Singularities of Møller-Plesset series: example "na-pl aug-cc-pvdz"

Molecule Na+. 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 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 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-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 [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
-1.8459
0.00226
Singularities of quadratic [1, 1, 0] approximant
2
-36.9167
0.0101 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
2.9386
0.00229
Singularities of quadratic [1, 1, 1] approximant
2
-5.7357
0.109
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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
2.9988
0.00226
Singularities of quadratic [2, 1, 1] approximant
2
-7.6232
0.0144
3
-19.2624
0.00407 i
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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
-3.8117
0.0148
Singularities of quadratic [2, 2, 1] approximant
2
5.0311 + 1.2806 i
0.0157 - 0.00834 i
3
5.0311 - 1.2806 i
0.0157 + 0.00834 i
4
-17.4649
0.053 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
-3.6217
0.0103
Singularities of quadratic [2, 2, 2] approximant
2
4.7561
0.0818
3
7.2134
0.0139 i
4
-10.4802
3.77 i
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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
-3.5849
0.00943
Singularities of quadratic [3, 2, 2] approximant
2
4.9838
0.402
3
6.5914
0.0177 i
4
-9.5891
0.686 i
5
-302.1717
0.0116
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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
2.1256
0.000249
Singularities of quadratic [3, 3, 2] approximant
2
2.1471
0.00025 i
3
-3.5516
0.00784
4
4.2243
0.00556
5
6.0771
2.77 i
6
-12.0814
0.252 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
-3.7446
0.0199
Singularities of quadratic [3, 3, 3] approximant
2
4.4954 + 0.1734 i
0.00382 - 0.00255 i
3
4.4954 - 0.1734 i
0.00382 + 0.00255 i
4
-7.04
0.0273 i
5
11.7542
0.00242
6
-834.8222
0.000369
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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
-3.6935
0.0144
Singularities of quadratic [4, 3, 3] approximant
2
5.255 + 0.2409 i
0.0616 + 0.166 i
3
5.255 - 0.2409 i
0.0616 - 0.166 i
4
-7.9885
0.0402 i
5
-14.1523 + 10.7658 i
0.00328 + 0.0088 i
6
-14.1523 - 10.7658 i
0.00328 - 0.0088 i
7
54.5959
0.00862
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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
-1.128
0.0000103
Singularities of quadratic [4, 4, 3] approximant
2
-1.128
0.0000103 i
3
-3.7874
0.0327
4
6.5056 + 0.9939 i
0.000522 - 0.00384 i
5
6.5056 - 0.9939 i
0.000522 + 0.00384 i
6
-7.7189
0.0434 i
7
14.0979 + 9.8152 i
0.00282 - 0.00086 i
8
14.0979 - 9.8152 i
0.00282 + 0.00086 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
-2.3562 + 0.0041 i
0.00038 + 0.000377 i
Singularities of quadratic [4, 4, 4] approximant
2
-2.3562 - 0.0041 i
0.00038 - 0.000377 i
3
-3.7802
0.0193
4
3.9237 + 0.0757 i
0.000749 - 0.000672 i
5
3.9237 - 0.0757 i
0.000749 + 0.000672 i
6
-6.2007
0.0202 i
7
12.494
0.00177
8
-35.5137
0.0018
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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
-2.8658
0.000746
Singularities of quadratic [5, 4, 4] approximant
2
-2.9555
0.000793 i
3
-4.2303
0.0946
4
5.3881 + 1.7906 i
0.00214 + 0.00193 i
5
5.3881 - 1.7906 i
0.00214 - 0.00193 i
6
-6.5757
0.0188 i
7
6.3078 + 2.3615 i
0.00232 - 0.00159 i
8
6.3078 - 2.3615 i
0.00232 + 0.00159 i
9
-156.5684
0.0103
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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
-2.8309
0.000622
Singularities of quadratic [5, 5, 4] approximant
2
-2.9164
0.000663 i
3
-4.2183
0.0896
4
4.6906 + 2.1383 i
0.00113 + 0.000587 i
5
4.6906 - 2.1383 i
0.00113 - 0.000587 i
6
5.0418 + 2.5064 i
0.000756 - 0.00107 i
7
5.0418 - 2.5064 i
0.000756 + 0.00107 i
8
-6.8832
0.0232 i
9
88.2578 + 50.2963 i
0.0181 - 0.0162 i
10
88.2578 - 50.2963 i
0.0181 + 0.0162 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
-1.2581 + 0.e-4 i
4.43e-7 + 4.43e-7 i
Singularities of quadratic [5, 5, 5] approximant
2
-1.2581 - 0.e-4 i
4.43e-7 - 4.43e-7 i
3
-2.9644
0.000255
4
-3.4233
0.000631 i
5
3.7782
0.0000754
6
4.1176 + 0.2592 i
6.93e-6 + 0.000128 i
7
4.1176 - 0.2592 i
6.93e-6 - 0.000128 i
8
5.4553 + 2.0701 i
0.000383 - 0.000236 i
9
5.4553 - 2.0701 i
0.000383 + 0.000236 i
10
-7.5278
7.43
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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
0.2176
0
Singularities of quadratic [6, 5, 5] approximant
2
0.2176
0
3
-2.3104 + 0.0149 i
0.0000151 + 0.0000148 i
4
-2.3104 - 0.0149 i
0.0000151 - 0.0000148 i
5
-3.1321
0.000293
6
-4.0925
0.00626 i
7
5.3689 + 2.1145 i
0.000375 - 0.00107 i
8
5.3689 - 2.1145 i
0.000375 + 0.00107 i
9
6.3601
0.00919
10
10.8353
0.000786 i
11
-14.4557
0.00367
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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
0.1018 + 0.9527 i
6.87e-8 - 2.46e-8 i
Singularities of quadratic [6, 6, 5] approximant
2
0.1018 - 0.9527 i
6.87e-8 + 2.46e-8 i
3
0.1018 + 0.9527 i
2.46e-8 + 6.87e-8 i
4
0.1018 - 0.9527 i
2.46e-8 - 6.87e-8 i
5
-2.8942
0.00022
6
-3.2314
0.000396 i
7
4.7158
0.0049
8
5.7063
0.00905 i
9
-6.3908
0.028
10
7.2573
0.00118
11
-34.5765
0.00177 i
12
125.6381
0.00207 i
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Table 19. 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
1.002 + 0.e-5 i
2.74e-8 - 2.74e-8 i
Singularities of quadratic [6, 6, 6] approximant
2
1.002 - 0.e-5 i
2.74e-8 + 2.74e-8 i
3
-0.3109 + 1.0427 i
4.64e-8 + 1.08e-7 i
4
-0.3109 - 1.0427 i
4.64e-8 - 1.08e-7 i
5
-0.3109 + 1.0427 i
1.08e-7 - 4.64e-8 i
6
-0.3109 - 1.0427 i
1.08e-7 + 4.64e-8 i
7
-2.934
0.000289
8
-3.2782
0.000493 i
9
5.0527
0.00923
10
5.4639 + 2.1438 i
0.000376 - 0.000389 i
11
5.4639 - 2.1438 i
0.000376 + 0.000389 i
12
-6.8447
0.0612
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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 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 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-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.