Singularities of Møller-Plesset series: example "BH-cc-pVQZ-1.5Re"

Molecule X 1^Sigma+ State of BH. Basis CC-PVQZ. Structure ""

Content


ExamplesBH-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-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 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 O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-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 [2, 2, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.7343 + 0.6044 i
0.573 - 0.0942 i
Singularities of quadratic [2, 2, 2] approximant
2
1.7343 - 0.6044 i
0.573 + 0.0942 i
3
3.1691
1.46
4
-3.3344
0.181
Top of Page  Top of the page    

Table 2. Singularities with their weights for the quadratic approximant [2, 2, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.3214 + 0.1106 i
0.0952 - 0.068 i
Singularities of quadratic [2, 2, 3] approximant
2
1.3214 - 0.1106 i
0.0952 + 0.068 i
3
2.1918
0.627
4
-4.8031 + 0.4622 i
1.17 - 0.957 i
5
-4.8031 - 0.4622 i
1.17 + 0.957 i
Top of Page  Top of the page    

Table 3. Singularities with their weights for the quadratic approximant [2, 3, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5854 + 0.4341 i
0.407 - 0.682 i
Singularities of quadratic [2, 3, 3] approximant
2
1.5854 - 0.4341 i
0.407 + 0.682 i
3
1.933
0.464
4
-3.1324
0.166
5
-15.7004
0.216 i
6
48.0364
0.48 i
Top of Page  Top of the page    

Table 4. 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
1.5794 + 0.4612 i
0.454 - 0.447 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5794 - 0.4612 i
0.454 + 0.447 i
3
1.9092
0.445
4
-3.1056
0.151
5
14.1375
0.457 i
6
-46.1227
0.176 i
Top of Page  Top of the page    

Table 5. Singularities with their weights for the quadratic approximant [3, 3, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5844 + 0.4349 i
0.368 - 0.694 i
Singularities of quadratic [3, 3, 4] approximant
2
1.5844 - 0.4349 i
0.368 + 0.694 i
3
1.9596
0.465
4
-3.179
0.186
5
-10.9266
0.243 i
6
20.8976
0.463 i
7
-2684.2286
19.
Top of Page  Top of the page    

Table 6. Singularities with their weights for the quadratic approximant [3, 4, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.3691 + 0.e-4 i
0.00017 + 0.00017 i
Singularities of quadratic [3, 4, 4] approximant
2
-0.3691 - 0.e-4 i
0.00017 - 0.00017 i
3
1.5865 + 0.45 i
0.498 - 0.537 i
4
1.5865 - 0.45 i
0.498 + 0.537 i
5
1.9104
0.451
6
-3.1612
0.182
7
-14.4413
0.21 i
8
46.5669
0.478 i
Top of Page  Top of the page    

Table 7. 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
1.2009
0.0506
Singularities of quadratic [4, 4, 4] approximant
2
1.2214
0.0509 i
3
1.6337 + 0.4014 i
2.78 - 1.02 i
4
1.6337 - 0.4014 i
2.78 + 1.02 i
5
1.7745
0.377
6
-3.4916
0.605
7
-4.8645
0.604 i
8
-9.7798
1.51
Top of Page  Top of the page    

Table 8. Singularities with their weights for the quadratic approximant [4, 4, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4669 + 0.4459 i
0.0646 - 0.171 i
Singularities of quadratic [4, 4, 5] approximant
2
1.4669 - 0.4459 i
0.0646 + 0.171 i
3
1.5579 + 0.0628 i
0.0994 - 0.062 i
4
1.5579 - 0.0628 i
0.0994 + 0.062 i
5
2.6605
0.607
6
-3.2846
0.239
7
-6.398
0.418 i
8
11.1149
0.673 i
9
-24.1957
2.04
Top of Page  Top of the page    

Table 9. Singularities with their weights for the quadratic approximant [4, 5, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4477 + 0.0117 i
0.0189 - 0.0176 i
Singularities of quadratic [4, 5, 5] approximant
2
1.4477 - 0.0117 i
0.0189 + 0.0176 i
3
1.4419 + 0.4564 i
0.044 - 0.104 i
4
1.4419 - 0.4564 i
0.044 + 0.104 i
5
2.8654
0.872
6
-3.2149
0.146
7
-4.5363
8.35 i
8
-6.2263
0.182
9
12.8422
0.365 i
10
-31.6283
0.293 i
Top of Page  Top of the page    

