Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 2.1r_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
1.0265
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
0.8089
0.116
Singularities of quadratic [1, 1, 0] approximant
2
64.1685
1.04 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
1.2732
0.783
Singularities of quadratic [1, 1, 1] approximant
2
-2.2979
0.234
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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
1.3448
1.17
Singularities of quadratic [2, 1, 1] approximant
2
-2.5106
0.243
3
12.1865
0.272 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
-1.5605
0.0613
Singularities of quadratic [2, 2, 1] approximant
2
1.9849
0.815
3
3.3802
0.182 i
4
-5.0453
0.099 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
1.3095 + 0.6115 i
0.305 - 0.0314 i
Singularities of quadratic [2, 2, 2] approximant
2
1.3095 - 0.6115 i
0.305 + 0.0314 i
3
-1.9704
0.123
4
2.5775
0.988
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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
0.4465 + 0.0041 i
0.0009 - 0.000882 i
Singularities of quadratic [3, 2, 2] approximant
2
0.4465 - 0.0041 i
0.0009 + 0.000882 i
3
-1.1025 + 0.8425 i
0.0131 + 0.00363 i
4
-1.1025 - 0.8425 i
0.0131 - 0.00363 i
5
-18.9707
0.246
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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
1.2335 + 0.2349 i
0.437 - 0.0288 i
Singularities of quadratic [3, 3, 2] approximant
2
1.2335 - 0.2349 i
0.437 + 0.0288 i
3
1.8172
0.41
4
-2.1679
0.313
5
-5.492
0.214 i
6
116.9271
0.985 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
1.2424 + 0.2977 i
0.398 + 0.188 i
Singularities of quadratic [3, 3, 3] approximant
2
1.2424 - 0.2977 i
0.398 - 0.188 i
3
-1.7775 + 0.5898 i
0.0314 + 0.0604 i
4
-1.7775 - 0.5898 i
0.0314 - 0.0604 i
5
1.9187
0.362
6
-2.4024
0.058
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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
1.2254 + 0.4127 i
0.101 - 0.384 i
Singularities of quadratic [4, 3, 3] approximant
2
1.2254 - 0.4127 i
0.101 + 0.384 i
3
1.6822
0.335
4
-2.6423 + 0.4183 i
0.643 + 0.398 i
5
-2.6423 - 0.4183 i
0.643 - 0.398 i
6
3.0167
18.9 i
7
14.3416
0.957
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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
0.2811
0.0000401
Singularities of quadratic [4, 4, 3] approximant
2
0.2811
0.0000401 i
3
1.2032
0.0795
4
1.2103 + 0.5726 i
0.0778 + 0.0565 i
5
1.2103 - 0.5726 i
0.0778 - 0.0565 i
6
-2.7856 + 0.6971 i
0.152 - 0.167 i
7
-2.7856 - 0.6971 i
0.152 + 0.167 i
8
14.0666
0.249 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
1.1592 + 0.3974 i
0.033 + 0.24 i
Singularities of quadratic [4, 4, 4] approximant
2
1.1592 - 0.3974 i
0.033 - 0.24 i
3
1.4888 + 0.3003 i
0.257 - 0.00816 i
4
1.4888 - 0.3003 i
0.257 + 0.00816 i
5
-2.3376 + 0.6372 i
0.196 + 0.159 i
6
-2.3376 - 0.6372 i
0.196 - 0.159 i
7
2.4461
0.347
8
-6.5225
0.451
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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
1.1372 + 0.4392 i
0.0757 - 0.109 i
Singularities of quadratic [5, 4, 4] approximant
2
1.1372 - 0.4392 i
0.0757 + 0.109 i
3
1.4564 + 0.0522 i
0.0978 - 0.0607 i
4
1.4564 - 0.0522 i
0.0978 + 0.0607 i
5
-2.3409 + 0.5718 i
0.133 + 0.272 i
6
-2.3409 - 0.5718 i
0.133 - 0.272 i
7
3.3516
0.778
8
-7.8259
0.32
9
8.1812
