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

Molecule H- ion. 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
1.1828
0.0693
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
1.3409
0.0896
Singularities of quadratic [1, 1, 0] approximant
2
319.9036
1.38 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
1.9678
0.728
Singularities of quadratic [1, 1, 1] approximant
2
-4.2649
0.0903
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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
1.9343
0.656
Singularities of quadratic [2, 1, 1] approximant
2
-3.7441
0.0777
3
-23.7095
0.0856 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
1.4291
0.0546
Singularities of quadratic [2, 2, 1] approximant
2
2.9181
0.263 i
3
-2.0134 + 6.5967 i
0.096 + 0.0000329 i
4
-2.0134 - 6.5967 i
0.096 - 0.0000329 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
1.3885
0.0483
Singularities of quadratic [2, 2, 2] approximant
2
2.4272
0.131 i
3
-2.732 + 12.0437 i
0.0946 - 0.053 i
4
-2.732 - 12.0437 i
0.0946 + 0.053 i
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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
1.4743
0.105
Singularities of quadratic [3, 2, 2] approximant
2
2.2158
0.133 i
3
3.9585 + 2.6145 i
0.0241 - 0.193 i
4
3.9585 - 2.6145 i
0.0241 + 0.193 i
5
-7.1873
0.201
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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
1.251 + 0.2626 i
0.0055 - 0.014 i
Singularities of quadratic [3, 3, 2] approximant
2
1.251 - 0.2626 i
0.0055 + 0.014 i
3
1.392
0.012
4
2.8847
0.36 i
5
-11.1413 + 7.3803 i
0.386 + 0.505 i
6
-11.1413 - 7.3803 i
0.386 - 0.505 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
1.3534 + 0.3682 i
0.0158 - 0.00653 i
Singularities of quadratic [3, 3, 3] approximant
2
1.3534 - 0.3682 i
0.0158 + 0.00653 i
3
2.4158
0.171
4
-3.2775 + 0.1918 i
0.00483 + 0.00434 i
5
-3.2775 - 0.1918 i
0.00483 - 0.00434 i
6
5.796
0.0971 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
0.2233
1.94e-6
Singularities of quadratic [4, 3, 3] approximant
2
0.2233
1.94e-6 i
3
1.3714 + 0.4411 i
0.0119 + 0.00408 i
4
1.3714 - 0.4411 i
0.0119 - 0.00408 i
5
4.4315
0.107
6
-0.6856 + 6.7612 i
0.013 - 0.0322 i
7
-0.6856 - 6.7612 i
0.013 + 0.0322 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
1.4262 + 0.43 i
0.0161 + 0.00327 i
Singularities of quadratic [4, 4, 3] approximant
2
1.4262 - 0.43 i
0.0161 - 0.00327 i
3
1.1522 + 1.7261 i
0.00587 + 0.00142 i
4
1.1522 - 1.7261 i
0.00587 - 0.00142 i
5
1.0515 + 1.9965 i
0.00261 - 0.00579 i
6
1.0515 - 1.9965 i
0.00261 + 0.00579 i
7
-8.2876 + 3.6523 i
0.0905 - 0.0377 i
8
-8.2876 - 3.6523 i
0.0905 + 0.0377 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
1.4627 + 0.3492 i
0.0284 - 0.0196 i
Singularities of quadratic [4, 4, 4] approximant
2
1.4627 - 0.3492 i
0.0284 + 0.0196 i
3
1.6751 + 1.3144 i
0.002 - 0.0215 i
4
1.6751 - 1.3144 i
0.002 + 0.0215 i
5
1.6947 + 1.9192 i
0.0191 + 0.00744 i
6
1.6947 - 1.9192 i
0.0191 - 0.00744 i
7
2.5361 + 7.8391 i
0.0284 - 0.0251 i
8
2.5361 - 7.8391 i
0.0284 + 0.0251 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
1.4426 + 0.4161 i
0.0197 + 0.00128 i
Singularities of quadratic [5, 4, 4] approximant
2
1.4426 - 0.4161 i
0.0197 - 0.00128 i
3
1.4838 + 1.5808 i
0.0123 - 0.00177 i
4
1.4838 - 1.5808 i
0.0123 + 0.00177 i
5
1.5667 + 2.0952 i
0.00248 - 0.0148 i
6
1.5667 - 2.0952 i
0.00248 + 0.0148 i
7
-10.0699
0.0984
8
-17.0384
0.456 i
9
-721.0959
16.3
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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
1.3245 + 0.0463 i
0.0052 - 0.0044 i
Singularities of quadratic [5, 5, 4] approximant
2
1.3245 - 0.0463 i
0.0052 + 0.0044 i
3
1.533 + 0.5798 i
