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

Molecule X 1^Sigma+ State of BH. Basis 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
0.797
0.105
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
1.2836
0.303
Singularities of quadratic [1, 1, 0] approximant
2
17.7315
1.13 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
1.5967
1.27
Singularities of quadratic [1, 1, 1] approximant
2
-10.3761
0.164
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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
-1.874 + 0.1418 i
0.0161 + 0.0155 i
Singularities of quadratic [2, 1, 1] approximant
2
-1.874 - 0.1418 i
0.0161 - 0.0155 i
3
1.8812
2.25e3
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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
0.9637 + 0.0373 i
0.0272 - 0.0251 i
Singularities of quadratic [2, 2, 1] approximant
2
0.9637 - 0.0373 i
0.0272 + 0.0251 i
3
2.0097
1.97
4
68.3057
1.07 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
1.5749 + 0.5911 i
0.408 - 0.2 i
Singularities of quadratic [2, 2, 2] approximant
2
1.5749 - 0.5911 i
0.408 + 0.2 i
3
2.2572
0.574
4
-13.4363
0.132
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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
0.8546 + 0.0174 i
0.00432 - 0.00415 i
Singularities of quadratic [3, 2, 2] approximant
2
0.8546 - 0.0174 i
0.00432 + 0.00415 i
3
1.4987 + 1.2165 i
0.0318 - 0.0721 i
4
1.4987 - 1.2165 i
0.0318 + 0.0721 i
5
3.0041
4.99
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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
1.5707 + 0.5057 i
0.491 - 0.428 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5707 - 0.5057 i
0.491 + 0.428 i
3
1.9575
0.458
4
-4.8456
0.0653
5
-6.3179
0.0685 i
6
120.6686
0.742 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
1.5668 + 0.5256 i
0.483 - 0.268 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5668 - 0.5256 i
0.483 + 0.268 i
3
1.9075
0.437
4
-5.2255
0.0556
5
-8.332
0.057 i
6
25.5125
111. 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
1.3748
0.0411
Singularities of quadratic [4, 3, 3] approximant
2
1.394 + 0.5596 i
0.0563 - 0.0492 i
3
1.394 - 0.5596 i
0.0563 + 0.0492 i
4
1.5577
0.0814 i
5
3.3388
2.98
6
-3.9809
0.021
7
-5.368
0.0238 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
1.2881
0.0198
Singularities of quadratic [4, 4, 3] approximant
2
1.3415
0.0229 i
3
1.4011 + 0.5183 i
0.0387 - 0.0725 i
4
1.4011 - 0.5183 i
0.0387 + 0.0725 i
5
2.933
1.22
6
-4.1242
0.0246
7
-5.6125
0.028 i
8
2732.5326
1.97 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
1.4826 + 0.441 i
0.195 + 0.345 i
Singularities of quadratic [4, 4, 4] approximant
2
1.4826 - 0.441 i
0.195 - 0.345 i
3
1.8736 + 0.2387 i
0.476 + 0.0559 i
4
1.8736 - 0.2387 i
0.476 - 0.0559 i
5
2.0586
0.736
6
-4.1889 + 0.3692 i
0.0209 + 0.0222 i
7
-4.1889 - 0.3692 i
0.0209 - 0.0222 i
8
-14.0292
0.0656
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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
-1.1846 + 0.0003 i
0.000216 + 0.000216 i
Singularities of quadratic [5, 4, 4] approximant
2
-1.1846 - 0.0003 i
0.000216 - 0.000216 i
3
1.4608 + 0.4738 i
0.0282 + 0.235 i
4
1.4608 - 0.4738 i
0.0282 - 0.235 i
5
1.8346 + 0.1344 i
0.521 - 0.0548 i
6
1.8346 - 0.1344 i
0.521 + 0.0548 i
7
2.7102
0.644
8
-3.9524
0.0127
9
-6.2466
0.0196 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
0.972