1.1 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
1.1269 + 0.4455 i
0.0685 - 0.0825 i
Singularities of quadratic [5, 5, 4] approximant
2
1.1269 - 0.4455 i
0.0685 + 0.0825 i
3
1.3343
0.0847
4
1.4928
0.176 i
5
-2.3217 + 0.5291 i
0.0342 + 0.312 i
6
-2.3217 - 0.5291 i
0.0342 - 0.312 i
7
3.4141
1.22
8
-6.7496
0.212
9
6.9715
0.971 i
10
-210.8127
1.6 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
1.1263 + 0.4452 i
0.0673 - 0.0827 i
Singularities of quadratic [5, 5, 5] approximant
2
1.1263 - 0.4452 i
0.0673 + 0.0827 i
3
1.3305
0.0863
4
1.5016
0.191 i
5
-2.3248 + 0.5419 i
0.0646 + 0.302 i
6
-2.3248 - 0.5419 i
0.0646 - 0.302 i
7
3.9659
3.66
8
4.7506
21.6 i
9
-6.7253
0.241
10
30.3837
10.2
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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
1.13 + 0.4409 i
0.0623 - 0.0986 i
Singularities of quadratic [6, 5, 5] approximant
2
1.13 - 0.4409 i
0.0623 + 0.0986 i
3
1.3676
0.114
4
-1.5668 + 0.0116 i
0.00606 + 0.00607 i
5
-1.5668 - 0.0116 i
0.00606 - 0.00607 i
6
1.6027
0.36 i
7
-2.1515 + 0.4141 i
0.0646 - 0.0594 i
8
-2.1515 - 0.4141 i
0.0646 + 0.0594 i
9
3.4356 + 1.8938 i
0.149 - 0.397 i
10
3.4356 - 1.8938 i
0.149 + 0.397 i
11
-10.6727
0.274
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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
1.1455 + 0.4239 i
0.00247 - 0.172 i
Singularities of quadratic [6, 6, 5] approximant
2
1.1455 - 0.4239 i
0.00247 + 0.172 i
3
1.5278
0.323
4
1.4286 + 0.6336 i
0.145 + 0.0473 i
5
1.4286 - 0.6336 i
0.145 - 0.0473 i
6
1.6451 + 0.8217 i
0.157 - 0.136 i
7
1.6451 - 0.8217 i
0.157 + 0.136 i
8
-2.342 + 0.6114 i
0.202 + 0.2 i
9
-2.342 - 0.6114 i
0.202 - 0.2 i
10
-5.2926
0.266
11
-22.5666
0.332 i
12
26.2049
0.376 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
0.2711 + 0.e-5 i
3.46e-7 - 3.46e-7 i
Singularities of quadratic [6, 6, 6] approximant
2
0.2711 - 0.e-5 i
3.46e-7 + 3.46e-7 i
3
0.8559 + 0.5337 i
0.00186 + 0.000454 i
4
0.8559 - 0.5337 i
0.00186 - 0.000454 i
5
0.8683 + 0.5487 i
0.000445 - 0.00196 i
6
0.8683 - 0.5487 i
0.000445 + 0.00196 i
7
1.0324 + 0.45 i
0.00573 - 0.00871 i
8
1.0324 - 0.45 i
0.00573 + 0.00871 i
9
1.7935
0.628
10
-2.3201 + 0.5823 i
0.1 + 0.22 i
11
-2.3201 - 0.5823 i
0.1 - 0.22 i
12
-8.035
0.642
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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
1.1609 + 0.4394 i
0.117 - 0.258 i
Singularities of quadratic [7, 6, 6] approximant
2
1.1609 - 0.4394 i
0.117 + 0.258 i
3
1.3408 + 0.4258 i
0.28 + 0.176 i
4
1.3408 - 0.4258 i
0.28 - 0.176 i
5
1.4806 + 0.332 i
1.99 - 1.12 i
6
1.4806 - 0.332 i
1.99 + 1.12 i
7
2.3977
0.437
8
-2.3332 + 0.6282 i
0.187 + 0.168 i
9
-2.3332 - 0.6282 i
0.187 - 0.168 i
10
-5.3071
0.559
11
5.8256
1.95 i
12
-7.5102
1.39 i
13
157.2949
8.81
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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
1.1482 + 0.4452 i
0.11 - 0.138 i
Singularities of quadratic [7, 7, 6] approximant
2
1.1482 - 0.4452 i
0.11 + 0.138 i
3
1.5172 + 0.4149 i
0.3 + 0.022 i
4
1.5172 - 0.4149 i
0.3 - 0.022 i
5
1.6453
0.276
6
1.8379 + 0.546 i
0.994 + 0.0134 i
7
1.8379 - 0.546 i
0.994 - 0.0134 i
8
-2.3063 + 0.5693 i
0.0124 + 0.278 i
9
-2.3063 - 0.5693 i
0.0124 - 0.278 i
10
-2.7067
21.8
11
-3.1885
0.119 i
12
-3.8018
0.088
13
12.0457
0.317 i
14
-18.5762
0.245 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.