Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 2.2r_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
1.0106
0.184
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
0.7662
0.108
Singularities of quadratic [1, 1, 0] approximant
2
45.8173
0.839 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
1.2363
0.801
Singularities of quadratic [1, 1, 1] approximant
2
-2.1073
0.221
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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
1.2957
1.14
Singularities of quadratic [2, 1, 1] approximant
2
-2.2453
0.225
3
14.3274
0.253 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
-1.4682
0.0623
Singularities of quadratic [2, 2, 1] approximant
2
1.9292
0.756
3
3.1918
0.179 i
4
-5.3013
0.106 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
1.216 + 0.5719 i
0.268 - 0.0554 i
Singularities of quadratic [2, 2, 2] approximant
2
1.216 - 0.5719 i
0.268 + 0.0554 i
3
-1.8149
0.119
4
2.1938
0.631
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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
0.8111 + 0.8903 i
0.0242 + 0.0212 i
Singularities of quadratic [3, 2, 2] approximant
2
0.8111 - 0.8903 i
0.0242 - 0.0212 i
3
-1.4454
0.0319
4
0.6374 + 1.4256 i
0.0324 - 0.0102 i
5
0.6374 - 1.4256 i
0.0324 + 0.0102 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
1.1676 + 0.2235 i
0.359 - 0.0379 i
Singularities of quadratic [3, 3, 2] approximant
2
1.1676 - 0.2235 i
0.359 + 0.0379 i
3
1.7579
0.383
4
-2.0786
0.415
5
-4.6581
0.235 i
6
212.7457
1.45 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
1.1889 + 0.3097 i
0.372 + 0.304 i
Singularities of quadratic [3, 3, 3] approximant
2
1.1889 - 0.3097 i
0.372 - 0.304 i
3
1.7441
0.35
4
-1.6889 + 0.5663 i
0.0357 + 0.0702 i
5
-1.6889 - 0.5663 i
0.0357 - 0.0702 i
6
-2.3402
0.0665
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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
1.1479 + 0.4157 i
0.1 - 0.286 i
Singularities of quadratic [4, 3, 3] approximant
2
1.1479 - 0.4157 i
0.1 + 0.286 i
3
1.6504
0.289
4
-2.3567 + 0.5555 i
0.334 + 0.226 i
5
-2.3567 - 0.5555 i
0.334 - 0.226 i
6
2.5387
23.3 i
7
13.7272
0.819
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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
0.2162
0.0000145
Singularities of quadratic [4, 4, 3] approximant
2
0.2162
0.0000145 i
3
1.1355
0.062
4
1.1114 + 0.5667 i
0.0577 + 0.0377 i
5
1.1114 - 0.5667 i
0.0577 - 0.0377 i
6
-2.4869 + 0.8558 i
0.111 - 0.108 i
7
-2.4869 - 0.8558 i
0.111 + 0.108 i
8
11.398
0.217 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
1.0996 + 0.4091 i
0.035 - 0.205 i
Singularities of quadratic [4, 4, 4] approximant
2
1.0996 - 0.4091 i
0.035 + 0.205 i
3
1.4808 + 0.3008 i
0.24 + 0.0186 i
4
1.4808 - 0.3008 i
0.24 - 0.0186 i
5
-2.1505 + 0.6264 i
0.174 + 0.162 i
6
-2.1505 - 0.6264 i
0.174 - 0.162 i
7
2.7069
0.339
8
-6.0522
0.372
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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
1.0772 + 0.4415 i
0.079 - 0.0888 i
Singularities of quadratic [5, 4, 4] approximant
2
1.0772 - 0.4415 i
0.079 + 0.0888 i
3
1.3621
0.117
4
1.5869
0.354 i
5
-2.1529 + 0.5671 i
0.106 + 0.254 i
6
-2.1529 - 0.5671 i
0.106 - 0.254 i
7
3.9769
1.92
8
6.0501
3.29 i
9
-7.8751
0.298
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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
