Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 0.9r_e"

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

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 [1, 0, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.354
0.212
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
1.2915
0.193
Singularities of quadratic [1, 1, 0] approximant
2
2368.5008
8.27 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
1.4845
0.324
Singularities of quadratic [1, 1, 1] approximant
2
-9.9785
1.31
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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
1.4348
0.28
Singularities of quadratic [2, 1, 1] approximant
2
-4.1327
0.62
3
-6.0073
0.391 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
1.3938
0.227
Singularities of quadratic [2, 2, 1] approximant
2
-8.1312 + 3.6367 i
0.814 + 0.12 i
3
-8.1312 - 3.6367 i
0.814 - 0.12 i
4
41.7592
2.43 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
1.4175
0.275
Singularities of quadratic [2, 2, 2] approximant
2
4.8152
0.882 i
3
-6.5317
0.717
4
8.1374
0.792
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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
1.075
0.0374
Singularities of quadratic [3, 2, 2] approximant
2
1.1853 + 0.0893 i
0.018 + 0.0389 i
3
1.1853 - 0.0893 i
0.018 - 0.0389 i
4
-5.4019
0.376
5
-24.4626
0.368 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
1.6134 + 0.254 i
0.46 - 0.198 i
Singularities of quadratic [3, 3, 2] approximant
2
1.6134 - 0.254 i
0.46 + 0.198 i
3
2.5216
1.68
4
-4.0643
0.126
5
-12.4173
0.178 i
6
20.8342
0.378 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
1.6038 + 0.2568 i
0.432 - 0.212 i
Singularities of quadratic [3, 3, 3] approximant
2
1.6038 - 0.2568 i
0.432 + 0.212 i
3
2.4539
1.32
4
-4.036
0.126
5
-10.9031
0.172 i
6
29.5176
0.367 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
1.6163 + 0.2644 i
0.439 - 0.124 i
Singularities of quadratic [4, 3, 3] approximant
2
1.6163 - 0.2644 i
0.439 + 0.124 i
3
2.5737
2.53
4
-3.8857
0.0946
5
-17.7095
0.157 i
6
-3.8944 + 21.937 i
0.0726 - 0.241 i
7
-3.8944 - 21.937 i
0.0726 + 0.241 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
-0.4622 + 0.e-5 i
0.000195 + 0.000195 i
Singularities of quadratic [4, 4, 3] approximant
2
-0.4622 - 0.e-5 i
0.000195 - 0.000195 i
3
1.5999 + 0.2494 i
0.42 - 0.281 i
4
1.5999 - 0.2494 i
0.42 + 0.281 i
5
2.441
1.14
6
-3.995
0.109
7
-13.345
0.18 i
8
19.2662
0.376 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
1.4519 + 0.1038 i
0.119 - 0.034 i
Singularities of quadratic [4, 4, 4] approximant
2
1.4519 - 0.1038 i
0.119 + 0.034 i
3
-1.549 + 0.0038 i
0.00101 + 0.00101 i
4
-1.549 - 0.0038 i
0.00101 - 0.00101 i
5
2.2944
0.174
6
2.8915
0.412 i
7
-3.5766
0.0337
8
7.4926
0.846
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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
1.4602 + 0.1079 i
0.137 - 0.0337 i
Singularities of quadratic [5, 4, 4] approximant
2
1.4602 - 0.1079 i
0.137 + 0.0337 i
3
-1.7367 + 0.0073 i
0.00155 + 0.00155 i
4
-1.7367 - 0.0073 i
0.00155 - 0.00155 i
5
2.2378
0.181
6
2.9397
0.478 i
7
-3.6059
0.034
8
7.2511
0.728
9
-81.8183
0.484 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
1.2862
0.0666
Singularities of quadratic [5, 5, 4] approximant
2
1.3137
0.0759 i
3
1.6255 + 0.2102 i
0.378 - 0.32 i
4
1.6255 - 0.2102 i
0.378 + 0.32 i
5
-2.6606
0.0153
6
2.8821
21.6
7
-2.919
0.0159 i
8
-5.5018 + 2.5193 i
0.0831 - 0.105 i
9
-5.5018 - 2.5193 i
0.0831 + 0.105 i
10
30.2407
0.413 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
1.3337
0.336
Singularities of quadratic [5, 5, 5] approximant
2
1.3495
0.507 i
3
1.6804 + 0.2167 i
0.573 + 0.127 i
4
1.6804 - 0.2167 i
0.573 - 0.127 i
5
-2.7566
0.0145
6
3.0217
102.
