
-0.4238
0.111
Singularities of quadratic [1, 1, 0] approximant
2
-2.1948
0.252 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
-0.5162
0.178
Singularities of quadratic [1, 1, 1] approximant
2
-29.6888
0.363 i
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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
-0.4446
0.0898
Singularities of quadratic [2, 1, 1] approximant
2
1.2687 + 1.4717 i
0.236 + 0.0225 i
3
1.2687 - 1.4717 i
0.236 - 0.0225 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
-0.455
0.102
Singularities of quadratic [2, 2, 1] approximant
2
1.64 + 0.9586 i
0.306 - 0.00739 i
3
1.64 - 0.9586 i
0.306 + 0.00739 i
4
-20.077
1.44 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
-0.5863 + 0.0429 i
0.605 + 1.34 i
Singularities of quadratic [2, 2, 2] approximant
2
-0.5863 - 0.0429 i
0.605 - 1.34 i
3
-1.2334
0.77
4
2.4084
2.34
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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
-0.5618 + 0.0736 i
0.171 + 0.518 i
Singularities of quadratic [3, 2, 2] approximant
2
-0.5618 - 0.0736 i
0.171 - 0.518 i
3
-1.0048
0.357
4
3.4026
38.8
5
4.9929
1.73 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
-0.5867
17.2
Singularities of quadratic [3, 3, 2] approximant
2
-0.6228
3.15 i
3
1.966
0.691
4
-2.0341
262.
5
-3.001
1.7 i
6
542.8084
10.2 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
-0.5917 + 0.0384 i
1.16 + 1.44 i
Singularities of quadratic [3, 3, 3] approximant
2
-0.5917 - 0.0384 i
1.16 - 1.44 i
3
0.8645
0.108
4
0.8811
0.109 i
5
-1.3193
1.1
6
2.7423
8.57
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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
-0.5795 + 0.062 i
0.624 + 0.528 i
Singularities of quadratic [4, 3, 3] approximant
2
-0.5795 - 0.062 i
0.624 - 0.528 i
3
-0.9227
0.532
4
-1.6747
0.345 i
5
1.7409
0.359
6
-0.9789 + 1.7239 i
0.356 - 0.216 i
7
-0.9789 - 1.7239 i
0.356 + 0.216 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
0.3188
0.000215
Singularities of quadratic [4, 4, 3] approximant
2
0.3189
0.000215 i
3
-0.4622 + 0.013 i
0.0155 + 0.0122 i
4
-0.4622 - 0.013 i
0.0155 - 0.0122 i
5
-0.8473
0.0911
6
1.3808
0.0568
7
-2.2351
0.86 i
8
5.8089
3.58 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
-0.5504 + 0.1338 i
0.0687 - 0.0038 i
Singularities of quadratic [4, 4, 4] approximant
2
-0.5504 - 0.1338 i
0.0687 + 0.0038 i
3
-0.629 + 0.1654 i
0.0253 + 0.0703 i
4
-0.629 - 0.1654 i
0.0253 - 0.0703 i
5
-1.4604
0.433
6
1.5615
0.183
7
3.7696
0.661 i
8
-4.9544
1.59 i
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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
-0.5715 + 0.0931 i
0.239 + 0.015 i
Singularities of quadratic [5, 4, 4] approximant
2
-0.5715 - 0.0931 i
0.239 - 0.015 i
3
-0.7446 + 0.1043 i
0.186 + 0.233 i
4
-0.7446 - 0.1043 i
0.186 - 0.233 i
5
1.5373
0.199
6
-2.1683 + 0.9468 i
1.63 + 0.172 i
7
-2.1683 - 0.9468 i
1.63 - 0.172 i
8
2.4067
0.354 i
9
4.5023
4.31
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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
-0.5918 + 0.0694 i
0.0738 + 0.372 i
Singularities of quadratic [5, 5, 4] approximant
2
-0.5918 - 0.0694 i
0.0738 - 0.372 i
3
-0.5976
0.358
4
-0.509 + 0.5523 i
0.00852 - 0.0055 i
5
-0.509 - 0.5523 i
0.00852 + 0.0055 i
