Singularities of Møller-Plesset series: example "a16"

Molecule BH. Basis cc-pVQZ. 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

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 [3, 3, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5711 + 0.3143 i
0.278 - 0.223 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5711 - 0.3143 i
0.278 + 0.223 i
3
2.1419
0.501
4
-4.2286
0.157
5
-17.6661
0.22 i
6
45.1719
0.471 i
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Table 2. 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
1.5988 + 0.3244 i
0.321 - 0.174 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5988 - 0.3244 i
0.321 + 0.174 i
3
2.3332
0.828
4
-4.266
0.152
5
11.4301
0.49 i
6
-224.8279
0.111 i
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Table 3. 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
1.6049 + 0.3342 i
0.319 - 0.128 i
Singularities of quadratic [4, 3, 3] approximant
2
1.6049 - 0.3342 i
0.319 + 0.128 i
3
2.402
1.11
4
-4.159
0.127
5
13.8183
0.448 i
6
-0.5204 + 17.4617 i
0.0733 + 0.274 i
7
-0.5204 - 17.4617 i
0.0733 - 0.274 i
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Table 4. 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
1.6043 + 0.3399 i
0.314 - 0.0993 i
Singularities of quadratic [4, 4, 3] approximant
2
1.6043 - 0.3399 i
0.314 + 0.0993 i
3
2.3637
1.07
4
-3.1665
0.03
5
-3.544
0.0319 i
6
-6.5087 + 2.4242 i
0.062 - 0.198 i
7
-6.5087 - 2.4242 i
0.062 + 0.198 i
8
63.3988
0.602 i
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Table 5. 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
1.6 + 0.3118 i
0.315 - 0.249 i
Singularities of quadratic [4, 4, 4] approximant
2
1.6 - 0.3118 i
0.315 + 0.249 i
3
-1.9444 + 0.0014 i
0.00402 + 0.00403 i
4
-1.9444 - 0.0014 i
0.00402 - 0.00403 i
5
2.3916
0.817
6
-4.0796
0.0955
7
6.0118
0.794 i
8
14.2009
7.06
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Table 6. 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
-0.2487 + 0.e-5 i
2.81e-6 + 2.81e-6 i
Singularities of quadratic [5, 4, 4] approximant
2
-0.2487 - 0.e-5 i
2.81e-6 - 2.81e-6 i
3
1.5974 + 0.3079 i
0.287 - 0.272 i
4
1.5974 - 0.3079 i
0.287 + 0.272 i
5
2.4255
0.888
6
-4.0841
0.105
7
6.6919
0.556 i
8
10.9588 + 16.2174 i
0.154 + 0.424 i
9
10.9588 - 16.2174 i
0.154 - 0.424 i
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Table 7. 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
1.2265 + 0.0048 i
0.0213 - 0.0215 i
Singularities of quadratic [5, 5, 4] approximant
2
1.2265 - 0.0048 i
0.0213 + 0.0215 i
3
1.6418 + 0.3752 i
0.32 + 0.12 i
4
1.6418 - 0.3752 i
0.32 - 0.12 i
5
2.3689
1.49
6
-3.1548
0.043
7
-3.3424
0.0446 i
8
-5.5501
123.
9
-9.8609
0.22 i
10
82.8276
0.694 i
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Table 8. 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
1.2934 + 0.0093 i
0.03 - 0.0305 i
Singularities of quadratic [5, 5, 5] approximant
2
1.2934 - 0.0093 i
0.03 + 0.0305 i
3
1.6559 + 0.3853 i
0.293 + 0.18 i
4
1.6559 - 0.3853 i
0.293 - 0.18 i
5
2.3776
1.81
6
-3.5435
0.0491
7
-4.7537
0.0539 i
8
-4.982 + 3.2699 i
0.0712 - 0.112 i
9
-4.982 - 3.2699 i
0.0712 + 0.112 i
10
-22.3706
4.41
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Table 9. 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
1.3937 + 0.0365 i
0.0338 - 0.0298 i
Singularities of quadratic [6, 5, 5] approximant
2
1.3937 - 0.0365 i
0.0338 + 0.0298 i
3
1.7322 + 0.4588 i
0.0791 - 0.279 i
4
1.7322 - 0.4588 i
0.0791 + 0.279 i
5
2.079
1.29
6
-3.0593 + 0.0721 i
0.017 + 0.0172 i
7
-3.0593 - 0.0721 i
0.017 - 0.0172 i
8
-4.3937
0.0964
9
4.814
36.5 i
10
7.3289
0.63
11
-11.1419
0.48 i
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Table 10. 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
1.4408 + 0.065 i
0.0492 - 0.0375 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4408 - 0.065 i
0.0492 + 0.0375 i
3
1.6892 + 0.5332 i
0.0325 - 0.148 i
4
1.6892 - 0.5332 i
0.0325 + 0.148 i
5
2.0631 + 0.2204 i
0.735 + 0.0419 i
6
2.0631 - 0.2204 i
0.735 - 0.0419 i
7
3.0388
134.
