Singularities of Møller-Plesset series: example "H- cc-pV5Z"

Molecule H- ion. Basis AUG-CC-PV5Z. 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
1.272
0.0757
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
1.2502
0.0731
Singularities of quadratic [1, 1, 0] approximant
2
16955.5251
8.51 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
1.8532
0.477
Singularities of quadratic [1, 1, 1] approximant
2
-3.8431
0.103
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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
1.8646
0.497
Singularities of quadratic [2, 1, 1] approximant
2
-3.9396
0.105
3
103.4358
0.112 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
1.4576
0.0659
Singularities of quadratic [2, 2, 1] approximant
2
3.5623
0.778 i
3
-2.2607 + 5.5462 i
0.101 + 0.00514 i
4
-2.2607 - 5.5462 i
0.101 - 0.00514 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
1.3368
0.0434
Singularities of quadratic [2, 2, 2] approximant
2
2.1034
0.0871 i
3
10.0647
0.0755
4
-10.7919
2.73
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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
1.3731
0.0603
Singularities of quadratic [3, 2, 2] approximant
2
2.0557
0.095 i
3
5.7988 + 2.6513 i
0.0628 - 0.0905 i
4
5.7988 - 2.6513 i
0.0628 + 0.0905 i
5
-6.3948
0.366
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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
0.6336
0.000614
Singularities of quadratic [3, 3, 2] approximant
2
0.6377
0.000615 i
3
1.22
0.0116
4
2.8067
0.326 i
5
-6.189
0.138
6
-37.2236
1.84 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
-0.0973 + 0.e-5 i
1.7e-7 + 1.7e-7 i
Singularities of quadratic [3, 3, 3] approximant
2
-0.0973 - 0.e-5 i
1.7e-7 - 1.7e-7 i
3
1.1673 + 0.3612 i
0.00506 - 0.00132 i
4
1.1673 - 0.3612 i
0.00506 + 0.00132 i
5
1.7743
0.0199
6
32.989
0.0303 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
1.1799
0.00413
Singularities of quadratic [4, 3, 3] approximant
2
1.3876
0.00603 i
3
1.3227 + 0.6004 i
0.00242 - 0.0103 i
4
1.3227 - 0.6004 i
0.00242 + 0.0103 i
5
3.6513
0.149
6
-2.749 + 5.4597 i
0.038 - 0.0304 i
7
-2.749 - 5.4597 i
0.038 + 0.0304 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
1.4154 + 0.3593 i
0.0225 - 0.00144 i
Singularities of quadratic [4, 4, 3] approximant
2
1.4154 - 0.3593 i
0.0225 + 0.00144 i
3
1.6895 + 1.7105 i
0.0207 + 0.00195 i
4
1.6895 - 1.7105 i
0.0207 - 0.00195 i
5
1.5273 + 2.9773 i
0.0151 - 0.0167 i
6
1.5273 - 2.9773 i
0.0151 + 0.0167 i
7
-6.6635 + 2.073 i
0.0794 - 0.00343 i
8
-6.6635 - 2.073 i
0.0794 + 0.00343 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
1.4489 + 0.281 i
0.0272 - 0.0439 i
Singularities of quadratic [4, 4, 4] approximant
2
1.4489 - 0.281 i
0.0272 + 0.0439 i
3
1.9501 + 0.9484 i
0.0238 + 0.0476 i
4
1.9501 - 0.9484 i
0.0238 - 0.0476 i
5
1.7157 + 2.8947 i
0.0272 + 0.0161 i
6
1.7157 - 2.8947 i
0.0272 - 0.0161 i
7
-0.0112 + 6.6159 i
0.0281 - 0.0231 i
8
-0.0112 - 6.6159 i
0.0281 + 0.0231 i
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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
0.8302 + 0.0009 i
0.000122 - 0.000122 i
Singularities of quadratic [5, 4, 4] approximant
2
0.8302 - 0.0009 i
0.000122 + 0.000122 i
3
1.4232 + 0.5143 i
0.00219 + 0.0105 i
4
1.4232 - 0.5143 i
0.00219 - 0.0105 i
5
1.5023 + 2.1632 i
0.00623 - 0.0118 i
6
1.5023 - 2.1632 i
0.00623 + 0.0118 i
7
0.9715 + 5.5472 i
0.00281 + 0.0226 i
8
0.9715 - 5.5472 i
0.00281 - 0.0226 i
9
8.1948
0.0764
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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
1.4438 + 0.2595 i
0.0093 - 0.0525 i
Singularities of quadratic [5, 5, 4] approximant
2
1.4438 - 0.2595 i
