Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 0.9r_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 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
1.2862
0.0666
Singularities of quadratic [5, 5, 4] approximant
2
1.3137
0.0759 i
3
1.6255 + 0.2102 i
0.378 - 0.32 i
4
1.6255 - 0.2102 i
0.378 + 0.32 i
5
-2.6606
0.0153
6
2.8821
21.6
7
-2.919
0.0159 i
8
-5.5018 + 2.5193 i
0.0831 - 0.105 i
9
-5.5018 - 2.5193 i
0.0831 + 0.105 i
10
30.2407
0.413 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
1.3337
0.336
Singularities of quadratic [5, 5, 5] approximant
2
1.3495
0.507 i
3
1.6804 + 0.2167 i
0.573 + 0.127 i
4
1.6804 - 0.2167 i
0.573 - 0.127 i
5
-2.7566
0.0145
6
3.0217
102.
7
-3.237
0.015 i
8
-4.1807 + 2.8681 i
0.0438 - 0.0473 i
9
-4.1807 - 2.8681 i
0.0438 + 0.0473 i
10
-43.8563
28.2
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
1.3944 + 0.0868 i
0.0441 - 0.0185 i
Singularities of quadratic [6, 5, 5] approximant
2
1.3944 - 0.0868 i
0.0441 + 0.0185 i
3
1.8592 + 1.0325 i
0.032 + 0.0201 i
4
1.8592 - 1.0325 i
0.032 - 0.0201 i
5
2.0048 + 1.2835 i
0.032 - 0.0246 i
6
2.0048 - 1.2835 i
0.032 + 0.0246 i
7
-2.645 + 0.1326 i
0.0056 + 0.00534 i
8
-2.645 - 0.1326 i
0.0056 - 0.00534 i
9
-4.3387
0.0416
10
4.9452
0.343
11
-6.8888
16.1 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
1.3976 + 0.0919 i
0.0449 - 0.0169 i
Singularities of quadratic [6, 6, 5] approximant
2
1.3976 - 0.0919 i
0.0449 + 0.0169 i
3
1.6533 + 1.0221 i
0.0221 + 0.00514 i
4
1.6533 - 1.0221 i
0.0221 - 0.00514 i
5
1.7365 + 1.1302 i
0.00918 - 0.023 i
6
1.7365 - 1.1302 i
0.00918 + 0.023 i
7
-2.6927 + 0.1104 i
0.00959 + 0.00874 i
8
-2.6927 - 0.1104 i
0.00959 - 0.00874 i
9
3.8096
1.21
10
-5.6528 + 0.3401 i
0.447 - 0.101 i
11
-5.6528 - 0.3401 i
0.447 + 0.101 i
12
242.4857
1.92 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
0.779 + 0.e-4 i
0.000041 - 0.000041 i
Singularities of quadratic [6, 6, 6] approximant
2
0.779 - 0.e-4 i
0.000041 + 0.000041 i
3
1.3636 + 0.1102 i
0.0186 - 0.0018 i
4
1.3636 - 0.1102 i
0.0186 + 0.0018 i
5
1.967 + 0.9145 i
0.00602 + 0.0536 i
6
1.967 - 0.9145 i
0.00602 - 0.0536 i
7
-2.5607
0.00761
8
-2.8516
0.00891 i
9
2.952 + 0.5213 i
0.192 - 0.00344 i
10
2.952 - 0.5213 i
0.192 + 0.00344 i
11
-5.7697
1.07
12
-47.6945
0.15 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
1.2703
0.00298
Singularities of quadratic [7, 6, 6] approximant
2
1.2562 + 0.3112 i
0.0014 - 0.00105 i
3
1.2562 - 0.3112 i
0.0014 + 0.00105 i
4
1.3289 + 0.3326 i
0.00137 + 0.00193 i
5
1.3289 - 0.3326 i
0.00137 - 0.00193 i
6
1.9437 + 0.7473 i
0.000271 + 0.0289 i
7
1.9437 - 0.7473 i
0.000271 - 0.0289 i
8
-2.4578
0.00227
9
-3.1578
0.00382 i
10
-1.3773 + 3.3373 i
0.00204 + 0.00218 i
11
-1.3773 - 3.3373 i
0.00204 - 0.00218 i
12
-1.5855 + 3.664 i
0.00278 - 0.00219 i
13
-1.5855 - 3.664 i
0.00278 + 0.00219 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
1.3185 + 0.1548 i
0.00722 - 0.000898 i