8
-3.2432
0.208
9
-3.3141
0.205 i
10
-5.164
0.922
11
-9.9841
0.29 i
12
156.5158
1.06 i
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Table 11. 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
1.5753 + 0.1598 i
0.923 - 3.46 i
Singularities of quadratic [6, 6, 6] approximant
2
1.5753 - 0.1598 i
0.923 + 3.46 i
3
1.5774 + 0.4361 i
0.159 - 0.0536 i
4
1.5774 - 0.4361 i
0.159 + 0.0536 i
5
1.6759 + 0.172 i
0.0187 - 0.195 i
6
1.6759 - 0.172 i
0.0187 + 0.195 i
7
1.9546
0.172
8
-3.1416
0.0334
9
-3.3477
0.0359 i
10
-5.219
5.52
11
17.7145
0.469 i
12
-17.843
0.176 i
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Table 12. 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
1.4616
0.0494
Singularities of quadratic [7, 6, 6] approximant
2
1.4751 + 0.3218 i
0.0262 + 0.00637 i
3
1.4751 - 0.3218 i
0.0262 - 0.00637 i
4
1.4641 + 0.4295 i
0.0134 - 0.0205 i
5
1.4641 - 0.4295 i
0.0134 + 0.0205 i
6
1.9438 + 0.5333 i
0.0706 + 0.118 i
7
1.9438 - 0.5333 i
0.0706 - 0.118 i
8
-3.1049
0.0132
9
-3.5762
0.016 i
10
-4.1153 + 7.9739 i
0.000498 - 0.0628 i
11
-4.1153 - 7.9739 i
0.000498 + 0.0628 i
12
-10.8104 + 2.4534 i
0.0385 + 0.0328 i
13
-10.8104 - 2.4534 i
0.0385 - 0.0328 i
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Table 13. 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
1.4253 + 0.2636 i
0.0302 - 0.0184 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4253 - 0.2636 i
0.0302 + 0.0184 i
3
1.485 + 0.3406 i
0.0159 + 0.0437 i
4
1.485 - 0.3406 i
0.0159 - 0.0437 i
5
1.5298
0.0716
6
1.8707 + 0.4191 i
0.214 + 0.147 i
7
1.8707 - 0.4191 i
0.214 - 0.147 i
8
-3.1509
0.0308
9
-3.3832
0.0335 i
10
-5.3578
28.1
11
6.8793
1.09 i
12
9.9577
6.69
13
-13.295
0.199 i
14
153.6699
0.97 i
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Table 14. Singularities with their weights for the quadratic approximant [7, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4246 + 0.2389 i
0.0368 - 0.0447 i
Singularities of quadratic [7, 7, 7] approximant
2
1.4246 - 0.2389 i
0.0368 + 0.0447 i
3
1.5143 + 0.2833 i
0.0669 + 0.0468 i
4
1.5143 - 0.2833 i
0.0669 - 0.0468 i
5
1.6989
0.136
6
1.7772 + 0.328 i
0.399 + 0.424 i
7
1.7772 - 0.328 i
0.399 - 0.424 i
8
-3.1839
0.0638
9
-3.3232
0.0686 i
10
-5.1058
0.953
11
7.0035
1.23 i
12
-9.8048
0.36 i
13
11.5368
5.42
14
-37.0839
5.01
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Table 15. Singularities with their weights for the quadratic approximant [8, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.1376 + 0.3026 i
0.000311 - 0.000597 i
Singularities of quadratic [8, 7, 7] approximant
2
1.1376 - 0.3026 i
0.000311 + 0.000597 i
3
1.1419 + 0.3043 i
0.000605 + 0.00031 i
4
1.1419 - 0.3043 i
0.000605 - 0.00031 i
5
1.3492
0.00785
6
1.6383
0.268 i
7
1.6689 + 0.5648 i
0.0432 - 0.0401 i
8
1.6689 - 0.5648 i
0.0432 + 0.0401 i
9
2.4344
4.35
10
-3.0999
0.0134
11
-3.5372
0.0165 i
12
-6.6707
0.213
13
-4.263 + 12.4613 i
0.0451 + 0.114 i
14
-4.263 - 12.4613 i
0.0451 - 0.114 i
15
30.2555
0.407 i
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Table 16. Singularities with their weights for the quadratic approximant [8, 8, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-1.0189 + 0.e-5 i
6.75e-6 + 6.75e-6 i
Singularities of quadratic [8, 8, 7] approximant
2
-1.0189 - 0.e-5 i
6.75e-6 - 6.75e-6 i
3
1.4226 + 0.311 i
0.0179 - 0.00106 i
4
1.4226 - 0.311 i
0.0179 + 0.00106 i
5
1.4593
0.0384
6
1.4406 + 0.3935 i
0.00422 - 0.0191 i
7
