Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 1.1r_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
1.2966
0.205
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
1.2337
0.186
Singularities of quadratic [1, 1, 0] approximant
2
2046.2907
7.58 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
1.5166
0.415
Singularities of quadratic [1, 1, 1] approximant
2
-6.6362
0.696
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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
1.4961
0.39
Singularities of quadratic [2, 1, 1] approximant
2
-5.4455
0.582
3
-23.6825
0.383 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
1.5242
0.461
Singularities of quadratic [2, 2, 1] approximant
2
-4.1963
0.29
3
-11.0109
0.254 i
4
162.0552
1.13 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
1.5857
0.718
Singularities of quadratic [2, 2, 2] approximant
2
3.3214
0.72 i
3
4.6131
315.
4
-4.9565
0.338
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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
0.6966 + 0.0012 i
0.014 - 0.0139 i
Singularities of quadratic [3, 2, 2] approximant
2
0.6966 - 0.0012 i
0.014 + 0.0139 i
3
1.5382
0.587
4
-5.1756
0.815
5
-12.0964
0.401 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
1.5608 + 0.3748 i
0.236 - 0.153 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5608 - 0.3748 i
0.236 + 0.153 i
3
2.0473
0.413
4
-3.6626
0.118
5
-13.2757
0.186 i
6
17.4851
0.351 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
1.555 + 0.3692 i
0.23 - 0.164 i
Singularities of quadratic [3, 3, 3] approximant
2
1.555 - 0.3692 i
0.23 + 0.164 i
3
2.008
0.38
4
-3.6527
0.119
5
-11.9113
0.181 i
6
21.8453
0.343 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
1.5654 + 0.4306 i
0.196 - 0.033 i
Singularities of quadratic [4, 3, 3] approximant
2
1.5654 - 0.4306 i
0.196 + 0.033 i
3
2.2434
0.85
4
-3.3477
0.0626
5
-0.8372 + 8.5072 i
0.0504 + 0.118 i
6
-0.8372 - 8.5072 i
0.0504 - 0.118 i
7
132.932
1.78 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
1.5659 + 0.4072 i
0.222 - 0.0692 i
Singularities of quadratic [4, 4, 3] approximant
2
1.5659 - 0.4072 i
0.222 + 0.0692 i
3
2.1345
0.554
4
-2.5546
0.0225
5
-2.7853
0.0237 i
6
-6.2771 + 0.6113 i
0.062 + 0.212 i
7
-6.2771 - 0.6113 i
0.062 - 0.212 i
8
23.8536
0.367 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
1.5643 + 0.4151 i
0.212 - 0.0488 i
Singularities of quadratic [4, 4, 4] approximant
2
1.5643 - 0.4151 i
0.212 + 0.0488 i
3
2.1263
0.567
4
-2.5309
0.0165
5
-2.8565
0.0172 i
6
-4.5918 + 2.3647 i
0.0661 - 0.0816 i
7
-4.5918 - 2.3647 i
0.0661 + 0.0816 i
8
-374.2068
0.277
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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
1.5644 + 0.4145 i
0.213 - 0.0503 i
Singularities of quadratic [5, 4, 4] approximant
2
1.5644 - 0.4145 i
0.213 + 0.0503 i
3
2.1279
0.567
4
-2.5001
0.0163
5
-2.7773
0.017 i
6
-4.8137 + 2.2171 i
0.0749 - 0.0946 i
7
-4.8137 - 2.2171 i
0.0749 + 0.0946 i
8
3.5409 + 94.764 i
0.118 + 0.572 i
9
3.5409 - 94.764 i
0.118 - 0.572 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
-1.5291 + 0.005 i
0.00112 + 0.00114 i
Singularities of quadratic [5, 5, 4] approximant
2
-1.5291 - 0.005 i
