Singularities of Møller-Plesset series: example "h- cc-pv5z"

Molecule H- ion. Basis AUG-CC-PV5Z. 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
1.4438 + 0.2595 i
0.0093 - 0.0525 i
Singularities of quadratic [5, 5, 4] approximant
2
1.4438 - 0.2595 i
0.0093 + 0.0525 i
3
1.8662 + 0.9293 i
0.0237 + 0.0299 i
4
1.8662 - 0.9293 i
0.0237 - 0.0299 i
5
1.6285 + 2.7816 i
0.0193 + 0.00899 i
6
1.6285 - 2.7816 i
0.0193 - 0.00899 i
7
-0.7559 + 5.6106 i
0.0181 - 0.0159 i
8
-0.7559 - 5.6106 i
0.0181 + 0.0159 i
9
11.4034 + 21.2162 i
0.0577 - 0.00222 i
10
11.4034 - 21.2162 i
0.0577 + 0.00222 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
1.3793 + 0.3146 i
0.013 - 0.0126 i
Singularities of quadratic [5, 5, 5] approximant
2
1.3793 - 0.3146 i
0.013 + 0.0126 i
3
1.6896 + 0.2609 i
0.0154 + 0.0305 i
4
1.6896 - 0.2609 i
0.0154 - 0.0305 i
5
1.7107 + 0.9299 i
0.0142 + 0.0201 i
6
1.7107 - 0.9299 i
0.0142 - 0.0201 i
7
1.6481 + 2.9057 i
0.0233 + 0.0113 i
8
1.6481 - 2.9057 i
0.0233 - 0.0113 i
9
-0.0018 + 6.1414 i
0.0245 - 0.0212 i
10
-0.0018 - 6.1414 i
0.0245 + 0.0212 i
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
1.4397 + 0.282 i
0.0221 - 0.0388 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4397 - 0.282 i
0.0221 + 0.0388 i
3
1.881 + 1.0862 i
0.00241 + 0.0364 i
4
1.881 - 1.0862 i
0.00241 - 0.0364 i
5
1.4978 + 3.2623 i
0.00303 + 0.0191 i
6
1.4978 - 3.2623 i
0.00303 - 0.0191 i
7
-2.6988 + 3.4815 i
0.00302 + 0.00505 i
8
-2.6988 - 3.4815 i
0.00302 - 0.00505 i
9
-3.2268 + 3.1279 i
0.00566 - 0.00213 i
10
-3.2268 - 3.1279 i
0.00566 + 0.00213 i
11
-26.2762
100.
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
1.4537 + 0.2868 i
0.0462 - 0.0361 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4537 - 0.2868 i
0.0462 + 0.0361 i
3
1.9234 + 0.7462 i
0.06 - 0.0304 i
4
1.9234 - 0.7462 i
0.06 + 0.0304 i
5
2.2977
0.123
6
2.0474 + 1.8019 i
0.00147 + 0.033 i
7
2.0474 - 1.8019 i
0.00147 - 0.033 i
8
0.4942 + 4.2162 i
0.0178 + 0.0116 i
9
0.4942 - 4.2162 i
0.0178 - 0.0116 i
10
-4.5638 + 0.1289 i
0.00466 + 0.0043 i
11
-4.5638 - 0.1289 i
0.00466 - 0.0043 i
12
10.4785
0.0561 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
1.4559 + 0.3036 i
0.0435 - 0.00935 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4559 - 0.3036 i
0.0435 + 0.00935 i
3
1.7119
0.0621
4
2.0313 + 0.42 i
0.0498 + 0.125 i
5
2.0313 - 0.42 i
0.0498 - 0.125 i
6
2.1325 + 1.5777 i
0.0267 + 0.0394 i
7
2.1325 - 1.5777 i
0.0267 - 0.0394 i
8
-3.8379 + 0.0543 i
0.00236 + 0.00227 i
9
-3.8379 - 0.0543 i
0.00236 - 0.00227 i
10
0.5927 + 4.2771 i
0.02 + 0.0123 i
11
0.5927 - 4.2771 i
0.02 - 0.0123 i
12
9.0224
0.0761 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
1.4555 + 0.2995 i