6
-0.5016 + 0.5829 i
0.00583 + 0.00848 i
7
-0.5016 - 0.5829 i
0.00583 - 0.00848 i
8
1.4941
0.107
9
-1.5098
0.158 i
10
7.5008
9.58 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
0.3452
0.0000641
Singularities of quadratic [5, 5, 5] approximant
2
0.3453
0.0000641 i
3
-0.4841 + 0.0164 i
0.0093 + 0.00639 i
4
-0.4841 - 0.0164 i
0.0093 - 0.00639 i
5
-0.5782 + 0.1969 i
0.0225 + 0.0126 i
6
-0.5782 - 0.1969 i
0.0225 - 0.0126 i
7
-0.6505
0.668
8
-0.8653
0.0528 i
9
1.414
0.0546
10
-25.9719
0.457
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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
-0.5687 + 0.0692 i
0.379 + 0.416 i
Singularities of quadratic [6, 5, 5] approximant
2
-0.5687 - 0.0692 i
0.379 - 0.416 i
3
-0.8281
1.97
4
-0.8835
8.19 i
5
-1.4658 + 1.0136 i
0.335 + 0.651 i
6
-1.4658 - 1.0136 i
0.335 - 0.651 i
7
1.8885 + 0.5385 i
0.278 + 0.0219 i
8
1.8885 - 0.5385 i
0.278 - 0.0219 i
9
1.5405 + 1.3706 i
0.0874 - 0.213 i
10
1.5405 - 1.3706 i
0.0874 + 0.213 i
11
3.8427
0.424
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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
-0.5696 + 0.0698 i
0.436 + 0.386 i
Singularities of quadratic [6, 6, 5] approximant
2
-0.5696 - 0.0698 i
0.436 - 0.386 i
3
-0.7764
0.647
4
-0.9641
0.552 i
5
1.5454 + 0.4115 i
0.0909 - 0.107 i
6
1.5454 - 0.4115 i
0.0909 + 0.107 i
7
-1.3203 + 1.2212 i
0.447 + 0.104 i
8
-1.3203 - 1.2212 i
0.447 - 0.104 i
9
2.0455 + 1.0137 i
0.172 + 0.143 i
10
2.0455 - 1.0137 i
0.172 - 0.143 i
11
-1.4415 + 6.3421 i
0.67 + 0.469 i
12
-1.4415 - 6.3421 i
0.67 - 0.469 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
-0.5734 + 0.0706 i
0.671 + 0.209 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.5734 - 0.0706 i
0.671 - 0.209 i
3
-0.7177
0.335
4
1.2516
0.0116
5
-1.2964
0.116 i
6
1.2896 + 0.6064 i
0.0106 + 0.0255 i
7
1.2896 - 0.6064 i
0.0106 - 0.0255 i
8
-1.6548
0.176
9
1.6722
0.0089 i
10
1.767
0.0116
11
-1.2203 + 1.3043 i
0.156 - 0.223 i
12
-1.2203 - 1.3043 i
0.156 + 0.223 i
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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
-0.5667 + 0.0695 i
0.259 + 0.408 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.5667 - 0.0695 i
0.259 - 0.408 i
3
-0.7729 + 0.0998 i
0.0316 - 0.261 i
4
-0.7729 - 0.0998 i
0.0316 + 0.261 i
5
-0.8924
0.195
6
-1.1718
0.591 i
7
-1.3778 + 0.8834 i
0.197 - 0.621 i
8
-1.3778 - 0.8834 i
0.197 + 0.621 i
9
1.5928 + 0.4795 i
0.118 - 0.0462 i
10
1.5928 - 0.4795 i
0.118 + 0.0462 i
11
1.7574 + 1.3453 i
0.0374 - 0.19 i
12
1.7574 - 1.3453 i
0.0374 + 0.19 i
13
44.728
4.03
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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
-0.5716 + 0.0741 i
0.451 + 0.13 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.5716 - 0.0741 i
0.451 - 0.13 i
3
-0.6312
0.639
4
-0.6788
0.547 i
5
-0.8665 + 0.1295 i
0.289 + 0.169 i
6
-0.8665 - 0.1295 i
0.289 - 0.169 i
7
1.6247 + 0.4484 i
0.139 - 0.125 i
8
1.6247 - 0.4484 i
0.139 + 0.125 i
9
-1.3744 + 1.0876 i
0.349 + 0.315 i
10
-1.3744 - 1.0876 i
0.349 - 0.315 i
11
1.8228 + 1.1486 i
0.119 + 0.206 i
12
1.8228 - 1.1486 i
0.119 - 0.206 i
13
4.8696 + 10.6601 i
0.973 + 0.0647 i
14
4.8696 - 10.6601 i
0.973 - 0.0647 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.