Singularities of Møller-Plesset series: example "a90"

Molecule OH-. Basis aug-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

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
-7.8958
3.81
Singularities of quadratic [1, 0, 0] approximant
Top of Page  Top of the page    

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
-0.3163
0.0283
Singularities of quadratic [1, 1, 0] approximant
2
-0.4944
0.0353 i
Top of Page  Top of the page    

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
-0.9395
0.237
Singularities of quadratic [1, 1, 1] approximant
2
13.4259
1.1
Top of Page  Top of the page    

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
-0.6024
0.0356
Singularities of quadratic [2, 1, 1] approximant
2
0.5924 + 1.0918 i
0.0599 + 0.00836 i
3
0.5924 - 1.0918 i
0.0599 - 0.00836 i
Top of Page  Top of the page    

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
-0.6772
0.0624
Singularities of quadratic [2, 2, 1] approximant
2
1.1411 + 1.4055 i
0.137 + 0.0235 i
3
1.1411 - 1.4055 i
0.137 - 0.0235 i
4
-20.7838
1.18 i
Top of Page  Top of the page    

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
-0.4456
0.0047
Singularities of quadratic [2, 2, 2] approximant
2
-0.4992 + 0.064 i
0.00172 - 0.00597 i
3
-0.4992 - 0.064 i
0.00172 + 0.00597 i
4
1.9049
0.316
Top of Page  Top of the page    

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
-0.6642
0.0565
Singularities of quadratic [3, 2, 2] approximant
2
0.7553 + 1.8063 i
0.111 + 0.0504 i
3
0.7553 - 1.8063 i
0.111 - 0.0504 i
4
2.1002
22.3
5
3.1396
0.274 i
Top of Page  Top of the page    

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
-0.6775
0.0711
Singularities of quadratic [3, 3, 2] approximant
2
-2.4382
0.18 i
3
2.7694
3.57e4
4
-0.7364 + 2.9562 i
0.0674 + 0.231 i
5
-0.7364 - 2.9562 i
0.0674 - 0.231 i
6
14.6157
0.907 i
Top of Page  Top of the page    

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
-0.6828
0.0924
Singularities of quadratic [3, 3, 3] approximant
2
-0.9616 + 0.5508 i
0.0499 - 0.0517 i
3
-0.9616 - 0.5508 i
0.0499 + 0.0517 i
4
-1.1169 + 0.6652 i
0.0481 + 0.0722 i
5
-1.1169 - 0.6652 i
0.0481 - 0.0722 i
6
2.2951
1.06
Top of Page  Top of the page    

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
-0.6821
0.0894
Singularities of quadratic [4, 3, 3] approximant
2
-0.9695 + 0.5853 i
0.0441 - 0.0558 i
3
-0.9695 - 0.5853 i
0.0441 + 0.0558 i
4
-1.1053 + 0.7221 i
0.0584 + 0.066 i
5
-1.1053 - 0.7221 i
0.0584 - 0.066 i
6
2.2991
1.08
7
535.1893
1.35 i
Top of Page  Top of the page    

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
-0.6675
0.0849
Singularities of quadratic [4, 4, 3] approximant
2
-0.7001
0.349 i
3
-0.7206
0.18
4
-1.9567
0.153 i
5
2.686
32.9
6
-1.3377 + 3.0196 i
0.0303 + 0.302 i
7
-1.3377 - 3.0196 i
0.0303 - 0.302 i
8
17.1222
1.04 i
Top of Page  Top of the page    

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
-0.6604
0.0843
Singularities of quadratic [4, 4, 4] approximant
2
-0.683
0.259 i
3
-0.7081
0.149
4
-2.1904
0.152 i
5
2.602
9.97
6
-1.1915 + 2.607 i
0.0106 - 0.255 i
7
-1.1915 - 2.607 i
0.0106 + 0.255 i
8
-20.2966
76.
Top of Page  Top of the page    

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
-0.5584 + 0.0012 i
0.0081 + 0.00831 i
Singularities of quadratic [5, 4, 4] approximant
2
-0.5584 - 0.0012 i
0.0081 - 0.00831 i
3
-0.6687
0.0474
4
-1.8007
0.163 i
5
2.6051
6.94
6
-1.8543 + 2.8684 i
0.0997 - 0.474 i
7
-1.8543 - 2.8684 i
0.0997 + 0.474 i
8
6.2307
1.46 i
9
18.3346
53.4
Top of Page  Top of the page    

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
0.4221
0.000111
Singularities of quadratic [5, 5, 4] approximant
2
0.4221
0.000111 i
3
-0.5485 + 0.0011 i
0.00575 + 0.00583 i
4
-0.5485 - 0.0011 i
0.00575 - 0.00583 i
5
-0.6674
0.0449
6
-1.824
0.155 i
7
2.691
52.7
8
-1.5444 + 2.8719 i
0.0455 - 0.325 i
9
-1.5444 - 2.8719 i
0.0455 + 0.325 i
10
22.4239
1.26 i
Top of Page  Top of the page    