0.043 - 0.0161 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4555 - 0.2995 i
0.043 + 0.0161 i
3
1.6779
0.0711
4
1.9442
0.195 i
5
2.2373 + 1.3513 i
0.106 + 0.0629 i
6
2.2373 - 1.3513 i
0.106 - 0.0629 i
7
3.0051
0.241
8
0.744 + 4.5198 i
0.0326 + 0.0183 i
9
0.744 - 4.5198 i
0.0326 - 0.0183 i
10
-5.2031 + 0.2688 i
0.0104 + 0.00882 i
11
-5.2031 - 0.2688 i
0.0104 - 0.00882 i
12
17.9879
0.134 i
13
-90.8105
0.358
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
1.4565 + 0.2904 i
0.0462 - 0.0285 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4565 - 0.2904 i
0.0462 + 0.0285 i
3
1.8269
0.0697
4
2.2655 + 0.3361 i
0.0497 + 0.15 i
5
2.2655 - 0.3361 i
0.0497 - 0.15 i
6
2.1867 + 1.422 i
0.0795 + 0.0467 i
7
2.1867 - 1.422 i
0.0795 - 0.0467 i
8
-2.8625 + 1.7238 i
0.000897 + 0.00164 i
9
-2.8625 - 1.7238 i
0.000897 - 0.00164 i
10
-2.8886 + 1.7634 i
0.00166 - 0.000901 i
11
-2.8886 - 1.7634 i
0.00166 + 0.000901 i
12
0.8128 + 4.1899 i
0.0262 + 0.00177 i
13
0.8128 - 4.1899 i
0.0262 - 0.00177 i
14
15.6562
0.0825 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
1.4521 + 0.2767 i
0.0307 - 0.0484 i
Singularities of quadratic [7, 7, 7] approximant
2
1.4521 - 0.2767 i
0.0307 + 0.0484 i
3
2.1759 + 0.2358 i
0.158 - 0.0351 i
4
2.1759 - 0.2358 i
0.158 + 0.0351 i
5
2.0244 + 1.1892 i
0.012 - 0.0722 i
6
2.0244 - 1.1892 i
0.012 + 0.0722 i
7
1.6423 + 3.4423 i
0.0112 + 0.0177 i
8
1.6423 - 3.4423 i
0.0112 - 0.0177 i
9
-0.4875 + 5.1182 i
0.0212 - 0.00987 i
10
-0.4875 - 5.1182 i
0.0212 + 0.00987 i
11
4.4553 + 3.2769 i
0.0564 - 0.00374 i
12
4.4553 - 3.2769 i
0.0564 + 0.00374 i
13
-5.9051
0.283
14
-6.034
1.01 i
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
-0.5832
2.01e-7
Singularities of quadratic [8, 7, 7] approximant
2
-0.5832
2.01e-7 i
3
1.4512 + 0.277 i
0.0282 - 0.0462 i
4
1.4512 - 0.277 i
0.0282 + 0.0462 i
5
1.9772 + 0.1075 i
0.144 - 0.0457 i
6
1.9772 - 0.1075 i
0.144 + 0.0457 i
7
2.022 + 1.2185 i
0.0367 - 0.0541 i
8
2.022 - 1.2185 i
0.0367 + 0.0541 i
9
1.1924 + 4.1697 i
0.0242 - 0.0155 i
10
1.1924 - 4.1697 i
0.0242 + 0.0155 i
11
6.4824
2.23
12
-5.9001 + 3.6957 i
0.00252 + 0.0448 i
13
-5.9001 - 3.6957 i
0.00252 - 0.0448 i
14
-3.9475 + 5.7423 i
0.0194 - 0.0207 i
15
-3.9475 - 5.7423 i
0.0194 + 0.0207 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
-1.2013
0.0000103
Singularities of quadratic [8, 8, 7] approximant
2
-1.2013
0.0000103 i
3
1.4519 + 0.278 i
0.0307 - 0.0457 i
4
1.4519 - 0.278 i
0.0307 + 0.0457 i
5
2.0109 + 0.1091 i
0.119 - 0.0522 i
6
2.0109 - 0.1091 i
0.119 + 0.0522 i
7
2.0446 + 1.2278 i
0.0453 - 0.0578 i
8
2.0446 - 1.2278 i
0.0453 + 0.0578 i
9
1.0809 + 4.0737 i
0.0206 - 0.0119 i
10
1.0809 - 4.0737 i
0.0206 + 0.0119 i
11
4.877
0.786
12
-3.3418 + 3.9496 i
0.00615 - 0.00795 i
13
-3.3418 - 3.9496 i
