Singularities of Møller-Plesset series: example "hf aug-cc-pVDZ r_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 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

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 [5, 5, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.8275 + 0.0272 i
0.00704 + 0.0114 i
Singularities of quadratic [5, 5, 4] approximant
2
-0.8275 - 0.0272 i
0.00704 - 0.0114 i
3
-0.8939
0.0142
4
-2.1761
49.5 i
5
2.9704
18.5
6
0.3635 + 3.804 i
0.127 + 0.204 i
7
0.3635 - 3.804 i
0.127 - 0.204 i
8
-3.4599 + 1.9188 i
0.173 + 0.0763 i
9
-3.4599 - 1.9188 i
0.173 - 0.0763 i
10
56.9262
2.8 i
Top of Page  Top of the page    

Table 2. 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
-0.8048 + 0.0269 i
0.00258 + 0.00446 i
Singularities of quadratic [5, 5, 5] approximant
2
-0.8048 - 0.0269 i
0.00258 - 0.00446 i
3
-0.8461
0.00514
4
2.4891 + 0.0387 i
0.0766 - 0.0682 i
5
2.4891 - 0.0387 i
0.0766 + 0.0682 i
6
-3.1275
0.261 i
7
-1.2541 + 3.4607 i
0.361 + 0.0969 i
8
-1.2541 - 3.4607 i
0.361 - 0.0969 i
9
3.7859
0.966
10
-11.6994
0.551
Top of Page  Top of the page    

Table 3. 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
-0.7993 + 0.0241 i
0.00226 + 0.00383 i
Singularities of quadratic [6, 5, 5] approximant
2
-0.7993 - 0.0241 i
0.00226 - 0.00383 i
3
-0.8389
0.00451
4
-1.0244 + 2.0626 i
0.00204 + 0.0499 i
5
-1.0244 - 2.0626 i
0.00204 - 0.0499 i
6
-1.2213 + 2.485 i
0.0489 - 0.00854 i
7
-1.2213 - 2.485 i
0.0489 + 0.00854 i
8
3.0043
33.2
9
0.6711 + 3.3519 i
0.0935 + 0.0798 i
10
0.6711 - 3.3519 i
0.0935 - 0.0798 i
11
-3.5092
0.145 i
Top of Page  Top of the page    

Table 4. 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
-0.7865 + 0.0207 i
0.00129 + 0.00221 i
Singularities of quadratic [6, 6, 5] approximant
2
-0.7865 - 0.0207 i
0.00129 - 0.00221 i
3
-0.8173
0.00256
4
1.7168
0.00924
5
1.7327
0.0094 i
6
-2.0795 + 0.8297 i
0.194 - 0.055 i
7
-2.0795 - 0.8297 i
0.194 + 0.055 i
8
-2.5924
0.192 i
9
-1.2732 + 3.4611 i
0.177 + 0.0829 i
10
-1.2732 - 3.4611 i
0.177 - 0.0829 i
11
3.9369
0.722
12
10.8764
3.2 i
Top of Page  Top of the page    

Table 5. 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
-0.7861 + 0.0206 i
0.00127 + 0.00217 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.7861 - 0.0206 i
0.00127 - 0.00217 i
3
-0.8167
0.00252
4
1.6192
0.00655
5
1.6293
0.00663 i
6
-2.0788 + 0.829 i
0.193 - 0.06 i
7
-2.0788 - 0.829 i
0.193 + 0.06 i
8
-2.5815
0.195 i
9
-1.2285 + 3.4791 i
0.18 + 0.0703 i
10
-1.2285 - 3.4791 i
0.18 - 0.0703 i
11
3.8236
0.817
12
11.4128
3.55 i
Top of Page  Top of the page    

Table 6. 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
-0.7825 + 0.0183 i
0.00119 + 0.00195 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.7825 - 0.0183 i
0.00119 - 0.00195 i
3
-0.8132
0.00237
4
-1.4407
1.68 i
5
-1.538
0.444
6
-2.533
0.333 i
7
2.8496
2.07
8
-0.9879 + 2.788 i
0.0725 + 0.0522 i
9
-0.9879 - 2.788 i
0.0725 - 0.0522 i
10
1.6716 + 2.8265 i
0.058 - 0.087 i
11
1.6716 - 2.8265 i
0.058 + 0.087 i
12
1.6783 + 4.5028 i
0.0396 + 0.11 i
13
1.6783 - 4.5028 i
0.0396 - 0.11 i
Top of Page  Top of the page    