1.4406 - 0.3935 i
0.00422 + 0.0191 i
8
1.9112 + 0.5378 i
0.0993 + 0.115 i
9
1.9112 - 0.5378 i
0.0993 - 0.115 i
10
-3.2104 + 0.141 i
0.0152 + 0.0123 i
11
-3.2104 - 0.141 i
0.0152 - 0.0123 i
12
-4.7654
0.169
13
5.0624
6.52 i
14
6.2288
1.34
15
-10.008
0.326 i
16
190.4278
1.19 i
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Table 17. Singularities with their weights for the quadratic approximant [8, 8, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4287 + 0.2692 i
0.0277 - 0.00414 i
Singularities of quadratic [8, 8, 8] approximant
2
1.4287 - 0.2692 i
0.0277 + 0.00414 i
3
1.5123
0.0468
4
1.5133 + 0.373 i
0.0169 - 0.0445 i
5
1.5133 - 0.373 i
0.0169 + 0.0445 i
6
-0.9789 + 1.4279 i
3.53e-6 - 0.0000924 i
7
-0.9789 - 1.4279 i
3.53e-6 + 0.0000924 i
8
-0.9792 + 1.4279 i
0.0000924 + 3.55e-6 i
9
-0.9792 - 1.4279 i
0.0000924 - 3.55e-6 i
10
1.9261 + 0.2197 i
0.149 + 0.339 i
11
1.9261 - 0.2197 i
0.149 - 0.339 i
12
-3.0261
0.00567
13
-3.8559
0.0121 i
14
5.0737
461. i
15
8.7206
0.741
16
-8.9469
0.123
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Table 18. Singularities with their weights for the quadratic approximant [9, 8, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.0969 + 0.89 i
7.05e-7 + 1.42e-6 i
Singularities of quadratic [9, 8, 8] approximant
2
0.0969 - 0.89 i
7.05e-7 - 1.42e-6 i
3
0.0969 + 0.89 i
1.42e-6 - 7.05e-7 i
4
0.0969 - 0.89 i
1.42e-6 + 7.05e-7 i
5
1.4516 + 0.2865 i
0.0144 - 0.0161 i
6
1.4516 - 0.2865 i
0.0144 + 0.0161 i
7
1.4281 + 0.3955 i
0.00567 + 0.0125 i
8
1.4281 - 0.3955 i
0.00567 - 0.0125 i
9
1.5274
0.203
10
1.8908 + 0.6374 i
0.0286 + 0.0541 i
11
1.8908 - 0.6374 i
0.0286 - 0.0541 i
12
-2.2442
0.000142
13
-2.2641
0.000142 i
14
-2.8294
0.00114
15
-4.4275
0.018 i
16
-8.1071
0.27
17
-11.0867
4.33 i
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Table 19. Singularities with their weights for the quadratic approximant [9, 9, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.881 + 0.9214 i
7.79e-6 + 6.02e-6 i
Singularities of quadratic [9, 9, 8] approximant
2
-0.881 - 0.9214 i
7.79e-6 - 6.02e-6 i
3
-0.881 + 0.9214 i
6.02e-6 - 7.79e-6 i
4
-0.881 - 0.9214 i
6.02e-6 + 7.79e-6 i
5
1.4173 + 0.2646 i
0.0159 - 0.0017 i
6
1.4173 - 0.2646 i
0.0159 + 0.0017 i
7
1.478
0.0173
8
1.5125 + 0.4153 i
0.0202 - 0.0188 i
9
1.5125 - 0.4153 i
0.0202 + 0.0188 i
10
1.5726
0.042 i
11
2.4008 + 0.6617 i
0.21 + 0.0318 i
12
2.4008 - 0.6617 i
0.21 - 0.0318 i
13
-3.0095
0.005
14
3.247
14.5
15
-3.8282
0.012 i
16
-6.894
0.22
17
-16.0895
0.332 i
18
1790.4099
4.95 i
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Table 20. Singularities with their weights for the quadratic approximant [9, 9, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.3744
4.28e-9 - 4.28e-9 i
Singularities of quadratic [9, 9, 9] approximant
2
0.3744
4.28e-9 + 4.28e-9 i
3
-0.8036 + 1.0938 i
3.98e-6 + 0.0000139 i
4
-0.8036 - 1.0938 i
3.98e-6 - 0.0000139 i
5
-0.8036 + 1.0938 i
0.0000139 - 3.98e-6 i
6
-0.8036 - 1.0938 i
0.0000139 + 3.98e-6 i
7
1.4419 + 0.2712 i
0.0223 - 0.0218 i
8
1.4419 - 0.2712 i
0.0223 + 0.0218 i
9
1.4605 + 0.3749 i
0.0088 + 0.0256 i
10
1.4605 - 0.3749 i
0.0088 - 0.0256 i
11
1.5259
0.112
12
1.9133 + 0.493 i
0.0971 + 0.12 i
13
1.9133 - 0.493 i
0.0971 - 0.12 i
14
-3.0082
0.00483
15
-3.8925
0.0121 i
16
8.2741
0.83 i
17
-8.4795
0.133
18
19.2918
137.
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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.