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

Molecule X 1^Sigma+ State of BH. Basis CC-PVDZ. Structure ""

Content


ExamplesBH-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-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 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 O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-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 [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 2. Singularities with their weights for the quadratic approximant [2, 2, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.7843 + 0.0112 i
0.003 - 0.00292 i
Singularities of quadratic [2, 2, 3] approximant
2
0.7843 - 0.0112 i
0.003 + 0.00292 i
3
1.4757 + 1.1771 i
0.0228 - 0.0728 i
4
1.4757 - 1.1771 i
0.0228 + 0.0728 i
5
2.8499
20.2
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Table 3. Singularities with their weights for the quadratic approximant [2, 3, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5708 + 0.5055 i
0.491 - 0.43 i
Singularities of quadratic [2, 3, 3] approximant
2
1.5708 - 0.5055 i
0.491 + 0.43 i
3
1.958
0.458
4
-4.8419
0.0654
5
-6.3032
0.0686 i
6
124.7306
0.714 i
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Table 4. 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 5. Singularities with their weights for the quadratic approximant [3, 3, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.3702
0.0396
Singularities of quadratic [3, 3, 4] approximant
2
1.3939 + 0.557 i
0.0553 - 0.0505 i
3
1.3939 - 0.557 i
0.0553 + 0.0505 i
4
1.5424
0.0745 i
5
3.3071
2.73
6
-3.9905
0.0212
7
-5.3851
0.0241 i
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Table 6. Singularities with their weights for the quadratic approximant [3, 4, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2884
0.0198
Singularities of quadratic [3, 4, 4] approximant
2
1.3417
0.0229 i
3
1.4012 + 0.5183 i
0.0387 - 0.0725 i
4
1.4012 - 0.5183 i
0.0387 + 0.0725 i
5
2.9326
1.22
6
-4.1243
0.0246
7
-5.6114
0.028 i
8
3152.967
1.8 i
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Table 7. 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 8. Singularities with their weights for the quadratic approximant [4, 4, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-1.2103 + 0.0004 i
0.000236 + 0.000236 i
Singularities of quadratic [4, 4, 5] approximant
2
-1.2103 - 0.0004 i
0.000236 - 0.000236 i
3
1.4612 + 0.4757 i
0.018 + 0.238 i
4
1.4612 - 0.4757 i
0.018 - 0.238 i
5
1.8107 + 0.1256 i
0.483 - 0.0795 i
6
1.8107 - 0.1256 i
0.483 + 0.0795 i
7
2.7058
0.651
8
-3.9603
0.0128
9
-6.2494
0.0198 i
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Table 9. Singularities with their weights for the quadratic approximant [4, 5, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.9715
0.00156
Singularities of quadratic [4, 5, 5] approximant
2
0.9734
0.00157 i
3
1.4111 + 0.4835 i
0.00155 - 0.086 i
4
1.4111 - 0.4835 i
0.00155 + 0.086 i
5
2.6911
0.947
6
-2.904
0.00486
7
-3.1409
0.00486 i
8
-5.7956 + 1.3896 i
0.0315 + 0.00113 i
9
-5.7956 - 1.3896 i
0.0315 - 0.00113 i
10
159.7966
0.838 i
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Table 10. 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 11. Singularities with their weights for the quadratic approximant [5, 5, 6]
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 [5, 5, 6] approximant
2
1.4321 - 0.4885 i
0.0236 - 0.13 i
3
1.8927
0.606
4
1.9753 + 1.7564 i
0.011 + 0.052 i
5
1.9753 - 1.7564 i
0.011 - 0.052 i
6
2.4433 + 1.3352 i
0.096 - 0.0243 i
7
2.4433 - 1.3352 i
0.096 + 0.0243 i
8
-3.4147 + 0.4666 i
0.00238 + 0.00291 i
9
-3.4147 - 0.4666 i
0.00238 - 0.00291 i
10
-5.2587
0.00563
11
91.1465
0.0939 i
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Table 12. Singularities with their weights for the quadratic approximant [5, 6, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4512 + 0.5118 i
0.0987 - 0.186 i
Singularities of quadratic [5, 6, 6] approximant
2
1.4512 - 0.5118 i
0.0987 + 0.186 i
3
1.7328
0.18
4
1.9092
0.41 i
5
2.4802 + 1.3369 i
0.239 + 0.135 i
6
2.4802 - 1.3369 i
0.239 - 0.135 i
7
-3.5381
0.0198
8
-4.056
0.0186 i
9
4.653
0.264
10
9.155
0.997 i
11
-9.5719 + 7.6776 i
0.0766 + 0.00668 i
12
-9.5719 - 7.6776 i
0.0766 - 0.00668 i
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Table 13. 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 14. Singularities with their weights for the quadratic approximant [6, 6, 7]
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 [6, 6, 7] approximant
2
1.4516 - 0.5179 i
0.132 + 0.161 i
3
1.6713
0.106
4
1.7592
0.155 i
5
2.5341 + 1.4235 i
0.159 + 0.123 i
6
2.5341 - 1.4235 i
0.159 - 0.123 i
7
-3.2782
0.00387
8
-3.808 + 3.7515 i
0.00545 + 0.000229 i
9
-3.808 - 3.7515 i
0.00545 - 0.000229 i
10
-4.7519 + 2.4821 i
0.0009 - 0.00352 i
11
-4.7519 - 2.4821 i
0.0009 + 0.00352 i
12
5.9949 + 3.5449 i
0.148 + 0.184 i
13
5.9949 - 3.5449 i
0.148 - 0.184 i
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Table 15. Singularities with their weights for the quadratic approximant [6, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.1709
1.09e-9
Singularities of quadratic [6, 7, 7] approximant
2
0.1709
1.09e-9 i
3
1.444 + 0.5119 i
0.0617 - 0.146 i
4
1.444 - 0.5119 i
0.0617 + 0.146 i
5
1.9337 + 0.0999 i
0.322 - 0.135 i
6
1.9337 - 0.0999 i
0.322 + 0.135 i
7
2.391 + 0.9644 i
0.302 - 0.527 i
8
2.391 - 0.9644 i
0.302 + 0.527 i
9
-3.3461
0.00528
10
-4.9136
0.00613 i
11
4.8492 + 1.2096 i
0.109 - 0.174 i
12
4.8492 - 1.2096 i
0.109 + 0.174 i
13
-4.2323 + 8.2125 i
0.0181 - 0.0211 i
14
-4.2323 - 8.2125 i
0.0181 + 0.0211 i
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ExamplesBH-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-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 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 O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-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.