Table 7. 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
-0.7795 + 0.0163 i
0.00115 + 0.0018 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.7795 - 0.0163 i
0.00115 - 0.0018 i
3
-0.8107
0.00232
4
-1.1133
0.206 i
5
-1.1351
0.354
6
2.6046
0.32
7
-1.4014 + 2.805 i
0.0811 + 0.0958 i
8
-1.4014 - 2.805 i
0.0811 - 0.0958 i
9
-2.8892 + 1.2264 i
0.122 - 0.0956 i
10
-2.8892 - 1.2264 i
0.122 + 0.0956 i
11
3.4333
4.6 i
12
3.0934 + 3.2114 i
0.121 + 0.334 i
13
3.0934 - 3.2114 i
0.121 - 0.334 i
14
-9.633
0.989 i
Top of Page  Top of the page    

Table 8. Singularities with their weights for the quadratic approximant [7, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.7419 + 0.0353 i
0.000198 - 0.000112 i
Singularities of quadratic [7, 7, 7] approximant
2
-0.7419 - 0.0353 i
0.000198 + 0.000112 i
3
-0.7442 + 0.0294 i
0.0000874 + 0.00017 i
4
-0.7442 - 0.0294 i
0.0000874 - 0.00017 i
5
-0.7603
0.00029
6
1.9255 + 1.1293 i
0.0225 - 0.0103 i
7
1.9255 - 1.1293 i
0.0225 + 0.0103 i
8
2.004 + 1.134 i
0.0115 + 0.0236 i
9
2.004 - 1.134 i
0.0115 - 0.0236 i
10
-3.4548
0.349 i
11
-2.26 + 3.1803 i
0.672 - 0.823 i
12
-2.26 - 3.1803 i
0.672 + 0.823 i
13
4.2216
0.641
14
-17.3859
0.536
Top of Page  Top of the page    

Table 9. Singularities with their weights for the quadratic approximant [8, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.7439 + 0.0354 i
0.000199 - 0.000122 i
Singularities of quadratic [8, 7, 7] approximant
2
-0.7439 - 0.0354 i
0.000199 + 0.000122 i
3
-0.747 + 0.0301 i
0.0000915 + 0.000175 i
4
-0.747 - 0.0301 i
0.0000915 - 0.000175 i
5
-0.759
0.000283
6
1.939 + 1.2852 i
0.0334 - 0.00322 i
7
1.939 - 1.2852 i
0.0334 + 0.00322 i
8
2.013 + 1.3385 i
0.00318 + 0.0356 i
9
2.013 - 1.3385 i
0.00318 - 0.0356 i
10
-3.5348
0.35 i
11
3.6844
0.905
12
-2.4146 + 3.3087 i
1.35 - 1.18 i
13
-2.4146 - 3.3087 i
1.35 + 1.18 i
14
-6.8044 + 8.769 i
0.914 + 0.132 i
15
-6.8044 - 8.769 i
0.914 - 0.132 i
Top of Page  Top of the page    

Table 10. Singularities with their weights for the quadratic approximant [8, 8, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.6264
0.0000431
Singularities of quadratic [8, 8, 7] approximant
2
-0.6265
0.0000431 i
3
-0.7605 + 0.0151 i
0.000214 + 0.000394 i
4
-0.7605 - 0.0151 i
0.000214 - 0.000394 i
5
-0.7731
0.000406
6
1.9399 + 1.0416 i
0.0134 - 0.00739 i
7
1.9399 - 1.0416 i
0.0134 + 0.00739 i
8
2.0295 + 0.9961 i
0.00889 + 0.0139 i
9
2.0295 - 0.9961 i
0.00889 - 0.0139 i
10
-2.9885
0.541 i
11
-2.0666 + 2.7798 i
0.27 - 0.146 i
12
-2.0666 - 2.7798 i
0.27 + 0.146 i
13
5.088 + 2.8356 i
0.192 - 0.447 i
14
5.088 - 2.8356 i
0.192 + 0.447 i
15
3.206 + 6.5709 i
0.113 - 0.296 i
16
3.206 - 6.5709 i
0.113 + 0.296 i
Top of Page  Top of the page    

