Singularities of Møller-Plesset series: example "HF aug-cc-pVDZ 2.0r_e"

Molecule X 1^Sigma+ State of HF. Basis AUG-CC-PVDZ. 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
-7.4696
4.03
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
-0.2523
0.0238
Singularities of quadratic [1, 1, 0] approximant
2
-0.3787
0.0292 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
-0.923
0.312
Singularities of quadratic [1, 1, 1] approximant
2
4.1746
22.8
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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
-0.544
0.0349
Singularities of quadratic [2, 1, 1] approximant
2
0.5199 + 0.8239 i
0.0527 + 0.00335 i
3
0.5199 - 0.8239 i
0.0527 - 0.00335 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
-0.6698
0.0946
Singularities of quadratic [2, 2, 1] approximant
2
1.387 + 0.9708 i
0.253 + 0.0274 i
3
1.387 - 0.9708 i
0.253 - 0.0274 i
4
-7.5767
0.533 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
-0.643
0.0677
Singularities of quadratic [2, 2, 2] approximant
2
0.9154 + 0.6056 i
0.059 - 0.0297 i
3
0.9154 - 0.6056 i
0.059 + 0.0297 i
4
2.0759
0.138
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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
-0.6724
0.102
Singularities of quadratic [3, 2, 2] approximant
2
2.1209
8.84
3
2.7987 + 2.7759 i
0.185 + 0.272 i
4
2.7987 - 2.7759 i
0.185 - 0.272 i
5
-6.462
0.418 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
-0.6713
0.0998
Singularities of quadratic [3, 3, 2] approximant
2
1.8791
143.
3
1.7022 + 2.1974 i
0.182 + 0.247 i
4
1.7022 - 2.1974 i
0.182 - 0.247 i
5
-8.2492
0.495 i
6
17.6579
9.01 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
0.0041
1.96e-9
Singularities of quadratic [3, 3, 3] approximant
2
0.0041
1.96e-9 i
3
-0.6673
0.0891
4
1.8698
5.36
5
-3.0885
0.332 i
6
4.2315
0.751 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
-0.604
0.0277
Singularities of quadratic [4, 3, 3] approximant
2
-0.7364
0.0512 i
3
-0.9411
0.234
4
0.9531 + 0.3084 i
0.00539 - 0.0133 i
5
0.9531 - 0.3084 i
0.00539 + 0.0133 i
6
1.0851
0.00978
7
1.389
0.0257 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
-0.6254
0.0397
Singularities of quadratic [4, 4, 3] approximant
2
-0.8817
0.151 i
3
-1.1875
0.137
4
0.988 + 0.6737 i
0.0333 - 0.00194 i
5
0.988 - 0.6737 i
0.0333 + 0.00194 i
6
1.1641 + 1.0073 i
0.00894 - 0.0484 i
7
1.1641 - 1.0073 i
0.00894 + 0.0484 i
8
-46.292
638. 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
-0.6253
0.0395
Singularities of quadratic [4, 4, 4] approximant
2
-0.8828
0.152 i
3
0.9813 + 0.6738 i
0.0324 - 0.00183 i
4
0.9813 - 0.6738 i
0.0324 + 0.00183 i
5
-1.1916
0.136
6
1.1475 + 0.997 i
0.00834 - 0.0463 i
7
1.1475 - 0.997 i
0.00834 + 0.0463 i
8
-75.3756
32.2 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
-0.647 + 0.0089 i
0.194 + 0.374 i
Singularities of quadratic [5, 4, 4] approximant
2
-0.647 - 0.0089 i
0.194 - 0.374 i
3
-0.7428
0.207
4
1.2833 + 0.1937 i
0.105 - 0.0468 i
5
1.2833 - 0.1937 i
0.105 + 0.0468 i
6
-0.1792 + 1.8702 i
0.0554 - 0.0801 i
7
-0.1792 - 1.8702 i
0.0554 + 0.0801 i
8
5.4817
0.203
9
-9.3946
0.271 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
-0.5754 + 0.011 i
0.00567 + 0.00699 i
Singularities of quadratic [5, 5, 4] approximant
2
-0.5754 - 0.011 i