Singularities of quadratic [7, 7, 6] approximant
2
1.3185 - 0.1548 i
0.00722 + 0.000898 i
3
1.582 + 0.3947 i
0.0128 - 0.0000117 i
4
1.582 - 0.3947 i
0.0128 + 0.0000117 i
5
1.5669 + 0.6514 i
0.00642 - 0.0064 i
6
1.5669 - 0.6514 i
0.00642 + 0.0064 i
7
-2.348 + 0.1946 i
0.000213 + 0.000599 i
8
-2.348 - 0.1946 i
0.000213 - 0.000599 i
9
-2.4692
0.000504
10
2.9215 + 1.7014 i
0.0584 - 0.0214 i
11
2.9215 - 1.7014 i
0.0584 + 0.0214 i
12
-4.1561
0.0109 i
13
12.6495 + 10.7833 i
0.199 + 0.0865 i
14
12.6495 - 10.7833 i
0.199 - 0.0865 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
0.5433
2.74e-7
Singularities of quadratic [7, 7, 7] approximant
2
0.5433
2.74e-7 i
3
1.258 + 0.1647 i
0.00193 + 0.000203 i
4
1.258 - 0.1647 i
0.00193 - 0.000203 i
5
1.5572
0.0379
6
-0.7428 + 1.5164 i
0.0000352 + 0.0000135 i
7
-0.7428 - 1.5164 i
0.0000352 - 0.0000135 i
8
-0.7446 + 1.5183 i
0.0000136 - 0.0000353 i
9
-0.7446 - 1.5183 i
0.0000136 + 0.0000353 i
10
1.8456 + 0.9264 i
0.004 - 0.0124 i
11
1.8456 - 0.9264 i
0.004 + 0.0124 i
12
-2.3825
0.00101
13
-3.7271
0.00526 i
14
17.6041
0.255 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
1.3847
0.0213
Singularities of quadratic [8, 7, 7] approximant
2
1.3633 + 0.2627 i
0.011 - 0.00947 i
3
1.3633 - 0.2627 i
0.011 + 0.00947 i
4
1.4793 + 0.3277 i
0.00974 + 0.0195 i
5
1.4793 - 0.3277 i
0.00974 - 0.0195 i
6
1.9735 + 0.5453 i
0.045 + 0.0717 i
7
1.9735 - 0.5453 i
0.045 - 0.0717 i
8
-2.3256 + 0.102 i
2.14e-7 - 0.000472 i
9
-2.3256 - 0.102 i
2.14e-7 + 0.000472 i
10
-2.3296
0.000333
11
-3.5678
0.00586 i
12
-0.9494 + 5.6925 i
0.0198 - 0.0025 i
13
-0.9494 - 5.6925 i
0.0198 + 0.0025 i
14
0.3895 + 8.0787 i
0.00425 + 0.0331 i
15
0.3895 - 8.0787 i
0.00425 - 0.0331 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
1.3323
0.00993
Singularities of quadratic [8, 8, 7] approximant
2
1.3215 + 0.2478 i
0.00131 - 0.00674 i
3
1.3215 - 0.2478 i
0.00131 + 0.00674 i
4
1.4423 + 0.2824 i
0.00902 + 0.00338 i
5
1.4423 - 0.2824 i
0.00902 - 0.00338 i
6
1.7767 + 0.7411 i
0.0129 + 0.0114 i
7
1.7767 - 0.7411 i
0.0129 - 0.0114 i
8
-2.2634
0.000251
9
-2.2786 + 0.1323 i
8.85e-6 - 0.000356 i
10
-2.2786 - 0.1323 i
8.85e-6 + 0.000356 i
11
2.132 + 2.5421 i
0.00725 + 0.00955 i
12
2.132 - 2.5421 i
0.00725 - 0.00955 i
13
-3.9087
0.00779 i
14
3.0263 + 2.7444 i
0.019 - 0.00979 i
15
3.0263 - 2.7444 i
0.019 + 0.00979 i
16
54.7665
3.55 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
1.4172 + 0.1623 i
0.0789 - 0.0172 i
Singularities of quadratic [8, 8, 8] approximant
2
1.4172 - 0.1623 i
0.0789 + 0.0172 i
3
1.4648 + 0.2981 i
0.0079 - 0.0518 i
4
1.4648 - 0.2981 i
0.0079 + 0.0518 i
5
1.5898 + 0.416 i
0.0611 + 0.0392 i
6
1.5898 - 0.416 i
0.0611 - 0.0392 i
7
-2.3583
0.000959
8
-2.4495 + 0.8323 i
0.000195 - 0.000478 i
9
-2.4495 - 0.8323 i
0.000195 + 0.000478 i
10
-2.4963 + 0.8724 i
0.000495 + 0.000232 i
11
-2.4963 - 0.8724 i
0.000495 - 0.000232 i
12
2.8056
45.5
13
-4.6523
0.0177 i
14
4.6956
3.15 i