Table 11. Singularities with their weights for the quadratic approximant [8, 8, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.6371
0.0000465
Singularities of quadratic [8, 8, 8] approximant
2
-0.6372
0.0000464 i
3
-0.7595 + 0.0149 i
0.000196 + 0.000359 i
4
-0.7595 - 0.0149 i
0.000196 - 0.000359 i
5
-0.7714
0.000368
6
1.411
0.000807
7
1.412
0.000808 i
8
2.0669 + 1.1976 i
0.0139 - 0.0219 i
9
2.0669 - 1.1976 i
0.0139 + 0.0219 i
10
2.189 + 1.3162 i
0.0238 + 0.0193 i
11
2.189 - 1.3162 i
0.0238 - 0.0193 i
12
-3.1426
0.446 i
13
3.4523
1.39
14
-2.0869 + 2.9787 i
0.307 - 0.343 i
15
-2.0869 - 2.9787 i
0.307 + 0.343 i
16
248.4609
0.464 i
Top of Page  Top of the page    

Table 12. Singularities with their weights for the quadratic approximant [9, 8, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.6645
0.0000706
Singularities of quadratic [9, 8, 8] approximant
2
-0.6648
0.0000703 i
3
-0.7592 + 0.0155 i
0.000176 + 0.00033 i
4
-0.7592 - 0.0155 i
0.000176 - 0.00033 i
5
-0.7694
0.000324
6
1.9918 + 0.9011 i
0.0101 - 0.0158 i
7
1.9918 - 0.9011 i
0.0101 + 0.0158 i
8
2.0359 + 0.8288 i
0.017 + 0.00887 i
9
2.0359 - 0.8288 i
0.017 - 0.00887 i
10
-2.7817
1.62 i
11
-3.4831
0.333
12
-2.1311 + 3.2605 i
0.85 - 1.23 i
13
-2.1311 - 3.2605 i
0.85 + 1.23 i
14
-4.7131 + 2.1435 i
0.122 - 0.289 i
15
-4.7131 - 2.1435 i
0.122 + 0.289 i
16
4.7178 + 2.9365 i
0.185 + 0.561 i
17
4.7178 - 2.9365 i
0.185 - 0.561 i
Top of Page  Top of the page    

Table 13. Singularities with their weights for the quadratic approximant [9, 9, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.7271
0.000321
Singularities of quadratic [9, 9, 8] approximant
2
-0.7329
0.000261 i
3
-0.7675 + 0.0227 i
0.000279 + 0.000451 i
4
-0.7675 - 0.0227 i
0.000279 - 0.000451 i
5
-0.7708
0.00035
6
-1.0925 + 1.8188 i
0.00822 - 0.00349 i
7
-1.0925 - 1.8188 i
0.00822 + 0.00349 i
8
1.9702 + 0.8456 i
0.0179 + 0.0055 i
9
1.9702 - 0.8456 i
0.0179 - 0.0055 i
10
-1.19 + 1.8085 i
0.00417 + 0.00846 i
11
-1.19 - 1.8085 i
0.00417 - 0.00846 i
12
2.0468 + 0.8526 i
0.00685 - 0.0197 i
13
2.0468 - 0.8526 i
0.00685 + 0.0197 i
14
-2.5108
2.63 i
15
-1.3133 + 2.4708 i
0.00204 - 0.0285 i
16
-1.3133 - 2.4708 i
0.00204 + 0.0285 i
17
4.3693 + 0.7153 i
0.208 - 0.237 i
18
4.3693 - 0.7153 i
0.208 + 0.237 i
Top of Page  Top of the page    

Table 14. Singularities with their weights for the quadratic approximant [9, 9, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.4822 + 0.e-5 i
1.8e-6 + 1.8e-6 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.4822 - 0.e-5 i
1.8e-6 - 1.8e-6 i
3
-0.6821
0.000189
4
-0.6825
0.000187 i
5
-0.7629 + 0.0166 i
0.00023 + 0.000441 i
6
-0.7629 - 0.0166 i
0.00023 - 0.000441 i
7
-0.7742
0.000429
8
1.8561
0.00293
9
1.8943
0.00307 i
10
2.1048 + 1.1359 i
0.00558 - 0.0142 i
11
2.1048 - 1.1359 i
0.00558 + 0.0142 i
12
2.3053 + 1.3732 i
0.0196 + 0.0114 i
13
2.3053 - 1.3732 i
0.0196 - 0.0114 i
14
2.8116
0.319
15
-3.0198
0.52 i
16
-2.0265 + 2.8605 i
0.237 - 0.214 i
17
-2.0265 - 2.8605 i
0.237 + 0.214 i
18
17.4861
958. i
Top of Page  Top of the page    