0.00157
Singularities of quadratic [5, 5, 4] approximant
2
0.9739
0.00157 i
3
1.4111 + 0.4835 i
0.00157 - 0.086 i
4
1.4111 - 0.4835 i
0.00157 + 0.086 i
5
2.6915
0.948
6
-2.9049
0.00488
7
-3.1416
0.00488 i
8
-5.8025 + 1.3847 i
0.0318 + 0.00112 i
9
-5.8025 - 1.3847 i
0.0318 - 0.00112 i
10
155.0396
0.876 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
1.4316 + 0.4877 i
0.0253 + 0.127 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4316 - 0.4877 i
0.0253 - 0.127 i
3
1.9212
0.635
4
1.8932 + 1.7137 i
0.0152 + 0.0449 i
5
1.8932 - 1.7137 i
0.0152 - 0.0449 i
6
2.2427 + 1.3885 i
0.0715 - 0.0321 i
7
2.2427 - 1.3885 i
0.0715 + 0.0321 i
8
-3.3959 + 0.4592 i
0.00225 + 0.00279 i
9
-3.3959 - 0.4592 i
0.00225 - 0.00279 i
10
-5.1017
0.00521
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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
1.4321 + 0.4885 i
0.0236 + 0.13 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4321 - 0.4885 i
0.0236 - 0.13 i
3
1.8926
0.606
4
1.9756 + 1.7562 i
0.011 + 0.0521 i
5
1.9756 - 1.7562 i
0.011 - 0.0521 i
6
2.4436 + 1.3346 i
0.0961 - 0.0243 i
7
2.4436 - 1.3346 i
0.0961 + 0.0243 i
8
-3.415 + 0.4665 i
0.00238 + 0.00291 i
9
-3.415 - 0.4665 i
0.00238 - 0.00291 i
10
-5.2607
0.00564
11
91.0406
0.0939 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
1.4512 + 0.5119 i
0.0988 - 0.186 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4512 - 0.5119 i
0.0988 + 0.186 i
3
1.7326
0.18
4
1.9083
0.408 i
5
2.4811 + 1.3367 i
0.24 + 0.135 i
6
2.4811 - 1.3367 i
0.24 - 0.135 i
7
-3.5385
0.0198
8
-4.0547
0.0187 i
9
4.6669
0.263
10
9.0877
0.958 i
11
-9.6254 + 7.6876 i
0.0774 + 0.00656 i
12
-9.6254 - 7.6876 i
0.0774 - 0.00656 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
1.4477 + 0.5187 i
0.112 - 0.146 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4477 - 0.5187 i
0.112 + 0.146 i
3
1.7062 + 0.0229 i
0.0721 - 0.0595 i
4
1.7062 - 0.0229 i
0.0721 + 0.0595 i
5
2.7823 + 1.2586 i
0.474 + 0.145 i
6
2.7823 - 1.2586 i
0.474 - 0.145 i
7
-3.7198 + 0.0663 i
0.0751 + 0.104 i
8
-3.7198 - 0.0663 i
0.0751 - 0.104 i
9
3.8875 + 2.4762 i
0.183 - 0.261 i
10
3.8875 - 2.4762 i
0.183 + 0.261 i
11
-8.936
0.0677
12
16.7909
0.162
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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
1.4516 + 0.5179 i
0.132 - 0.161 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4516 - 0.5179 i
0.132 + 0.161 i
3
1.6713
0.106
4
1.7593
0.155 i
5
2.5342 + 1.4232 i
0.159 + 0.123 i
6
2.5342 - 1.4232 i
0.159 - 0.123 i
7
-3.2781
0.00386
8
-3.8123 + 3.7461 i
0.00545 + 0.000249 i
9
-3.8123 - 3.7461 i
0.00545 - 0.000249 i
10
-4.7439 + 2.4758 i
0.000903 - 0.00352 i
11
-4.7439 - 2.4758 i
0.000903 + 0.00352 i
12
5.9997 + 3.5396 i
0.15 + 0.184 i
13
5.9997 - 3.5396 i
0.15 - 0.184 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
0.2022
3.19e-9
Singularities of quadratic [7, 7, 6] approximant
2
0.2022
3.19e-9 i
3
1.4437 + 0.5119 i
0.0607 - 0.145 i
4
1.4437 - 0.5119 i
0.0607 + 0.145 i
5
1.9383 + 0.1068 i
0.336 - 0.133 i
6
1.9383 - 0.1068 i
0.336 + 0.133 i
7
2.3828 + 0.959 i
0.274 - 0.535 i
8
2.3828 - 0.959 i
0.274 + 0.535 i
9
-3.3464
0.00529
10
-4.9106
0.00613 i
11
4.8175 + 1.2507 i
0.107 - 0.178 i
12
4.8175 - 1.2507 i
0.107 + 0.178 i
13
-4.2345 + 8.2295 i
0.0181 - 0.0211 i
14
-4.2345 - 8.2295 i
0.0181 + 0.0211 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.