Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 1.2r_e"

Molecule X 1^Sigma+ State of BH. Basis AUG-CC-PVQZ. 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
1.2651
0.202
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
1.1973
0.181
Singularities of quadratic [1, 1, 0] approximant
2
1623.795
6.68 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
1.5219
0.47
Singularities of quadratic [1, 1, 1] approximant
2
-5.6344
0.555
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
1.5256
0.476
Singularities of quadratic [2, 1, 1] approximant
2
-5.7853
0.568
3
159.4821
0.394 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
1.6128
0.849
Singularities of quadratic [2, 2, 1] approximant
2
-3.3052
0.147
3
-7.5837
0.16 i
4
32.9484
0.475 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
1.7506
2.51
Singularities of quadratic [2, 2, 2] approximant
2
2.6236
1.12 i
3
4.0154
7.96
4
-4.4713
0.279
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
0.7131 + 0.0026 i
0.0061 - 0.00606 i
Singularities of quadratic [3, 2, 2] approximant
2
0.7131 - 0.0026 i
0.0061 + 0.00606 i
3
1.7129
6.02
4
-6.3322 + 0.3453 i
0.175 - 1.61 i
5
-6.3322 - 0.3453 i
0.175 + 1.61 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
1.5446 + 0.3869 i
0.218 - 0.205 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5446 - 0.3869 i
0.218 + 0.205 i
3
1.834
0.288
4
-3.5144
0.125
5
-13.4703
0.193 i
6
18.5776
0.352 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
1.5416 + 0.3765 i
0.213 - 0.226 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5416 - 0.3765 i
0.213 + 0.226 i
3
1.8043
0.278
4
-3.5105
0.127
5
-11.8688
0.19 i
6
24.553
0.344 i
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
1.5299 + 0.4475 i
0.177 - 0.0651 i
Singularities of quadratic [4, 3, 3] approximant
2
1.5299 - 0.4475 i
0.177 + 0.0651 i
3
1.9097
0.31
4
-3.2524
0.0707
5
-0.4322 + 9.033 i
0.0659 + 0.132 i
6
-0.4322 - 9.033 i
0.0659 - 0.132 i
7
34.0859
0.551 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
1.5383 + 0.4277 i
0.201 - 0.0959 i
Singularities of quadratic [4, 4, 3] approximant
2
1.5383 - 0.4277 i
0.201 + 0.0959 i
3
1.8734
0.293
4
-2.9249
0.0413
5
-4.0516
0.0531 i
6
-5.5936 + 3.3339 i
0.0186 - 0.147 i
7
-5.5936 - 3.3339 i
0.0186 + 0.147 i
8
25.8573
0.375 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
1.5194 + 0.4681 i
0.143 - 0.00838 i
Singularities of quadratic [4, 4, 4] approximant
2
1.5194 - 0.4681 i
0.143 + 0.00838 i
3
1.8025
0.238
4
-1.242 + 2.5101 i
0.00791 + 0.0113 i
5
-1.242 - 2.5101 i
0.00791 - 0.0113 i
6
-2.9246
0.027
7
-1.2911 + 2.74 i
0.013 - 0.00831 i
8
-1.2911 - 2.74 i
0.013 + 0.00831 i
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
1.5235 + 0.4608 i
0.155 - 0.0197 i
Singularities of quadratic [5, 4, 4] approximant
2
1.5235 - 0.4608 i
0.155 + 0.0197 i
3
1.8186
0.251
4
-2.8121
0.0209
5
-1.879 + 2.4823 i
0.0024 + 0.0176 i
6
-1.879 - 2.4823 i
0.0024 - 0.0176 i
7
-2.2828 + 2.7198 i
0.0202 + 0.00121 i
8
-2.2828 - 2.7198 i
0.0202 - 0.00121 i
9
-70.1191
0.588 i
