Singularities of Møller-Plesset series: example "a30"

Molecule BH. Basis aug-cc-pVTZ. 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 [1, 0, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.1388
0.169
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
1.3914
0.257
Singularities of quadratic [1, 1, 0] approximant
2
125.4315
2.44 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
1.5112
0.365
Singularities of quadratic [1, 1, 1] approximant
2
-20.3923
0.841
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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
0.9687
0.0485
Singularities of quadratic [2, 1, 1] approximant
2
1.1285
0.0564 i
3
2.1886
7.6
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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
1.4418
0.279
Singularities of quadratic [2, 2, 1] approximant
2
-6.6717 + 0.7311 i
1.18 + 0.432 i
3
-6.6717 - 0.7311 i
1.18 - 0.432 i
4
46.0893
1.91 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
1.5599
0.758
Singularities of quadratic [2, 2, 2] approximant
2
2.6831
0.595 i
3
4.3729
9.01
4
-6.8695
0.242
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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
1.5572 + 0.3191 i
0.247 - 0.238 i
Singularities of quadratic [3, 2, 2] approximant
2
1.5572 - 0.3191 i
0.247 + 0.238 i
3
2.0903
0.419
4
-5.0965
0.151
5
-12.4177
0.172 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
1.5925 + 0.3212 i
0.311 - 0.224 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5925 - 0.3212 i
0.311 + 0.224 i
3
2.2479
0.607
4
-4.8397
0.127
5
-11.1844
0.147 i
6
1515.8553
2.58 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
1.5566 + 0.2954 i
0.208 - 0.339 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5566 - 0.2954 i
0.208 + 0.339 i
3
2.0368
0.366
4
-4.8779 + 0.3642 i
0.182 + 0.317 i
5
-4.8779 - 0.3642 i
0.182 - 0.317 i
6
-9.942
0.242
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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
-1.441
0.0175
Singularities of quadratic [4, 3, 3] approximant
2
-1.4434
0.0176 i
3
1.5793 + 0.3222 i
0.29 - 0.22 i
4
1.5793 - 0.3222 i
0.29 + 0.22 i
5
2.1795
0.524
6
-5.2201
0.179
7
-11.9573
0.179 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
1.5934 + 0.3625 i
0.276 - 0.0573 i
Singularities of quadratic [4, 4, 3] approximant
2
1.5934 - 0.3625 i
0.276 + 0.0573 i
3
2.3112
0.972
4
-2.8768
0.0164
5
-3.3527
0.0167 i
6
-5.2728 + 5.294 i
0.0866 - 0.0528 i
7
-5.2728 - 5.294 i
0.0866 + 0.0528 i
8
49.8787
4.23 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
-1.173 + 0.5955 i
0.0000344 - 0.000436 i
Singularities of quadratic [4, 4, 4] approximant
2
-1.173 - 0.5955 i
0.0000344 + 0.000436 i
3
-1.1816 + 0.5944 i
0.000435 + 0.0000382 i
4
-1.1816 - 0.5944 i
0.000435 - 0.0000382 i
5
1.5975 + 0.3997 i
0.213 + 0.0621 i
6
1.5975 - 0.3997 i
0.213 - 0.0621 i
7
2.1802
0.861
8
-3.8669
0.0165
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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
1.5855 + 0.2983 i
0.166 - 0.362 i
Singularities of quadratic [5, 4, 4] approximant
2
1.5855 - 0.2983 i
0.166 + 0.362 i
3
-2.811 + 0.1542 i
0.00693 + 0.00749 i
4
-2.811 - 0.1542 i
0.00693 - 0.00749 i
5
2.8974 + 0.4075 i
0.668 + 1.42 i
6
2.8974 - 0.4075 i
0.668 - 1.42 i
7
-4.5793
0.025
8
6.688 + 4.3766 i
0.681 - 0.0983 i
9
6.688 - 4.3766 i
0.681 + 0.0983 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
