Singularities of Møller-Plesset series: example "HF aug-cc-pVDZ 1.5r_e"

Molecule X 1^Sigma+ State of HF. 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 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 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-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

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
-13.6099
6.72
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
-0.24
0.0169
Singularities of quadratic [1, 1, 0] approximant
2
-0.3191
0.0195 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
-1.1311
0.32
Singularities of quadratic [1, 1, 1] approximant
2
6.7082
5.87
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
-0.617
0.0263
Singularities of quadratic [2, 1, 1] approximant
2
0.5105 + 0.9034 i
0.0384 + 0.00343 i
3
0.5105 - 0.9034 i
0.0384 - 0.00343 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
-0.7852
0.0796
Singularities of quadratic [2, 2, 1] approximant
2
1.4326 + 1.324 i
0.189 + 0.0258 i
3
1.4326 - 1.324 i
0.189 - 0.0258 i
4
-10.0869
0.596 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
-0.1548
0.000231
Singularities of quadratic [2, 2, 2] approximant
2
-0.1551
0.000231 i
3
-0.6795
0.0246
4
1.5059
0.129
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
-0.7668
0.0704
Singularities of quadratic [3, 2, 2] approximant
2
1.3085 + 2.3763 i
0.139 + 0.0739 i
3
1.3085 - 2.3763 i
0.139 - 0.0739 i
4
2.9952
0.593
5
4.6308
0.254 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
-0.7611
0.0644
Singularities of quadratic [3, 3, 2] approximant
2
1.589 + 0.2838 i
0.119 - 0.0212 i
3
1.589 - 0.2838 i
0.119 + 0.0212 i
4
1.5274 + 1.3173 i
0.126 - 0.0638 i
5
1.5274 - 1.3173 i
0.126 + 0.0638 i
6
-39.7136
2.25 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
-0.5957 + 0.0073 i
0.00621 + 0.00648 i
Singularities of quadratic [3, 3, 3] approximant
2
-0.5957 - 0.0073 i
0.00621 - 0.00648 i
3
-0.7451
0.0302
4
-1.9282
0.346 i
5
1.9961
0.699
6
-5.7043
753.
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
-0.6947 + 0.2098 i
0.0118 + 0.00298 i
Singularities of quadratic [4, 3, 3] approximant
2
-0.6947 - 0.2098 i
0.0118 - 0.00298 i
3
-0.7028 + 0.2833 i
0.00171 - 0.0131 i
4
-0.7028 - 0.2833 i
0.00171 + 0.0131 i
5
-1.008
0.12
6
1.8978
0.337
7
5.4234
6.81 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
-0.7181
0.0365
Singularities of quadratic [4, 4, 3] approximant
2
-0.935
0.075 i
3
-1.1239
0.331
4
0.6679 + 2.2709 i
0.0826 + 0.0445 i
5
0.6679 - 2.2709 i
0.0826 - 0.0445 i
6
2.7132 + 1.6305 i
0.00958 - 0.206 i
7
2.7132 - 1.6305 i
0.00958 + 0.206 i
8
-12.7769
1.9 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
-0.7131
0.0304
Singularities of quadratic [4, 4, 4] approximant
2
-0.9848
0.0895 i
3
-1.2714
0.132
4
0.062 + 1.5876 i
0.0151 + 0.0263 i
5
0.062 - 1.5876 i
0.0151 - 0.0263 i
6
-0.1057 + 1.7637 i
0.0316 - 0.0121 i
7
-0.1057 - 1.7637 i
0.0316 + 0.0121 i
8
2.4895
24.9
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
-0.6766 + 0.0244 i
0.00192 + 0.00558 i
Singularities of quadratic [5, 4, 4] approximant
2
-0.6766 - 0.0244 i
0.00192 - 0.00558 i
3
-0.6921
0.00467
4
1.202 + 0.0128 i
0.00941 - 0.00915 i
5
1.202 - 0.0128 i
0.00941 + 0.00915 i
6
-2.4434
0.193 i
7
-0.6992 + 2.6705 i
0.154 - 0.102 i
8
-0.6992 - 2.6705 i
0.154 + 0.102 i
9
2.8839
0.97
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
-0.6642 + 0.0152 i
