Singularities of Møller-Plesset series: example "a62"

Molecule N2. Basis cc-pVDZ. Structure "mpn_Rfci"

Content


Examplesa1a2a8a16a22a30a38a44a45a51a62a69a75a83a84a85a86a87a88a90a91
MoleculeArBHBHBHBHBHBHBO+C2CN+N2HFHFHClHClF-Cl-Cl-NeOH-SH-
Basisaug-cc-pVDZcc-pVDZcc-pVTZcc-pVQZaug-cc-pVDZaug-cc-pVTZaug-cc-pVQZcc-pVDZcc-pVDZcc-pVDZcc-pVDZcc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-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 [0, 0, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
Singularities of quadratic [0, 0, 0] approximant
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Table 2. Singularities with their weights for the quadratic approximant [1, 0, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
Singularities of quadratic [1, 0, 0] approximant
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Table 3. 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
-0.2483
0.0241
Singularities of quadratic [1, 1, 0] approximant
2
-0.3448
0.0284 i
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Table 4. 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
-1.3063
0.686
Singularities of quadratic [1, 1, 1] approximant
2
2.7606
9.36
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Table 5. 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
-1.4118 + 0.9359 i
0.588 + 0.0961 i
Singularities of quadratic [2, 1, 1] approximant
2
-1.4118 - 0.9359 i
0.588 - 0.0961 i
3
1.7485
0.499
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Table 6. 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
-1.7693 + 0.8268 i
1.21 + 0.15 i
Singularities of quadratic [2, 2, 1] approximant
2
-1.7693 - 0.8268 i
1.21 - 0.15 i
3
1.9532
0.765
4
1393.8296
32.7 i
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Table 7. 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
-1.7516 + 0.8249 i
1.19 + 0.182 i
Singularities of quadratic [2, 2, 2] approximant
2
-1.7516 - 0.8249 i
1.19 - 0.182 i
3
1.9646
0.785
4
-112.3942
29.9
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Table 8. 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
0.0551
0.0000596
Singularities of quadratic [3, 2, 2] approximant
2
0.0551
0.0000596 i
3
-1.7581 + 0.8829 i
1.06 - 0.0838 i
4
-1.7581 - 0.8829 i
1.06 + 0.0838 i
5
2.0068
0.952
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Table 9. 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
-1.2342 + 0.8547 i
0.194 + 0.0276 i
Singularities of quadratic [3, 3, 2] approximant
2
-1.2342 - 0.8547 i
0.194 - 0.0276 i
3
1.7234
0.329
4
-1.9422 + 1.2041 i
0.0267 + 0.354 i
5
-1.9422 - 1.2041 i
0.0267 - 0.354 i
6
13.5081
1.59e5 i
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Table 10. 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
-1.5903 + 0.6767 i
0.956 + 0.938 i
Singularities of quadratic [3, 3, 3] approximant
2
-1.5903 - 0.6767 i
0.956 - 0.938 i
3
1.7733
0.634
4
2.7898
0.891 i
5
-3.7545
1.1
6
5.9917
5.12
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Table 11. 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
-1.5428 + 0.745 i
0.806 + 0.275 i
Singularities of quadratic [4, 3, 3] approximant
2
-1.5428 - 0.745 i
0.806 - 0.275 i
3
1.7166
0.416
4
-2.7704
1.47
5
3.042
0.85 i
6
5.6666
3.93
7
-5.8719
1.78 i
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Table 12. 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
-0.1833 + 0.e-5 i
0.0000174 + 0.0000174 i