1.0791 + 0.4402 i
0.0803 - 0.0941 i
Singularities of quadratic [5, 5, 4] approximant
2
1.0791 - 0.4402 i
0.0803 + 0.0941 i
3
1.3848
0.12
4
1.5817
0.309 i
5
-2.1553 + 0.5761 i
0.121 + 0.243 i
6
-2.1553 - 0.5761 i
0.121 - 0.243 i
7
3.9971
1.63
8
6.2553
3.63 i
9
-8.1631
0.333
10
-2570.5441
10.5 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
1.0788 + 0.44 i
0.0794 - 0.0943 i
Singularities of quadratic [5, 5, 5] approximant
2
1.0788 - 0.44 i
0.0794 + 0.0943 i
3
1.3805
0.121
4
1.5934
0.344 i
5
-2.1555 + 0.5815 i
0.129 + 0.235 i
6
-2.1555 - 0.5815 i
0.129 - 0.235 i
7
4.4299 + 0.9281 i
0.121 + 1.95 i
8
4.4299 - 0.9281 i
0.121 - 1.95 i
9
-7.778
0.353
10
30.2276
1.81
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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
0.0542
5.98e-9
Singularities of quadratic [6, 5, 5] approximant
2
0.0542
5.98e-9 i
3
1.079 + 0.4416 i
0.0838 - 0.0901 i
4
1.079 - 0.4416 i
0.0838 + 0.0901 i
5
1.3824
0.11
6
1.5453
0.237 i
7
-2.1576 + 0.5828 i
0.136 + 0.236 i
8
-2.1576 - 0.5828 i
0.136 - 0.236 i
9
3.4613
0.888
10
-7.5832
0.312
11
7.996
1.12 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
1.0912 + 0.4042 i
0.0636 + 0.147 i
Singularities of quadratic [6, 6, 5] approximant
2
1.0912 - 0.4042 i
0.0636 - 0.147 i
3
1.2464 + 0.6138 i
0.122 - 0.0214 i
4
1.2464 - 0.6138 i
0.122 + 0.0214 i
5
1.5302
0.417
6
1.472 + 0.6298 i
0.00754 - 0.247 i
7
1.472 - 0.6298 i
0.00754 + 0.247 i
8
-2.1623 + 0.6293 i
0.195 + 0.155 i
9
-2.1623 - 0.6293 i
0.195 - 0.155 i
10
-5.2027
0.276
11
-22.8448
0.334 i
12
27.5221
0.381 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
0.2796 + 1.1038 i
0.00115 - 0.00185 i
Singularities of quadratic [6, 6, 6] approximant
2
0.2796 - 1.1038 i
0.00115 + 0.00185 i
3
0.2806 + 1.1044 i
0.00185 + 0.00115 i
4
0.2806 - 1.1044 i
0.00185 - 0.00115 i
5
1.076 + 0.4634 i
0.0888 - 0.0249 i
6
1.076 - 0.4634 i
0.0888 + 0.0249 i
7
1.2844 + 0.1022 i
0.0896 - 0.0297 i
8
1.2844 - 0.1022 i
0.0896 + 0.0297 i
9
2.0823
0.46
10
-2.1489 + 0.6146 i
0.14 + 0.174 i
11
-2.1489 - 0.6146 i
0.14 - 0.174 i
12
-7.5326
0.627
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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
1.0996 + 0.435 i
0.107 - 0.192 i
Singularities of quadratic [7, 6, 6] approximant
2
1.0996 - 0.435 i
0.107 + 0.192 i
3
1.3496 + 0.395 i
0.226 + 0.143 i
4
1.3496 - 0.395 i
0.226 - 0.143 i
5
1.4505 + 0.2667 i
0.289 - 1.08 i
6
1.4505 - 0.2667 i
0.289 + 1.08 i
7
-2.1488 + 0.6398 i
0.169 + 0.138 i
8
-2.1488 - 0.6398 i
0.169 - 0.138 i
9
2.5922
0.458
10
-5.4574 + 0.17 i
2.56 - 1.61 i
11
-5.4574 - 0.17 i
2.56 + 1.61 i
12
5.5234
3.01 i
13
-68.0107
3.
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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
1.0929 + 0.4378 i
0.102 - 0.138 i
Singularities of quadratic [7, 7, 6] approximant
2
1.0929 - 0.4378 i
0.102 + 0.138 i
3
1.505 + 0.4338 i
0.307 + 0.0408 i
4
1.505 - 0.4338 i
0.307 - 0.0408 i
5
1.6116
0.277
6
1.848 + 0.5507 i
0.817 + 0.0563 i
7
1.848 - 0.5507 i
0.817 - 0.0563 i
8
-2.1301 + 0.6136 i
0.103 + 0.187 i
9
-2.1301 - 0.6136 i
0.103 - 0.187 i
10
-3.4251
0.179
11
-3.6842 + 0.8405 i
0.0807 - 0.0744 i
12
-3.6842 - 0.8405 i
0.0807 + 0.0744 i
13
10.9355
0.33 i
14
-20.2045
0.254 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.