Table 15. Singularities with their weights for the quadratic approximant [10, 9, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.7148
0.000176
Singularities of quadratic [10, 9, 9] approximant
2
-0.7183
0.000159 i
3
-0.7623 + 0.0206 i
0.000189 + 0.000333 i
4
-0.7623 - 0.0206 i
0.000189 - 0.000333 i
5
-0.7657
0.000267
6
-1.4968
0.871 i
7
-1.5122
3.52
8
1.8554 + 0.0085 i
0.00358 - 0.00356 i
9
1.8554 - 0.0085 i
0.00358 + 0.00356 i
10
2.1854 + 0.9243 i
0.000135 + 0.0285 i
11
2.1854 - 0.9243 i
0.000135 - 0.0285 i
12
2.1252 + 1.061 i
0.0302 + 0.00587 i
13
2.1252 - 1.061 i
0.0302 - 0.00587 i
14
-3.5954 + 1.4786 i
0.119 - 0.238 i
15
-3.5954 - 1.4786 i
0.119 + 0.238 i
16
-1.8932 + 3.6561 i
1.2 - 0.261 i
17
-1.8932 - 3.6561 i
1.2 + 0.261 i
18
7.3622 + 2.7572 i
1.68 - 2.98 i
19
7.3622 - 2.7572 i
1.68 + 2.98 i
Top of Page  Top of the page    

Table 16. Singularities with their weights for the quadratic approximant [10, 10, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.7175
0.000167
Singularities of quadratic [10, 10, 9] approximant
2
-0.7221
0.000145 i
3
-0.7615 + 0.0214 i
0.000174 + 0.000306 i
4
-0.7615 - 0.0214 i
0.000174 - 0.000306 i
5
-0.7624
0.000226
6
-1.1461
0.682 i
7
-1.1491
1.41
8
2.1771 + 0.0586 i
0.0146 - 0.0131 i
9
2.1771 - 0.0586 i
0.0146 + 0.0131 i
10
2.2891 + 0.8155 i
0.00147 - 0.0349 i
11
2.2891 - 0.8155 i
0.00147 + 0.0349 i
12
2.2641 + 1.0717 i
0.0389 + 0.0117 i
13
2.2641 - 1.0717 i
0.0389 - 0.0117 i
14
-3.2366
0.397 i
15
-2.2996 + 2.9502 i
0.694 - 0.141 i
16
-2.2996 - 2.9502 i
0.694 + 0.141 i
17
4.3433 + 3.8926 i
0.373 + 0.0385 i
18
4.3433 - 3.8926 i
0.373 - 0.0385 i
19
0.4181 + 6.7404 i
0.31 - 0.0687 i
20
0.4181 - 6.7404 i
0.31 + 0.0687 i
Top of Page  Top of the page    

Table 17. Singularities with their weights for the quadratic approximant [10, 10, 10]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5127
1.67e-6
Singularities of quadratic [10, 10, 10] approximant
2
-0.5127
1.67e-6 i
3
-0.7195
0.000605
4
-0.7214
0.000534 i
5
-0.7688 + 0.0198 i
0.000295 + 0.000596 i
6
-0.7688 - 0.0198 i
0.000295 - 0.000596 i
7
-0.7782
0.000529
8
-1.3559
3.1 i
9
-1.3612
1.12
10
2.2709 + 0.479 i
0.02 - 0.00972 i
11
2.2709 - 0.479 i
0.02 + 0.00972 i
12
2.3867
0.0293
13
2.2824 + 0.9945 i
0.00627 - 0.0272 i
14
2.2824 - 0.9945 i
0.00627 + 0.0272 i
15
2.8049 + 1.5096 i
0.0677 + 0.0448 i
16
2.8049 - 1.5096 i
0.0677 - 0.0448 i
17
-3.4035
0.351 i
18
-2.1922 + 3.0903 i
0.563 - 0.537 i
19
-2.1922 - 3.0903 i
0.563 + 0.537 i
20
-24.7841
0.59
Top of Page  Top of the page    