7
-3.237
0.015 i
8
-4.1807 + 2.8681 i
0.0438 - 0.0473 i
9
-4.1807 - 2.8681 i
0.0438 + 0.0473 i
10
-43.8563
28.2
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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
1.3944 + 0.0868 i
0.0441 - 0.0185 i
Singularities of quadratic [6, 5, 5] approximant
2
1.3944 - 0.0868 i
0.0441 + 0.0185 i
3
1.8592 + 1.0325 i
0.032 + 0.0201 i
4
1.8592 - 1.0325 i
0.032 - 0.0201 i
5
2.0048 + 1.2835 i
0.032 - 0.0246 i
6
2.0048 - 1.2835 i
0.032 + 0.0246 i
7
-2.645 + 0.1326 i
0.0056 + 0.00534 i
8
-2.645 - 0.1326 i
0.0056 - 0.00534 i
9
-4.3387
0.0416
10
4.9452
0.343
11
-6.8888
16.1 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
1.3976 + 0.0919 i
0.0449 - 0.0169 i
Singularities of quadratic [6, 6, 5] approximant
2
1.3976 - 0.0919 i
0.0449 + 0.0169 i
3
1.6533 + 1.0221 i
0.0221 + 0.00514 i
4
1.6533 - 1.0221 i
0.0221 - 0.00514 i
5
1.7365 + 1.1302 i
0.00918 - 0.023 i
6
1.7365 - 1.1302 i
0.00918 + 0.023 i
7
-2.6927 + 0.1104 i
0.00959 + 0.00874 i
8
-2.6927 - 0.1104 i
0.00959 - 0.00874 i
9
3.8096
1.21
10
-5.6528 + 0.3401 i
0.447 - 0.101 i
11
-5.6528 - 0.3401 i
0.447 + 0.101 i
12
242.4857
1.92 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
0.779 + 0.e-4 i
0.000041 - 0.000041 i
Singularities of quadratic [6, 6, 6] approximant
2
0.779 - 0.e-4 i
0.000041 + 0.000041 i
3
1.3636 + 0.1102 i
0.0186 - 0.0018 i
4
1.3636 - 0.1102 i
0.0186 + 0.0018 i
5
1.967 + 0.9145 i
0.00602 + 0.0536 i
6
1.967 - 0.9145 i
0.00602 - 0.0536 i
7
-2.5607
0.00761
8
-2.8516
0.00891 i
9
2.952 + 0.5213 i
0.192 - 0.00344 i
10
2.952 - 0.5213 i
0.192 + 0.00344 i
11
-5.7697
1.07
12
-47.6945
0.15 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
1.2703
0.00298
Singularities of quadratic [7, 6, 6] approximant
2
1.2562 + 0.3112 i
0.0014 - 0.00105 i
3
1.2562 - 0.3112 i
0.0014 + 0.00105 i
4
1.3289 + 0.3326 i
0.00137 + 0.00193 i
5
1.3289 - 0.3326 i
0.00137 - 0.00193 i
6
1.9437 + 0.7473 i
0.000271 + 0.0289 i
7
1.9437 - 0.7473 i
0.000271 - 0.0289 i
8
-2.4578
0.00227
9
-3.1578
0.00382 i
10
-1.3773 + 3.3373 i
0.00204 + 0.00218 i
11
-1.3773 - 3.3373 i
0.00204 - 0.00218 i
12
-1.5855 + 3.664 i
0.00278 - 0.00219 i
13
-1.5855 - 3.664 i
0.00278 + 0.00219 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
1.3185 + 0.1548 i
0.00722 - 0.000898 i
Singularities of quadratic [7, 7, 6] approximant
2
1.3185 - 0.1548 i
0.00722 + 0.000898 i
3
1.582 + 0.3947 i
0.0128 - 0.0000117 i
4
1.582 - 0.3947 i
0.0128 + 0.0000117 i
5
1.5669 + 0.6514 i
0.00642 - 0.0064 i
6
1.5669 - 0.6514 i
0.00642 + 0.0064 i
7
-2.348 + 0.1946 i
0.000213 + 0.000599 i
8
-2.348 - 0.1946 i
0.000213 - 0.000599 i
9
-2.4692
0.000504
10
2.9215 + 1.7014 i
0.0584 - 0.0214 i
11
2.9215 - 1.7014 i
0.0584 + 0.0214 i
12
-4.1561
0.0109 i
13
12.6495 + 10.7833 i
0.199 + 0.0865 i
14
12.6495 - 10.7833 i
0.199 - 0.0865 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.