Table 10. 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
-1.113
0.000349
Singularities of quadratic [5, 5, 5] approximant
2
-1.1132
0.000349 i
3
1.2098
0.0065
4
1.2239
0.0067 i
5
1.4159 + 0.4474 i
0.012 - 0.0697 i
6
1.4159 - 0.4474 i
0.012 + 0.0697 i
7
2.8505
1.06
8
-3.4411
0.987
9
-9.3884
0.162 i
10
37.1937
0.26 i
Top of Page  Top of the page    

Table 11. Singularities with their weights for the quadratic approximant [5, 5, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.2014
0.0062
Singularities of quadratic [5, 5, 6] approximant
2
1.2149
0.00638 i
3
-1.2757
0.000603
4
-1.2762
0.000603 i
5
1.415 + 0.4463 i
0.0104 - 0.0692 i
6
1.415 - 0.4463 i
0.0104 + 0.0692 i
7
2.8617
1.09
8
-3.4682
1.41
9
-10.0384
0.154 i
10
38.9602 + 39.2125 i
0.122 + 0.282 i
11
38.9602 - 39.2125 i
0.122 - 0.282 i
Top of Page  Top of the page    

Table 12. Singularities with their weights for the quadratic approximant [5, 6, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.371
0.0235
Singularities of quadratic [5, 6, 6] approximant
2
1.4127
0.0264 i
3
1.4253 + 0.4568 i
0.028 - 0.084 i
4
1.4253 - 0.4568 i
0.028 + 0.084 i
5
-1.1435 + 1.2795 i
0.00101 - 0.00233 i
6
-1.1435 - 1.2795 i
0.00101 + 0.00233 i
7
-1.1456 + 1.2782 i
0.00233 + 0.00101 i
8
-1.1456 - 1.2782 i
0.00233 - 0.00101 i
9
3.0761
1.41
10
-3.4339
1.12
11
12.5907
0.304 i
12
-14.4086
0.164 i
Top of Page  Top of the page    

Table 13. 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
1.4603 + 0.4638 i
0.0693 - 0.179 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4603 - 0.4638 i
0.0693 + 0.179 i
3
1.7208
0.205
4
2.1394 + 0.3208 i
0.805 + 0.343 i
5
2.1394 - 0.3208 i
0.805 - 0.343 i
6
2.252 + 1.0212 i
0.311 + 0.055 i
7
2.252 - 1.0212 i
0.311 - 0.055 i
8
-2.477 + 0.0066 i
0.129 + 0.132 i
9
-2.477 - 0.0066 i
0.129 - 0.132 i
10
-3.5252
0.548
11
-4.7991
0.838 i
12
-10.0505
1.16
Top of Page  Top of the page    

Table 14. Singularities with their weights for the quadratic approximant [6, 6, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.461 + 0.48 i
0.124 - 0.119 i
Singularities of quadratic [6, 6, 7] approximant
2
1.461 - 0.48 i
0.124 + 0.119 i
3
1.7714 + 0.0592 i
0.104 - 0.0673 i
4
1.7714 - 0.0592 i
0.104 + 0.0673 i
5
2.2648 + 0.7578 i
0.717 - 0.375 i
6
2.2648 - 0.7578 i
0.717 + 0.375 i
7
2.4124
18.9
8
-2.5172
0.0172
9
-2.6182
0.018 i
10
-4.1205
0.42
11
-7.8674
0.102 i
12
-4.9582 + 10.6579 i
0.0792 - 0.167 i
13
-4.9582 - 10.6579 i
0.0792 + 0.167 i
Top of Page  Top of the page    

Table 15. Singularities with their weights for the quadratic approximant [6, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4616 + 0.4791 i
0.125 - 0.124 i
Singularities of quadratic [6, 7, 7] approximant
2
1.4616 - 0.4791 i
0.125 + 0.124 i
3
1.791 + 0.0446 i
0.0889 - 0.065 i
4
1.791 - 0.0446 i
0.0889 + 0.065 i
5
2.3473
8.15
6
2.2588 + 0.7677 i
0.703 - 0.33 i
7
2.2588 - 0.7677 i
0.703 + 0.33 i
8
-2.5203
0.0178
9
-2.6203
0.0186 i
10
-4.1089
0.45
11
-7.4133
0.104 i
12
-5.8086 + 10.7523 i
0.0918 - 0.178 i
13
-5.8086 - 10.7523 i
0.0918 + 0.178 i
14
14373.5363
133. i
Top of Page  Top of the page    


ExamplesBH-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-cc-pVDZ-1.5ReHF-cc-pVDZ-2ReHF-cc-pVDZ-ReO2--aug-cc-pVDZ
MoleculeX 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 O2-
BasisCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZCC-PVDZCC-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.