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
-0.0577
2.33e-8 + 2.33e-8 i
Singularities of quadratic [5, 5, 5] approximant
2
-0.0577
2.33e-8 - 2.33e-8 i
3
-0.5412 + 0.0011 i
0.00439 + 0.00443 i
4
-0.5412 - 0.0011 i
0.00439 - 0.00443 i
5
-0.6666
0.0432
6
-1.8349
0.153 i
7
2.6768
32.9
8
-1.5031 + 2.899 i
0.026 - 0.317 i
9
-1.5031 - 2.899 i
0.026 + 0.317 i
10
21.4157
1.2 i
Top of Page  Top of the page    

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
-0.5851
0.198
Singularities of quadratic [6, 5, 5] approximant
2
-0.5859
0.3 i
3
-0.6746
0.0628
4
1.0719 + 0.1397 i
0.0000535 + 0.00112 i
5
1.0719 - 0.1397 i
0.0000535 - 0.00112 i
6
1.0786 + 0.1372 i
0.00111 - 0.0000834 i
7
1.0786 - 0.1372 i
0.00111 + 0.0000834 i
8
-1.7209
0.193 i
9
-2.2578 + 2.2834 i
0.877 - 0.316 i
10
-2.2578 - 2.2834 i
0.877 + 0.316 i
11
3.404
1.19
Top of Page  Top of the page    

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
-0.5834 + 0.0005 i
0.0969 + 0.133 i
Singularities of quadratic [6, 6, 5] approximant
2
-0.5834 - 0.0005 i
0.0969 - 0.133 i
3
-0.6739
0.0607
4
0.7771 + 0.5115 i
0.000638 - 0.00143 i
5
0.7771 - 0.5115 i
0.000638 + 0.00143 i
6
0.7781 + 0.5115 i
0.00143 + 0.000636 i
7
0.7781 - 0.5115 i
0.00143 - 0.000636 i
8
-1.74
0.183 i
9
2.9912
4.28
10
-2.063 + 2.4273 i
0.519 - 0.367 i
11
-2.063 - 2.4273 i
0.519 + 0.367 i
12
195.6441
6.63 i
Top of Page  Top of the page    

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
-0.5778 + 0.0016 i
0.0129 + 0.0136 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.5778 - 0.0016 i
0.0129 - 0.0136 i
3
-0.6707
0.0501
4
2.0489
0.884
5
2.1693
0.594 i
6
-2.2979 + 0.1721 i
0.0707 - 0.0957 i
7
-2.2979 - 0.1721 i
0.0707 + 0.0957 i
8
2.8525 + 1.032 i
0.712 + 0.621 i
9
2.8525 - 1.032 i
0.712 - 0.621 i
10
-2.2848 + 2.0031 i
0.22 - 0.765 i
11
-2.2848 - 2.0031 i
0.22 + 0.765 i
12
9.8341
7.95
Top of Page  Top of the page    

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
-0.5764 + 0.0016 i
0.0117 + 0.0123 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.5764 - 0.0016 i
0.0117 - 0.0123 i
3
-0.6699
0.0482
4
-1.3626
0.269 i
5
-1.4727 + 0.1802 i
0.0319 - 0.272 i
6
-1.4727 - 0.1802 i
0.0319 + 0.272 i
7
1.4004 + 0.7144 i
0.00358 - 0.0201 i
8
1.4004 - 0.7144 i
0.00358 + 0.0201 i
9
1.4223 + 0.6986 i
0.0202 + 0.00306 i
10
1.4223 - 0.6986 i
0.0202 - 0.00306 i
11
-2.3208 + 2.2486 i
0.772 - 0.311 i
12
-2.3208 - 2.2486 i
0.772 + 0.311 i
13
3.2638
1.41
Top of Page  Top of the page    

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
-0.5748 + 0.0023 i
0.00647 + 0.00659 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.5748 - 0.0023 i
0.00647 - 0.00659 i
3
-0.6678
0.0408
4
-0.3044 + 1.4816 i
0.00494 - 0.00759 i
5
-0.3044 - 1.4816 i
0.00494 + 0.00759 i
6
-0.2922 + 1.5145 i
0.00773 + 0.00489 i
7
-0.2922 - 1.5145 i
0.00773 - 0.00489 i
8
-1.6524
4.3 i
9
-1.7772 + 0.5243 i
0.0952 + 0.11 i
10
-1.7772 - 0.5243 i
0.0952 - 0.11 i
11
1.8881
0.0593
12
2.1767
0.0958 i
13
2.5539 + 4.209 i
0.0813 + 0.301 i
14
2.5539 - 4.209 i
0.0813 - 0.301 i
Top of Page  Top of the page    


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.