0.00615 + 0.00795 i
14
-3.9442 + 3.5584 i
0.00788 + 0.009 i
15
-3.9442 - 3.5584 i
0.00788 - 0.009 i
16
77.6424
0.24 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
-0.9774
0.0000134
Singularities of quadratic [8, 8, 8] approximant
2
-0.9774
0.0000134 i
3
1.4528 + 0.2785 i
0.0333 - 0.0463 i
4
1.4528 - 0.2785 i
0.0333 + 0.0463 i
5
2.1316 + 0.1601 i
0.107 - 0.052 i
6
2.1316 - 0.1601 i
0.107 + 0.052 i
7
2.0713 + 1.2217 i
0.0477 - 0.0798 i
8
2.0713 - 1.2217 i
0.0477 + 0.0798 i
9
1.3353 + 3.7924 i
0.0065 - 0.0236 i
10
1.3353 - 3.7924 i
0.0065 + 0.0236 i
11
4.2637
1.69
12
-1.7481 + 5.3652 i
0.0148 + 0.0104 i
13
-1.7481 - 5.3652 i
0.0148 - 0.0104 i
14
-7.8947
0.0879
15
-6.4297 + 5.681 i
0.031 - 0.0266 i
16
-6.4297 - 5.681 i
0.031 + 0.0266 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
0.9534 + 0.e-5 i
0.0000829 - 0.0000829 i
Singularities of quadratic [9, 8, 8] approximant
2
0.9534 - 0.e-5 i
0.0000829 + 0.0000829 i
3
-1.0832
3.72e-6
4
-1.0832
3.72e-6 i
5
1.4534 + 0.2764 i
0.0324 - 0.0522 i
6
1.4534 - 0.2764 i
0.0324 + 0.0522 i
7
2.188 + 0.1854 i
0.159 - 0.0473 i
8
2.188 - 0.1854 i
0.159 + 0.0473 i
9
2.0198 + 1.2002 i
0.0212 - 0.0573 i
10
2.0198 - 1.2002 i
0.0212 + 0.0573 i
11
1.0715 + 3.9565 i
0.0139 - 0.0113 i
12
1.0715 - 3.9565 i
0.0139 + 0.0113 i
13
-3.2001 + 4.4993 i
0.00638 - 0.00861 i
14
-3.2001 - 4.4993 i
0.00638 + 0.00861 i
15
6.0607
31.9
16
-4.6643 + 3.99 i
0.00804 + 0.0143 i
17
-4.6643 - 3.99 i
0.00804 - 0.0143 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
0.0756
0
Singularities of quadratic [9, 9, 8] approximant
2
0.0756
0
3
-1.1705 + 0.e-5 i
1.25e-6 + 1.25e-6 i
4
-1.1705 - 0.e-5 i
1.25e-6 - 1.25e-6 i
5
1.4429 + 0.2708 i
0.00481 - 0.0406 i
6
1.4429 - 0.2708 i
0.00481 + 0.0406 i
7
1.5229 + 0.0209 i
0.044 - 0.0549 i
8
1.5229 - 0.0209 i
0.044 + 0.0549 i
9
1.995 + 1.297 i
0.038 - 0.0126 i
10
1.995 - 1.297 i
0.038 + 0.0126 i
11
-3.4468 + 2.4984 i
0.00229 - 0.000711 i
12
-3.4468 - 2.4984 i
0.00229 + 0.000711 i
13
-3.7595 + 2.7101 i
0.000595 + 0.00299 i
14
-3.7595 - 2.7101 i
0.000595 - 0.00299 i
15
0.8021 + 4.7134 i
0.0154 + 0.0386 i
16
0.8021 - 4.7134 i
0.0154 - 0.0386 i
17
5.8702 + 0.7419 i
0.0429 - 0.0589 i
18
5.8702 - 0.7419 i
0.0429 + 0.0589 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
-0.8264 + 0.4356 i
1.15e-6 + 8.82e-7 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.8264 - 0.4356 i
1.15e-6 - 8.82e-7 i
3
-0.8264 + 0.4356 i
8.82e-7 - 1.15e-6 i
4
-0.8264 - 0.4356 i
8.82e-7 + 1.15e-6 i
5
1.4546 + 0.2784 i
0.0381 - 0.0494 i
6
1.4546 - 0.2784 i
0.0381 + 0.0494 i
7
2.0919 + 1.1294 i
0.0435 + 0.0755 i
8
2.0919 - 1.1294 i
0.0435 - 0.0755 i
9
2.3846 + 0.483 i
0.164 + 0.0449 i
10
2.3846 - 0.483 i
0.164 - 0.0449 i
11
1.5096 + 3.1883 i