0.00623 - 0.0211 i
4
1.533 - 0.5798 i
0.00623 + 0.0211 i
5
1.4799 + 2.1056 i
0.000668 - 0.0212 i
6
1.4799 - 2.1056 i
0.000668 + 0.0212 i
7
1.4164 + 2.5555 i
0.026 + 0.00427 i
8
1.4164 - 2.5555 i
0.026 - 0.00427 i
9
-11.507 + 7.3539 i
0.373 + 0.643 i
10
-11.507 - 7.3539 i
0.373 - 0.643 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
1.4964 + 0.2976 i
0.0207 - 0.0629 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4964 - 0.2976 i
0.0207 + 0.0629 i
3
1.9055 + 0.8803 i
0.0418 + 0.0268 i
4
1.9055 - 0.8803 i
0.0418 - 0.0268 i
5
1.8017 + 2.1756 i
0.0275 - 0.013 i
6
1.8017 - 2.1756 i
0.0275 + 0.013 i
7
1.9859 + 3.6028 i
0.0044 + 0.0325 i
8
1.9859 - 3.6028 i
0.0044 - 0.0325 i
9
-4.6853 + 0.163 i
0.00949 + 0.00919 i
10
-4.6853 - 0.163 i
0.00949 - 0.00919 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
1.4874 + 0.3084 i
0.0229 - 0.0496 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4874 - 0.3084 i
0.0229 + 0.0496 i
3
1.8808 + 1.0048 i
0.0223 + 0.035 i
4
1.8808 - 1.0048 i
0.0223 - 0.035 i
5
1.8771 + 2.3326 i
0.0293 + 0.00716 i
6
1.8771 - 2.3326 i
0.0293 - 0.00716 i
7
1.9781 + 4.5004 i
0.0266 - 0.0303 i
8
1.9781 - 4.5004 i
0.0266 + 0.0303 i
9
-8.6175 + 4.6438 i
0.457 - 0.0398 i
10
-8.6175 - 4.6438 i
0.457 + 0.0398 i
11
-10.0294
0.188
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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
1.4808 + 0.3021 i
0.00997 - 0.0445 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4808 - 0.3021 i
0.00997 + 0.0445 i
3
1.8978 + 1.1154 i
0.00657 - 0.0324 i
4
1.8978 - 1.1154 i
0.00657 + 0.0324 i
5
-2.8578 + 0.2027 i
0.000128 + 0.000198 i
6
-2.8578 - 0.2027 i
0.000128 - 0.000198 i
7
1.5187 + 2.6894 i
0.00287 - 0.0146 i
8
1.5187 - 2.6894 i
0.00287 + 0.0146 i
9
-3.1518 + 0.4103 i
0.000353 - 0.0000607 i
10
-3.1518 - 0.4103 i
0.000353 + 0.0000607 i
11
4.1195
0.127
12
5.6531
0.0557 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
1.5016 + 0.3139 i
0.0532 - 0.0539 i
Singularities of quadratic [6, 6, 6] approximant
2
1.5016 - 0.3139 i
0.0532 + 0.0539 i
3
1.8306 + 0.8659 i
0.0337 - 0.00116 i
4
1.8306 - 0.8659 i
0.0337 + 0.00116 i
5
1.649 + 1.8667 i
0.00424 - 0.01 i
6
1.649 - 1.8667 i
0.00424 + 0.01 i
7
0.822 + 3.5013 i
0.00402 + 0.00476 i
8
0.822 - 3.5013 i
0.00402 - 0.00476 i
9
-6.1426 + 2.1283 i
0.0102 + 0.00144 i
10
-6.1426 - 2.1283 i
0.0102 - 0.00144 i
11
-0.9194 + 9.9324 i
0.011 - 0.00232 i
12
-0.9194 - 9.9324 i
0.011 + 0.00232 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
1.5008 + 0.3108 i
0.0363 - 0.0542 i
Singularities of quadratic [7, 6, 6] approximant
2
1.5008 - 0.3108 i
0.0363 + 0.0542 i
3
1.9329 + 0.0815 i
0.212 - 0.0021 i
4
1.9329 - 0.0815 i
0.212 + 0.0021 i
5
1.9638 + 1.0933 i
0.0131 + 0.0598 i
6
1.9638 - 1.0933 i
0.0131 - 0.0598 i
7
2.0364 + 2.403 i
0.0367 + 0.0238 i
8
2.0364 - 2.403 i
0.0367 - 0.0238 i
9
2.2971 + 5.2207 i
0.0596 - 0.0221 i
10
2.2971 - 5.2207 i
0.0596 + 0.0221 i
11
-6.1386 + 5.7875 i
0.105 - 0.00376 i
12
-6.1386 - 5.7875 i
0.105 + 0.00376 i
13
-20.6511
0.25
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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
1.5035 + 0.3184 i
0.0545 - 0.042 i
Singularities of quadratic [7, 7, 6] approximant
2
1.5035 - 0.3184 i
0.0545 + 0.042 i
3
1.9775 + 0.7138 i
0.0655 - 0.0608 i
4
1.9775 - 0.7138 i
0.0655 + 0.0608 i
5
2.2726
0.104
6
1.9837 + 1.5712 i
0.0278 + 0.0326 i
7
1.9837 - 1.5712 i
0.0278 - 0.0326 i
8
1.7053 + 3.1847 i
0.0282 - 0.00837 i
9
1.7053 - 3.1847 i
0.0282 + 0.00837 i
10
-5.0239 + 4.2737 i
0.0205 + 0.0292 i
11
-5.0239 - 4.2737 i
0.0205 - 0.0292 i
12
-5.7869 + 7.425 i
0.0233 - 0.0326 i
13
-5.7869 - 7.425 i
0.0233 + 0.0326 i
14
17.2344
0.0723 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.