1.1154 + 0.0011 i
0.0222 - 0.0225 i
Singularities of quadratic [5, 5, 4] approximant
2
1.1154 - 0.0011 i
0.0222 + 0.0225 i
3
1.6072 + 0.38 i
0.272 + 0.0118 i
4
1.6072 - 0.38 i
0.272 - 0.0118 i
5
2.354
1.31
6
-2.994
0.0184
7
-3.6344
0.0187 i
8
-4.7614 + 5.7464 i
0.0781 - 0.0566 i
9
-4.7614 - 5.7464 i
0.0781 + 0.0566 i
10
35.0255
8.99 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
1.4998 + 0.0802 i
0.0963 - 0.0681 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4998 - 0.0802 i
0.0963 + 0.0681 i
3
1.7641 + 0.4726 i
0.144 - 0.305 i
4
1.7641 - 0.4726 i
0.144 + 0.305 i
5
2.1589
2.72
6
-3.2032
0.0188
7
-3.6926 + 1.6387 i
0.00601 - 0.0172 i
8
-3.6926 - 1.6387 i
0.00601 + 0.0172 i
9
-3.2824 + 2.6542 i
0.028 + 0.00901 i
10
-3.2824 - 2.6542 i
0.028 - 0.00901 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
-1.221
0.0000785
Singularities of quadratic [6, 5, 5] approximant
2
-1.2218
0.0000785 i
3
1.4767 + 0.1329 i
0.0468 - 0.0143 i
4
1.4767 - 0.1329 i
0.0468 + 0.0143 i
5
1.7459
0.394
6
1.8179 + 0.6416 i
0.12 + 0.0249 i
7
1.8179 - 0.6416 i
0.12 - 0.0249 i
8
-2.733
0.00335
9
-5.3269
0.0108 i
10
-1.7864 + 5.5903 i
0.0271 + 0.0247 i
11
-1.7864 - 5.5903 i
0.0271 - 0.0247 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
1.4297 + 0.022 i
0.101 - 0.137 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4297 - 0.022 i
0.101 + 0.137 i
3
1.6579 + 0.4269 i
0.176 + 0.157 i
4
1.6579 - 0.4269 i
0.176 - 0.157 i
5
2.4747
8.67
6
-2.9675
0.00524
7
-2.7124 + 1.6161 i
0.000715 + 0.0049 i
8
-2.7124 - 1.6161 i
0.000715 - 0.0049 i
9
-2.7035 + 2.1193 i
0.00663 - 0.00088 i
10
-2.7035 - 2.1193 i
0.00663 + 0.00088 i
11
18.0867
4.45 i
12
-57.7998
1.46 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
0.2544 + 0.e-5 i
6.27e-8 - 6.27e-8 i
Singularities of quadratic [6, 6, 6] approximant
2
0.2544 - 0.e-5 i
6.27e-8 + 6.27e-8 i
3
1.4488
0.139
4
1.5142
0.765 i
5
1.6549 + 0.4684 i
0.0684 + 0.111 i
6
1.6549 - 0.4684 i
0.0684 - 0.111 i
7
2.5653
5.24e4
8
-2.8514 + 0.814 i
0.004 + 0.00279 i
9
-2.8514 - 0.814 i
0.004 - 0.00279 i
10
-3.2502 + 1.5582 i
0.00425 - 0.0069 i
11
-3.2502 - 1.5582 i
0.00425 + 0.0069 i
12
-6.5728
0.235
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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
-0.4278 + 0.e-5 i
3.68e-7 + 3.68e-7 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.4278 - 0.e-5 i
3.68e-7 - 3.68e-7 i
3
1.3852
0.0349
4
1.4994
0.0931 i
5
1.5775 + 0.4526 i
0.0601 + 0.0246 i
6
1.5775 - 0.4526 i
0.0601 - 0.0246 i
7
-3.0933
0.0158
8
-2.2854 + 2.8671 i
0.00722 - 0.00361 i
9
-2.2854 - 2.8671 i
0.00722 + 0.00361 i
10
3.9442 + 1.1436 i
0.183 - 0.199 i
11
3.9442 - 1.1436 i
0.183 + 0.199 i
12
-3.7911 + 2.7039 i
0.000483 + 0.00862 i
13
-3.7911 - 2.7039 i
0.000483 - 0.00862 i
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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
-0.2539 + 0.4889 i
2.44e-7 + 4.e-8 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.2539 - 0.4889 i
2.44e-7 - 4.e-8 i
3
-0.2539 + 0.4889 i
4.e-8 - 2.44e-7 i
4
-0.2539 - 0.4889 i
4.e-8 + 2.44e-7 i
5
1.0336 + 0.0022 i
0.000139 - 0.000137 i
6
1.0336 - 0.0022 i
0.000139 + 0.000137 i
7
1.4468
0.0193
8
1.8305 + 0.697 i
0.0404 + 0.0382 i
9
1.8305 - 0.697 i
0.0404 - 0.0382 i
10
-2.3396 + 0.6743 i
0.000511 + 0.000222 i
11
-2.3396 - 0.6743 i
0.000511 - 0.000222 i
12
-3.6688
0.00131
13
-6.5053
0.0178 i
14
14.9597
4.58 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.