Table 18. Singularities with their weights for the quadratic approximant [11, 10, 10]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.6276
0.0000141
Singularities of quadratic [11, 10, 10] approximant
2
-0.6276
0.0000141 i
3
-0.7216 + 0.0017 i
0.000188 + 0.000179 i
4
-0.7216 - 0.0017 i
0.000188 - 0.000179 i
5
-0.7747 + 0.0146 i
0.0000959 + 0.00132 i
6
-0.7747 - 0.0146 i
0.0000959 - 0.00132 i
7
-0.7908
0.0011
8
-1.3983
1.73 i
9
-1.4039
1.86
10
2.2714 + 0.4806 i
0.0206 - 0.01 i
11
2.2714 - 0.4806 i
0.0206 + 0.01 i
12
2.3959
0.0309
13
2.2867 + 0.9916 i
0.00604 - 0.028 i
14
2.2867 - 0.9916 i
0.00604 + 0.028 i
15
2.8058 + 1.5101 i
0.0696 + 0.0453 i
16
2.8058 - 1.5101 i
0.0696 - 0.0453 i
17
-3.3905
0.357 i
18
-2.1877 + 3.0836 i
0.539 - 0.521 i
19
-2.1877 - 3.0836 i
0.539 + 0.521 i
20
-34.0883
0.468
21
-86.6253
0.63 i
Top of Page  Top of the page    

Table 19. Singularities with their weights for the quadratic approximant [11, 11, 10]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.672
0.000029
Singularities of quadratic [11, 11, 10] approximant
2
-0.6722
0.0000289 i
3
-0.7236 + 0.0028 i
0.0000948 + 0.0000879 i
4
-0.7236 - 0.0028 i
0.0000948 - 0.0000879 i
5
-0.7737
0.00112
6
-0.7856
0.0251 i
7
-0.8016
0.00222
8
-1.3648
2.53 i
9
-1.3694
1.39
10
2.3052 + 0.4792 i
0.0259 - 0.0121 i
11
2.3052 - 0.4792 i
0.0259 + 0.0121 i
12
2.3796
0.0347
13
2.2912 + 0.9926 i
0.00864 - 0.0328 i
14
2.2912 - 0.9926 i
0.00864 + 0.0328 i
15
2.8928 + 1.4198 i
0.0906 + 0.0519 i
16
2.8928 - 1.4198 i
0.0906 - 0.0519 i
17
-3.3299
0.375 i
18
-2.2097 + 3.0532 i
0.579 - 0.446 i
19
-2.2097 - 3.0532 i
0.579 + 0.446 i
20
-2.802 + 14.5111 i
0.894 - 0.142 i
21
-2.802 - 14.5111 i
0.894 + 0.142 i
22
55.8776
2.59 i
Top of Page  Top of the page    

Table 20. Singularities with their weights for the quadratic approximant [11, 11, 11]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.7152
0.000113
Singularities of quadratic [11, 11, 11] approximant
2
-0.7206
0.0000962 i
3
-0.7549
0.000149
4
-0.7576 + 0.0211 i
0.000124 + 0.000227 i
5
-0.7576 - 0.0211 i
0.000124 - 0.000227 i
6
-0.7506 + 0.2876 i
0.0000678 - 0.000319 i
7
-0.7506 - 0.2876 i
0.0000678 + 0.000319 i
8
-0.7506 + 0.2876 i
0.00032 + 0.0000678 i
9
-0.7506 - 0.2876 i
0.00032 - 0.0000678 i
10
-1.3003
23.8 i
11
-1.3057
0.698
12
2.2716 + 0.4793 i
0.0203 - 0.00987 i
13
2.2716 - 0.4793 i
0.0203 + 0.00987 i
14
2.389
0.0298
15
2.2834 + 0.9934 i
0.00614 - 0.0275 i
16
2.2834 - 0.9934 i
0.00614 + 0.0275 i
17
2.8057 + 1.5084 i
0.0684 + 0.0447 i
18
2.8057 - 1.5084 i
0.0684 - 0.0447 i
19
-3.4091
0.349 i
20
-2.1946 + 3.0906 i
0.57 - 0.534 i
21
-2.1946 - 3.0906 i
0.57 + 0.534 i
22
-24.4427
0.589
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 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.