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
1.5137 + 0.4569 i
0.145 - 0.0388 i
Singularities of quadratic [5, 5, 4] approximant
2
1.5137 - 0.4569 i
0.145 + 0.0388 i
3
1.845
0.264
4
-2.4634
0.0177
5
-2.732
0.019 i
6
3.4296
0.86 i
7
4.5967
3.55
8
-5.7444 + 1.588 i
0.00584 - 0.164 i
9
-5.7444 - 1.588 i
0.00584 + 0.164 i
10
12.7804
0.271 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
1.5156 + 0.4603 i
0.145 - 0.0296 i
Singularities of quadratic [5, 5, 5] approximant
2
1.5156 - 0.4603 i
0.145 + 0.0296 i
3
1.8287
0.256
4
-2.3427
0.0181
5
-2.4711
0.0196 i
6
-3.9792
0.584
7
2.5714 + 4.3529 i
0.059 + 0.125 i
8
2.5714 - 4.3529 i
0.059 - 0.125 i
9
4.2043 + 8.0113 i
0.266 + 0.0667 i
10
4.2043 - 8.0113 i
0.266 - 0.0667 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
1.5142 + 0.4673 i
0.135 - 0.0136 i
Singularities of quadratic [6, 5, 5] approximant
2
1.5142 - 0.4673 i
0.135 + 0.0136 i
3
1.7949
0.234
4
-2.3395
0.0113
5
-2.5373
0.0123 i
6
-4.4021
7.41
7
2.2836 + 5.7062 i
0.0368 - 0.0923 i
8
2.2836 - 5.7062 i
0.0368 + 0.0923 i
9
7.4129
7.99 i
10
-1.9156 + 7.1691 i
0.0345 + 0.0661 i
11
-1.9156 - 7.1691 i
0.0345 - 0.0661 i
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
1.5163 + 0.4595 i
0.146 - 0.0318 i
Singularities of quadratic [6, 6, 5] approximant
2
1.5163 - 0.4595 i
0.146 + 0.0318 i
3
1.8337
0.26
4
-2.3846
0.0191
5
-2.5416
0.0205 i
6
2.1615 + 2.7923 i
0.137 + 0.0299 i
7
2.1615 - 2.7923 i
0.137 - 0.0299 i
8
2.4805 + 2.7941 i
0.00763 - 0.171 i
9
2.4805 - 2.7941 i
0.00763 + 0.171 i
10
-4.3795
6.24
11
-10.669
0.169 i
12
29.5266
0.443 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
1.5379 + 0.461 i
0.215 - 0.00987 i
Singularities of quadratic [6, 6, 6] approximant
2
1.5379 - 0.461 i
0.215 + 0.00987 i
3
1.7124 + 0.1935 i
0.176 + 0.279 i
4
1.7124 - 0.1935 i
0.176 - 0.279 i
5
1.7308
0.602
6
-2.3788
0.0214
7
-2.515
0.0229 i
8
-4.1689
1.14
9
4.5738
0.579 i
10
4.4323 + 3.4864 i
0.0943 + 0.27 i
11
4.4323 - 3.4864 i
0.0943 - 0.27 i
12
-24.2879
0.163 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
0.1422
1.2e-9 - 1.2e-9 i
Singularities of quadratic [7, 6, 6] approximant
2
0.1422
1.2e-9 + 1.2e-9 i
3
1.5317 + 0.4524 i
0.213 - 0.0327 i
4
1.5317 - 0.4524 i
0.213 + 0.0327 i
5
2.0532
0.281
6
2.3255
1.04 i
7
-2.3991 + 0.1162 i
0.00567 + 0.00551 i
8
-2.3991 - 0.1162 i
0.00567 - 0.00551 i
9
-3.4695
0.0297
10
3.3669 + 1.152 i
0.493 + 0.273 i
11
3.3669 - 1.152 i
0.493 - 0.273 i
12
-6.5261
12.9 i
13
12.215
0.395
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
1.5135 + 0.4514 i
0.136 - 0.0595 i
Singularities of quadratic [7, 7, 6] approximant
2
1.5135 - 0.4514 i
0.136 + 0.0595 i
3
1.8409
0.282
4
1.9629 + 1.193 i
0.0779 - 0.0712 i
5
1.9629 - 1.193 i
0.0779 + 0.0712 i
6
-2.4107 + 0.0683 i
0.0123 + 0.0132 i
7
-2.4107 - 0.0683 i
0.0123 - 0.0132 i
8
2.0498 + 1.2808 i
0.0672 + 0.0928 i
9
2.0498 - 1.2808 i
0.0672 - 0.0928 i
10
-3.5403
0.05
11
-6.4981
8.01 i
12
8.6105
0.623 i
13
-10.8014 + 10.0159 i
0.225 + 0.0812 i
14
-10.8014 - 10.0159 i
0.225 - 0.0812 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.