0.0107 + 0.00795 i
12
1.5096 - 3.1883 i
0.0107 - 0.00795 i
13
3.2631 + 2.6146 i
0.0304 - 0.027 i
14
3.2631 - 2.6146 i
0.0304 + 0.027 i
15
-0.6149 + 4.9023 i
0.0136 - 0.0062 i
16
-0.6149 - 4.9023 i
0.0136 + 0.0062 i
17
-5.7741
0.0778
18
-6.1361
0.125 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
-0.6218 + 0.6948 i
3.72e-9 + 5.3e-7 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.6218 - 0.6948 i
3.72e-9 - 5.3e-7 i
3
-0.6218 + 0.6948 i
5.3e-7 - 3.72e-9 i
4
-0.6218 - 0.6948 i
5.3e-7 + 3.72e-9 i
5
1.4516 + 0.2787 i
0.0308 - 0.0442 i
6
1.4516 - 0.2787 i
0.0308 + 0.0442 i
7
-1.6197
6.83e-6
8
-1.62
6.84e-6 i
9
2.0223 + 0.1165 i
0.106 - 0.0528 i
10
2.0223 - 0.1165 i
0.106 + 0.0528 i
11
2.0719 + 1.2316 i
0.0614 - 0.0716 i
12
2.0719 - 1.2316 i
0.0614 + 0.0716 i
13
1.2091 + 3.8074 i
0.00628 - 0.0183 i
14
1.2091 - 3.8074 i
0.00628 + 0.0183 i
15
4.7002
1.3
16
-2.5433 + 4.166 i
0.0000907 - 0.00454 i
17
-2.5433 - 4.166 i
0.0000907 + 0.00454 i
18
-4.0329 + 4.0267 i
0.00536 + 0.00385 i
19
-4.0329 - 4.0267 i
0.00536 - 0.00385 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
-0.6407 + 0.7168 i
7.6e-8 + 9.81e-7 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.6407 - 0.7168 i
7.6e-8 - 9.81e-7 i
3
-0.6407 + 0.7168 i
9.81e-7 - 7.6e-8 i
4
-0.6407 - 0.7168 i
9.81e-7 + 7.6e-8 i
5
1.4516 + 0.2786 i
0.0306 - 0.0444 i
6
1.4516 - 0.2786 i
0.0306 + 0.0444 i
7
-1.7941
0.0000179
8
-1.7947
0.0000179 i
9
2.001 + 0.1041 i
0.108 - 0.0533 i
10
2.001 - 0.1041 i
0.108 + 0.0533 i
11
2.0625 + 1.2407 i
0.0588 - 0.0591 i
12
2.0625 - 1.2407 i
0.0588 + 0.0591 i
13
1.1317 + 3.9326 i
0.0142 - 0.0168 i
14
1.1317 - 3.9326 i
0.0142 + 0.0168 i
15
4.4276
0.713
16
-2.6107 + 3.6785 i
0.000413 - 0.00381 i
17
-2.6107 - 3.6785 i
0.000413 + 0.00381 i
18
-3.2581 + 3.5745 i
0.00411 + 0.00171 i
19
-3.2581 - 3.5745 i
0.00411 - 0.00171 i
20
104.871
0.253 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
-0.7682 + 0.8873 i
1.73e-7 - 2.38e-7 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.7682 - 0.8873 i
1.73e-7 + 2.38e-7 i
3
-0.7683 + 0.8874 i
2.38e-7 + 1.73e-7 i
4
-0.7683 - 0.8874 i
2.38e-7 - 1.73e-7 i
5
1.4545 + 0.2779 i
0.0368 - 0.0527 i
6
1.4545 - 0.2779 i
0.0368 + 0.0527 i
7
-0.9173 + 1.3659 i
8.19e-7 - 2.22e-6 i
8
-0.9173 - 1.3659 i
8.19e-7 + 2.22e-6 i
9
-0.9171 + 1.3677 i
2.23e-6 + 8.22e-7 i
10
-0.9171 - 1.3677 i
2.23e-6 - 8.22e-7 i
11
1.9149
0.0962
12
1.9979
0.17 i
13
1.95 + 1.3004 i
0.0216 - 0.0155 i
14
1.95 - 1.3004 i
0.0216 + 0.0155 i
15
3.1564
0.336
16
-4.2399 + 0.5124 i
0.000435 + 0.000134 i
17
-4.2399 - 0.5124 i
0.000435 - 0.000134 i
18
-0.1987 + 5.079 i
0.00866 - 0.000717 i
19
-0.1987 - 5.079 i
0.00866 + 0.000717 i
20
5.8492
0.056 i
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