0.0093 + 0.0525 i
3
1.8662 + 0.9293 i
0.0237 + 0.0299 i
4
1.8662 - 0.9293 i
0.0237 - 0.0299 i
5
1.6285 + 2.7816 i
0.0193 + 0.00899 i
6
1.6285 - 2.7816 i
0.0193 - 0.00899 i
7
-0.7559 + 5.6106 i
0.0181 - 0.0159 i
8
-0.7559 - 5.6106 i
0.0181 + 0.0159 i
9
11.4034 + 21.2162 i
0.0577 - 0.00222 i
10
11.4034 - 21.2162 i
0.0577 + 0.00222 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
1.3793 + 0.3146 i
0.013 - 0.0126 i
Singularities of quadratic [5, 5, 5] approximant
2
1.3793 - 0.3146 i
0.013 + 0.0126 i
3
1.6896 + 0.2609 i
0.0154 + 0.0305 i
4
1.6896 - 0.2609 i
0.0154 - 0.0305 i
5
1.7107 + 0.9299 i
0.0142 + 0.0201 i
6
1.7107 - 0.9299 i
0.0142 - 0.0201 i
7
1.6481 + 2.9057 i
0.0233 + 0.0113 i
8
1.6481 - 2.9057 i
0.0233 - 0.0113 i
9
-0.0018 + 6.1414 i
0.0245 - 0.0212 i
10
-0.0018 - 6.1414 i
0.0245 + 0.0212 i
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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
1.4397 + 0.282 i
0.0221 - 0.0388 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4397 - 0.282 i
0.0221 + 0.0388 i
3
1.881 + 1.0862 i
0.00241 + 0.0364 i
4
1.881 - 1.0862 i
0.00241 - 0.0364 i
5
1.4978 + 3.2623 i
0.00303 + 0.0191 i
6
1.4978 - 3.2623 i
0.00303 - 0.0191 i
7
-2.6988 + 3.4815 i
0.00302 + 0.00505 i
8
-2.6988 - 3.4815 i
0.00302 - 0.00505 i
9
-3.2268 + 3.1279 i
0.00566 - 0.00213 i
10
-3.2268 - 3.1279 i
0.00566 + 0.00213 i
11
-26.2762
100.
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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
1.4537 + 0.2868 i
0.0462 - 0.0361 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4537 - 0.2868 i
0.0462 + 0.0361 i
3
1.9234 + 0.7462 i
0.06 - 0.0304 i
4
1.9234 - 0.7462 i
0.06 + 0.0304 i
5
2.2977
0.123
6
2.0474 + 1.8019 i
0.00147 + 0.033 i
7
2.0474 - 1.8019 i
0.00147 - 0.033 i
8
0.4942 + 4.2162 i
0.0178 + 0.0116 i
9
0.4942 - 4.2162 i
0.0178 - 0.0116 i
10
-4.5638 + 0.1289 i
0.00466 + 0.0043 i
11
-4.5638 - 0.1289 i
0.00466 - 0.0043 i
12
10.4785
0.0561 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
1.4559 + 0.3036 i
0.0435 - 0.00935 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4559 - 0.3036 i
0.0435 + 0.00935 i
3
1.7119
0.0621
4
2.0313 + 0.42 i
0.0498 + 0.125 i
5
2.0313 - 0.42 i
0.0498 - 0.125 i
6
2.1325 + 1.5777 i
0.0267 + 0.0394 i
7
2.1325 - 1.5777 i
0.0267 - 0.0394 i
8
-3.8379 + 0.0543 i
0.00236 + 0.00227 i
9
-3.8379 - 0.0543 i
0.00236 - 0.00227 i
10
0.5927 + 4.2771 i
0.02 + 0.0123 i
11
0.5927 - 4.2771 i
0.02 - 0.0123 i
12
9.0224
0.0761 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
1.4555 + 0.2995 i
0.043 - 0.0161 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4555 - 0.2995 i
0.043 + 0.0161 i
3
1.6779
0.0711
4
1.9442
0.195 i
5
2.2373 + 1.3513 i
0.106 + 0.0629 i
6
2.2373 - 1.3513 i
0.106 - 0.0629 i
7
3.0051
0.241
8
0.744 + 4.5198 i
0.0326 + 0.0183 i
9
0.744 - 4.5198 i
0.0326 - 0.0183 i
10
-5.2031 + 0.2688 i
0.0104 + 0.00882 i
11
-5.2031 - 0.2688 i
0.0104 - 0.00882 i
12
17.9879
0.134 i
13
-90.8105
0.358
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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
1.4565 + 0.2904 i
0.0462 - 0.0285 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4565 - 0.2904 i
0.0462 + 0.0285 i
3
1.8269
0.0697
4
2.2655 + 0.3361 i
0.0497 + 0.15 i
5
2.2655 - 0.3361 i
0.0497 - 0.15 i
6
2.1867 + 1.422 i
0.0795 + 0.0467 i
7
2.1867 - 1.422 i
0.0795 - 0.0467 i
8
-2.8625 + 1.7238 i
0.000897 + 0.00164 i
9
-2.8625 - 1.7238 i
0.000897 - 0.00164 i
10
-2.8886 + 1.7634 i
0.00166 - 0.000901 i
11
-2.8886 - 1.7634 i
0.00166 + 0.000901 i
12
0.8128 + 4.1899 i
0.0262 + 0.00177 i
13
0.8128 - 4.1899 i
0.0262 - 0.00177 i
14
15.6562
0.0825 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.