0.00258 + 0.00407 i
Singularities of quadratic [5, 5, 4] approximant
2
-0.6642 - 0.0152 i
0.00258 - 0.00407 i
3
-0.6928
0.00519
4
1.6408 + 0.0805 i
0.058 - 0.0467 i
5
1.6408 - 0.0805 i
0.058 + 0.0467 i
6
-2.1422
0.253 i
7
2.7952
0.871
8
-1.0412 + 2.9184 i
0.292 - 0.0865 i
9
-1.0412 - 2.9184 i
0.292 + 0.0865 i
10
128.3564
58.3 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
-0.6714 + 0.0185 i
0.00283 + 0.00521 i
Singularities of quadratic [5, 5, 5] approximant
2
-0.6714 - 0.0185 i
0.00283 - 0.00521 i
3
-0.6973
0.00567
4
1.8169 + 0.1574 i
0.164 - 0.0918 i
5
1.8169 - 0.1574 i
0.164 + 0.0918 i
6
-2.198
0.251 i
7
2.5856
0.998
8
-1.2605 + 2.8409 i
0.375 - 0.0416 i
9
-1.2605 - 2.8409 i
0.375 + 0.0416 i
10
-14.3086
1.29
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
-0.6683 + 0.0172 i
0.00258 + 0.00457 i
Singularities of quadratic [6, 5, 5] approximant
2
-0.6683 - 0.0172 i
0.00258 - 0.00457 i
3
-0.6939
0.00514
4
1.8829 + 0.2455 i
0.247 - 0.0492 i
5
1.8829 - 0.2455 i
0.247 + 0.0492 i
6
-2.2281
0.23 i
7
-1.0723 + 2.6974 i
0.258 - 0.0323 i
8
-1.0723 - 2.6974 i
0.258 + 0.0323 i
9
3.0312
0.391
10
3.7068
0.709 i
11
11.0655
0.907
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
-0.6536 + 0.0112 i
0.00186 + 0.00257 i
Singularities of quadratic [6, 6, 5] approximant
2
-0.6536 - 0.0112 i
0.00186 - 0.00257 i
3
-0.683
0.00398
4
-1.714
0.203 i
5
-1.6736 + 0.449 i
0.278 - 0.0532 i
6
-1.6736 - 0.449 i
0.278 + 0.0532 i
7
1.7527 + 0.1326 i
0.0908 - 0.057 i
8
1.7527 - 0.1326 i
0.0908 + 0.057 i
9
2.9999
0.581
10
-1.5589 + 2.6832 i
0.254 + 0.165 i
11
-1.5589 - 2.6832 i
0.254 - 0.165 i
12
23.0475
1.34e3 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
-0.6517 + 0.0105 i
0.00184 + 0.00246 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.6517 - 0.0105 i
0.00184 - 0.00246 i
3
-0.6826
0.00407
4
-1.4109
0.33 i
5
-1.6092 + 0.2291 i
0.708 - 0.0333 i
6
-1.6092 - 0.2291 i
0.708 + 0.0333 i
7
1.765 + 0.138 i
0.1 - 0.0612 i
8
1.765 - 0.138 i
0.1 + 0.0612 i
9
2.9086
0.635
10
-1.519 + 2.7368 i
0.303 + 0.159 i
11
-1.519 - 2.7368 i
0.303 - 0.159 i
12
56.1709
13.2 i
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
-0.6521 + 0.0106 i
0.00186 + 0.0025 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.6521 - 0.0106 i
0.00186 - 0.0025 i
3
-0.6829
0.0041
4
-1.4164
0.327 i
5
-1.6083 + 0.2382 i
0.689 + 0.0304 i
6
-1.6083 - 0.2382 i
0.689 - 0.0304 i
7
1.7699 + 0.1389 i
0.105 - 0.0643 i
8
1.7699 - 0.1389 i
0.105 + 0.0643 i
9
2.844
0.688
10
-1.5924 + 2.7652 i
0.332 + 0.2 i
11
-1.5924 - 2.7652 i
0.332 - 0.2 i
12
-12.6494 + 20.1422 i
5.49 - 0.197 i
13
-12.6494 - 20.1422 i
5.49 + 0.197 i
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
0.0387
0
Singularities of quadratic [7, 7, 6] approximant
2
0.0387
0
3
-0.6507 + 0.0104 i
0.0017 + 0.00226 i
4
-0.6507 - 0.0104 i
0.0017 - 0.00226 i
5
-0.6811
0.00379
6
-1.6233
0.226 i
7
-1.6584 + 0.4006 i
0.314 - 0.0926 i
8
-1.6584 - 0.4006 i
0.314 + 0.0926 i
9
1.7706 + 0.1349 i
0.109 - 0.0695 i
10
1.7706 - 0.1349 i
0.109 + 0.0695 i
11
2.8407
0.686
12
-1.4651 + 2.7851 i
0.298 + 0.102 i
13
-1.4651 - 2.7851 i
0.298 - 0.102 i
14
34.0991
316. i
Top of Page  Top of the page    


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 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 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-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.