Singularities of quadratic [4, 4, 3] approximant
2
-0.1833 - 0.e-5 i
0.0000174 - 0.0000174 i
3
-1.5189 + 0.6622 i
0.219 + 0.636 i
4
-1.5189 - 0.6622 i
0.219 - 0.636 i
5
1.6595
0.24
6
-4.866 + 3.7463 i
0.785 + 1.23 i
7
-4.866 - 3.7463 i
0.785 - 1.23 i
8
7.2088
13.9 i
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Table 13. 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
1.6303 + 0.2927 i
0.0811 - 0.145 i
Singularities of quadratic [4, 4, 4] approximant
2
1.6303 - 0.2927 i
0.0811 + 0.145 i
3
-1.5106 + 0.6911 i
0.412 + 0.674 i
4
-1.5106 - 0.6911 i
0.412 - 0.674 i
5
1.9116
0.154
6
-2.9377 + 1.233 i
0.321 - 0.764 i
7
-2.9377 - 1.233 i
0.321 + 0.764 i
8
-7.8066
0.633
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Table 14. 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
-1.5049 + 0.639 i
0.0451 - 0.731 i
Singularities of quadratic [5, 4, 4] approximant
2
-1.5049 - 0.639 i
0.0451 + 0.731 i
3
1.6439 + 0.3105 i
0.101 - 0.133 i
4
1.6439 - 0.3105 i
0.101 + 0.133 i
5
2.0082
0.183
6
-2.2102 + 1.489 i
0.413 - 0.233 i
7
-2.2102 - 1.489 i
0.413 + 0.233 i
8
-4.5764
0.391
9
-7.4485
0.391 i
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Table 15. 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
-1.5042 + 0.6357 i
0.0716 - 0.719 i
Singularities of quadratic [5, 5, 4] approximant
2
-1.5042 - 0.6357 i
0.0716 + 0.719 i
3
1.6473 + 0.3119 i
0.104 - 0.133 i
4
1.6473 - 0.3119 i
0.104 + 0.133 i
5
2.0234
0.189
6
-2.1744 + 1.492 i
0.41 - 0.214 i
7
-2.1744 - 1.492 i
0.41 + 0.214 i
8
-4.7158
0.334
9
-6.7241
0.329 i
10
74381.264
92.6 i
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Table 16. 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
-1.5011 + 0.6444 i
0.000293 - 0.702 i
Singularities of quadratic [5, 5, 5] approximant
2
-1.5011 - 0.6444 i
0.000293 + 0.702 i
3
1.6577 + 0.3203 i
0.114 - 0.129 i
4
1.6577 - 0.3203 i
0.114 + 0.129 i
5
2.0989
0.219
6
-2.3029 + 1.6204 i
0.334 - 0.28 i
7
-2.3029 - 1.6204 i
0.334 + 0.28 i
8
-5.5917
0.368
9
11.2627
3.89 i
10
-45.5406
0.338 i
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Table 17. 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
0.3845
0.00522
Singularities of quadratic [6, 5, 5] approximant
2
0.3845
0.00522 i
3
-1.5046 + 0.6375 i
0.0571 - 0.727 i
4
-1.5046 - 0.6375 i
0.0571 + 0.727 i
5
1.6441 + 0.3109 i
0.101 - 0.132 i
6
1.6441 - 0.3109 i
0.101 + 0.132 i
7
2.01
0.184
8
-2.1962 + 1.4869 i
0.414 - 0.224 i
9
-2.1962 - 1.4869 i
0.414 + 0.224 i
10
-4.5382
0.39
11
-7.298
0.387 i
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Table 18. 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
1.4822
0.0472
Singularities of quadratic [6, 6, 5] approximant
2
-1.5979 + 0.015 i
2.62 + 0.738 i
3
-1.5979 - 0.015 i
2.62 - 0.738 i
4
1.6185
0.0342 i
5
1.6228 + 0.3946 i
0.149 + 0.0123 i
6
1.6228 - 0.3946 i
0.149 - 0.0123 i
7
-1.5377 + 0.704 i
0.755 + 0.574 i
8
-1.5377 - 0.704 i
0.755 - 0.574 i
9
1.7836
0.0559
10
-3.1762
1.41
11
-7.1121
3.15 i
12
43.6751
7.91 i
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Examplesa1a2a8a16a22a30a38a44a45a51a62a69a75a83a84a85a86a87a88a90a91
MoleculeArBHBHBHBHBHBHBO+C2CN+N2HFHFHClHClF-Cl-Cl-NeOH-SH-
Basisaug-cc-pVDZcc-pVDZcc-pVTZcc-pVQZaug-cc-pVDZaug-cc-pVTZaug-cc-pVQZcc-pVDZcc-pVDZcc-pVDZcc-pVDZcc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZcc-pVDZaug-cc-pVDZaug-cc-pVDZaug-cc-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.