-0.7327 + 0.8092 i
1.61e-7 - 2.3e-7 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.7327 - 0.8092 i
1.61e-7 + 2.3e-7 i
3
-0.7327 + 0.8092 i
2.3e-7 + 1.61e-7 i
4
-0.7327 - 0.8092 i
2.3e-7 - 1.61e-7 i
5
1.4573 + 0.2784 i
0.0479 - 0.0581 i
6
1.4573 - 0.2784 i
0.0479 + 0.0581 i
7
1.8059
0.137
8
1.8773
89.7 i
9
1.8901 + 1.2376 i
0.0064 - 0.0177 i
10
1.8901 - 1.2376 i
0.0064 + 0.0177 i
11
-1.0214 + 2.1916 i
0.0000394 + 1.45e-6 i
12
-1.0214 - 2.1916 i
0.0000394 - 1.45e-6 i
13
-1.06 + 2.1856 i
3.24e-6 - 0.0000386 i
14
-1.06 - 2.1856 i
3.24e-6 + 0.0000386 i
15
2.627 + 0.5741 i
2.84 + 0.413 i
16
2.627 - 0.5741 i
2.84 - 0.413 i
17
-3.1548 + 0.092 i
0.000063 + 0.0000512 i
18
-3.1548 - 0.092 i
0.000063 - 0.0000512 i
19
-0.2071 + 4.1576 i
0.00149 - 0.00256 i
20
-0.2071 - 4.1576 i
0.00149 + 0.00256 i
21
-80.8635
0.525
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
-0.4529
0
Singularities of quadratic [11, 11, 10] approximant
2
-0.4529
0
3
-0.8101 + 0.8538 i
1.77e-7 + 7.88e-8 i
4
-0.8101 - 0.8538 i
1.77e-7 - 7.88e-8 i
5
-0.8101 + 0.8538 i
7.88e-8 - 1.77e-7 i
6
-0.8101 - 0.8538 i
7.88e-8 + 1.77e-7 i
7
1.4559 + 0.2769 i
0.0396 - 0.0614 i
8
1.4559 - 0.2769 i
0.0396 + 0.0614 i
9
-0.7821 + 1.4584 i
2.19e-6 + 1.58e-6 i
10
-0.7821 - 1.4584 i
2.19e-6 - 1.58e-6 i
11
-0.7838 + 1.4582 i
1.59e-6 - 2.18e-6 i
12
-0.7838 - 1.4582 i
1.59e-6 + 2.18e-6 i
13
1.7129
0.145
14
1.7539
2.82 i
15
1.9122 + 1.3121 i
0.0158 - 0.00956 i
16
1.9122 - 1.3121 i
0.0158 + 0.00956 i
17
3.5868 + 1.0202 i
0.0529 + 0.143 i
18
3.5868 - 1.0202 i
0.0529 - 0.143 i
19
-4.3599
0.0119
20
-4.4466
0.0752 i
21
0.1437 + 5.0674 i
0.0214 - 0.00504 i
22
0.1437 - 5.0674 i
0.0214 + 0.00504 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
-0.1204 + 0.946 i
1.8e-8 + 1.87e-8 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.1204 - 0.946 i
1.8e-8 - 1.87e-8 i
3
-0.1204 + 0.946 i
1.87e-8 - 1.8e-8 i
4
-0.1204 - 0.946 i
1.87e-8 + 1.8e-8 i
5
-0.7064 + 0.7237 i
1.66e-9 + 1.66e-8 i
6
-0.7064 - 0.7237 i
1.66e-9 - 1.66e-8 i
7
-0.7064 + 0.7237 i
1.66e-8 - 1.66e-9 i
8
-0.7064 - 0.7237 i
1.66e-8 + 1.66e-9 i
9
1.4547 + 0.2803 i
0.0423 - 0.0424 i
10
1.4547 - 0.2803 i
0.0423 + 0.0424 i
11
1.8956 + 1.1735 i
0.00419 + 0.0139 i
12
1.8956 - 1.1735 i
0.00419 - 0.0139 i
13
-2.3042
1.64e-6
14
-2.4185
1.87e-6 i
15
2.3034 + 0.9155 i
0.069 - 0.07 i
16
2.3034 - 0.9155 i
0.069 + 0.07 i
17
-2.6029 + 1.8291 i
0.0000148 + 0.0000133 i
18
-2.6029 - 1.8291 i
0.0000148 - 0.0000133 i
19
-2.4657 + 2.8043 i
6.78e-6 - 0.0000659 i
20
-2.4657 - 2.8043 i
6.78e-6 + 0.0000659 i
21
6.0216 + 1.8068 i
0.00059 - 0.0239 i
22
6.0216 - 1.8068 i
0.00059 + 0.0239 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 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.