0.00567 - 0.00699 i
3
-0.622
0.014
4
1.3349 + 0.4717 i
0.0393 - 0.317 i
5
1.3349 - 0.4717 i
0.0393 + 0.317 i
6
-1.4898
0.511 i
7
2.0627
0.268
8
-1.9762 + 3.1743 i
0.894 + 0.289 i
9
-1.9762 - 3.1743 i
0.894 - 0.289 i
10
15.4612
75.8 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
-0.5896 + 0.0143 i
0.0082 + 0.0114 i
Singularities of quadratic [5, 5, 5] approximant
2
-0.5896 - 0.0143 i
0.0082 - 0.0114 i
3
-0.6328
0.0176
4
1.3114 + 0.5051 i
0.131 - 0.212 i
5
1.3114 - 0.5051 i
0.131 + 0.212 i
6
-1.544
0.527 i
7
1.8927
0.242
8
-2.3537 + 2.0461 i
0.0706 - 1.77 i
9
-2.3537 - 2.0461 i
0.0706 + 1.77 i
10
-6.6906
0.916
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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
-0.5731 + 0.0114 i
0.00428 + 0.00531 i
Singularities of quadratic [6, 5, 5] approximant
2
-0.5731 - 0.0114 i
0.00428 - 0.00531 i
3
-0.6147
0.0103
4
1.2641 + 0.4089 i
0.138 + 0.072 i
5
1.2641 - 0.4089 i
0.138 - 0.072 i
6
-1.6508
0.274 i
7
1.5747 + 0.661 i
0.166 - 0.0712 i
8
1.5747 - 0.661 i
0.166 + 0.0712 i
9
2.1084
5.02
10
-0.9536 + 2.5405 i
0.242 - 0.0743 i
11
-0.9536 - 2.5405 i
0.242 + 0.0743 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
-0.566 + 0.0099 i
0.00339 + 0.00401 i
Singularities of quadratic [6, 6, 5] approximant
2
-0.566 - 0.0099 i
0.00339 - 0.00401 i
3
-0.6094
0.00891
4
1.2745 + 0.4251 i
0.105 + 0.0912 i
5
1.2745 - 0.4251 i
0.105 - 0.0912 i
6
-1.7977
0.189 i
7
1.6304 + 0.9748 i
0.133 + 0.0164 i
8
1.6304 - 0.9748 i
0.133 - 0.0164 i
9
-0.7685 + 2.1301 i
0.119 - 0.0295 i
10
-0.7685 - 2.1301 i
0.119 + 0.0295 i
11
4.9099 + 6.171 i
0.356 + 0.00316 i
12
4.9099 - 6.171 i
0.356 - 0.00316 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
-0.5625 + 0.0094 i
0.00294 + 0.0034 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.5625 - 0.0094 i
0.00294 - 0.0034 i
3
-0.6065
0.00809
4
1.1485
0.0127
5
1.1682 + 0.1752 i
0.00554 - 0.0172 i
6
1.1682 - 0.1752 i
0.00554 + 0.0172 i
7
1.2997 + 0.7123 i
0.0117 + 0.0885 i
8
1.2997 - 0.7123 i
0.0117 - 0.0885 i
9
-2.0511
0.131 i
10
-0.9758 + 2.1887 i
0.15 - 0.0549 i
11
-0.9758 - 2.1887 i
0.15 + 0.0549 i
12
-3.5498
0.214
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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
-0.5563 + 0.0067 i
0.00322 + 0.00359 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.5563 - 0.0067 i
0.00322 - 0.00359 i
3
-0.6066
0.0102
4
-0.7271
0.136 i
5
-0.7401
29.1
6
1.2811 + 0.4612 i
0.0615 + 0.192 i
7
1.2811 - 0.4612 i
0.0615 - 0.192 i
8
-1.641
0.3 i
9
1.8277 + 0.731 i
0.208 + 0.0384 i
10
1.8277 - 0.731 i
0.208 - 0.0384 i
11
-1.0793 + 2.381 i
0.258 + 0.00495 i
12
-1.0793 - 2.381 i
0.258 - 0.00495 i
13
4.0844
0.446
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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
-0.558 + 0.0068 i
0.00357 + 0.00399 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.558 - 0.0068 i
0.00357 - 0.00399 i
3
-0.6088
0.0111
4
-0.7337
0.144 i
5
-0.7476
24.
6
1.2795 + 0.4768 i
0.00353 + 0.206 i
7
1.2795 - 0.4768 i
0.00353 - 0.206 i
8
-1.6273
0.327 i
9
1.9296 + 0.6241 i
0.236 + 0.0543 i
10
1.9296 - 0.6241 i
0.236 - 0.0543 i
11
-1.1805 + 2.4137 i
0.313 + 0.0439 i
12
-1.1805 - 2.4137 i
0.313 - 0.0439 i
13
4.392
0.485
14
241.1159
58.2 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.