0.00112 - 0.00114 i
3
1.5654 + 0.4141 i
0.216 - 0.0489 i
4
1.5654 - 0.4141 i
0.216 + 0.0489 i
5
-1.9612 + 0.0326 i
0.00418 + 0.00346 i
6
-1.9612 - 0.0326 i
0.00418 - 0.00346 i
7
2.1227
0.555
8
-3.9711
0.179
9
-10.5803
0.198 i
10
25.5448
0.385 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
0.5936
0.00167
Singularities of quadratic [5, 5, 5] approximant
2
0.5936
0.00167 i
3
1.5638 + 0.416 i
0.21 - 0.0475 i
4
1.5638 - 0.416 i
0.21 + 0.0475 i
5
2.1277
0.572
6
-2.5589
0.0161
7
-2.959
0.0169 i
8
-4.2885 + 2.5121 i
0.0525 - 0.068 i
9
-4.2885 - 2.5121 i
0.0525 + 0.068 i
10
-71.1216
1.18
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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
1.3574 + 0.005 i
0.00578 - 0.00573 i
Singularities of quadratic [6, 5, 5] approximant
2
1.3574 - 0.005 i
0.00578 + 0.00573 i
3
1.6707
0.117
4
1.6301 + 0.5065 i
0.0155 - 0.193 i
5
1.6301 - 0.5065 i
0.0155 + 0.193 i
6
-2.5077 + 0.086 i
0.0125 + 0.0122 i
7
-2.5077 - 0.086 i
0.0125 - 0.0122 i
8
-4.1128
0.0976
9
5.1247
109. i
10
-7.2862
1.34 i
11
15.1725
0.695
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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
1.2008 + 0.0024 i
0.00308 - 0.00306 i
Singularities of quadratic [6, 6, 5] approximant
2
1.2008 - 0.0024 i
0.00308 + 0.00306 i
3
1.6191 + 0.4822 i
0.0451 + 0.216 i
4
1.6191 - 0.4822 i
0.0451 - 0.216 i
5
1.7734
0.219
6
-2.4221 + 0.1297 i
0.00378 + 0.00417 i
7
-2.4221 - 0.1297 i
0.00378 - 0.00417 i
8
-3.232
0.0117
9
-5.4026
0.151 i
10
8.0796
0.737 i
11
-8.0346 + 9.5741 i
0.181 + 0.0188 i
12
-8.0346 - 9.5741 i
0.181 - 0.0188 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
1.2663 + 0.0044 i
0.00697 - 0.00693 i
Singularities of quadratic [6, 6, 6] approximant
2
1.2663 - 0.0044 i
0.00697 + 0.00693 i
3
1.6108 + 0.4654 i
0.134 + 0.229 i
4
1.6108 - 0.4654 i
0.134 - 0.229 i
5
1.8358
0.27
6
-2.4764 + 0.074 i
0.0125 + 0.0126 i
7
-2.4764 - 0.074 i
0.0125 - 0.0126 i
8
-3.8598
0.0707
9
10.1101
0.672 i
10
-12.2231
0.472 i
11
0.6234 + 13.5181 i
0.313 - 1.31 i
12
0.6234 - 13.5181 i
0.313 + 1.31 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
1.2863 + 0.0052 i
0.00886 - 0.00881 i
Singularities of quadratic [7, 6, 6] approximant
2
1.2863 - 0.0052 i
0.00886 + 0.00881 i
3
1.6078 + 0.4622 i
0.159 + 0.22 i
4
1.6078 - 0.4622 i
0.159 - 0.22 i
5
1.8523
0.284
6
-2.4828 + 0.0551 i
0.02 + 0.0203 i
7
-2.4828 - 0.0551 i
0.02 - 0.0203 i
8
-3.9696
0.109
9
8.8904
1.19 i
10
-9.893 + 8.9531 i
0.136 - 0.306 i
11
-9.893 - 8.9531 i
0.136 + 0.306 i
12
2.7199 + 13.8219 i
1.07 + 0.214 i
13
2.7199 - 13.8219 i
1.07 - 0.214 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
1.2179 + 0.4909 i
0.00282 - 0.00321 i
Singularities of quadratic [7, 7, 6] approximant
2
1.2179 - 0.4909 i
0.00282 + 0.00321 i
3
1.2242 + 0.4927 i
0.00325 + 0.00283 i
4
1.2242 - 0.4927 i
0.00325 - 0.00283 i
5
1.6653
0.144
6
1.648 + 0.5439 i
0.0746 - 0.0908 i
7
1.648 - 0.5439 i
0.0746 + 0.0908 i
8
-2.4701 + 0.0674 i
0.013 + 0.0145 i
9
-2.4701 - 0.0674 i
0.013 - 0.0145 i
10
-3.6773
0.0459
11
-7.0501
1.8 i
12
8.291
0.582 i
13
-7.829 + 9.0126 i
0.195 + 0.0656 i
14
-7.829 - 9.0126 i
0.195 - 0.0656 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.