15
8.5294 + 11.4682 i
0.291 + 0.127 i
16
8.5294 - 11.4682 i
0.291 - 0.127 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
1.4448 + 0.1752 i
0.218 - 0.0515 i
Singularities of quadratic [9, 8, 8] approximant
2
1.4448 - 0.1752 i
0.218 + 0.0515 i
3
1.466 + 0.2741 i
0.0092 + 0.105 i
4
1.466 - 0.2741 i
0.0092 - 0.105 i
5
1.602 + 0.378 i
0.139 + 0.0432 i
6
1.602 - 0.378 i
0.139 - 0.0432 i
7
-1.7658 + 0.4545 i
0.0000395 - 0.0000267 i
8
-1.7658 - 0.4545 i
0.0000395 + 0.0000267 i
9
-1.7669 + 0.4513 i
0.0000265 + 0.0000392 i
10
-1.7669 - 0.4513 i
0.0000265 - 0.0000392 i
11
-2.3199
0.000516
12
2.4243
1.25
13
-3.9269
0.00757 i
14
1.329 + 7.8406 i
0.0196 - 0.0715 i
15
1.329 - 7.8406 i
0.0196 + 0.0715 i
16
8.5454 + 5.8989 i
0.152 + 0.0707 i
17
8.5454 - 5.8989 i
0.152 - 0.0707 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
1.4368 + 0.2133 i
0.0172 + 0.194 i
Singularities of quadratic [9, 9, 8] approximant
2
1.4368 - 0.2133 i
0.0172 - 0.194 i
3
1.515 + 0.2859 i
0.182 + 0.00573 i
4
1.515 - 0.2859 i
0.182 - 0.00573 i
5
1.6654 + 0.2742 i
1.74 + 0.288 i
6
1.6654 - 0.2742 i
1.74 - 0.288 i
7
1.9828
0.205
8
-1.9888 + 0.5435 i
0.000102 - 0.0000751 i
9
-1.9888 - 0.5435 i
0.000102 + 0.0000751 i
10
-1.9981 + 0.5351 i
0.0000726 + 0.000101 i
11
-1.9981 - 0.5351 i
0.0000726 - 0.000101 i
12
-2.3071
0.000492
13
-4.1167
0.00956 i
14
3.5245 + 2.821 i
0.00482 + 0.0952 i
15
3.5245 - 2.821 i
0.00482 - 0.0952 i
16
5.7143 + 4.6502 i
0.0637 + 0.0555 i
17
5.7143 - 4.6502 i
0.0637 - 0.0555 i
18
38.6181
1.57 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
1.442 + 0.1299 i
0.0277 + 0.0907 i
Singularities of quadratic [9, 9, 9] approximant
2
1.442 - 0.1299 i
0.0277 - 0.0907 i
3
1.4235 + 0.2801 i
0.0191 + 0.022 i
4
1.4235 - 0.2801 i
0.0191 - 0.022 i
5
1.5882 + 0.4297 i
0.038 + 0.0168 i
6
1.5882 - 0.4297 i
0.038 - 0.0168 i
7
-1.22 + 1.228 i
0.0000118 + 0.0000201 i
8
-1.22 - 1.228 i
0.0000118 - 0.0000201 i
9
-1.2201 + 1.2287 i
0.0000201 - 0.0000118 i
10
-1.2201 - 1.2287 i
0.0000201 + 0.0000118 i
11
-2.364
0.00088
12
2.8114
5.69
13
-3.9963
0.00659 i
14
-0.0416 + 4.3404 i
0.00199 + 0.00392 i
15
-0.0416 - 4.3404 i
0.00199 - 0.00392 i
16
-0.1035 + 4.8329 i
0.00527 - 0.00159 i
17
-0.1035 - 4.8329 i
0.00527 + 0.00159 i
18
5.471
3.57 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
0.7083 + 0.e-5 i
4.62e-7 - 4.62e-7 i
Singularities of quadratic [10, 9, 9] approximant
2
0.7083 - 0.e-5 i
4.62e-7 + 4.62e-7 i
3
1.3789 + 0.2129 i
0.00444 + 0.0137 i
4
1.3789 - 0.2129 i
0.00444 - 0.0137 i
5
1.4737 + 0.39 i
0.00729 + 0.0135 i
6
1.4737 - 0.39 i
0.00729 - 0.0135 i
7
1.5807
1.04
8
-1.4813 + 1.1481 i
1.38e-6 + 0.0000402 i
9
-1.4813 - 1.1481 i
1.38e-6 - 0.0000402 i
10
-1.483 + 1.148 i
0.0000402 - 1.31e-6 i
11
-1.483 - 1.148 i
0.0000402 + 1.31e-6 i
12
1.9673 + 0.4638 i
0.0337 + 0.0574 i
13
1.9673 - 0.4638 i
0.0337 - 0.0574 i
14
-2.3583
0.000816
15
-3.9416
0.00678 i
16
3.0913 + 6.0706 i
0.175 + 0.0431 i
17
3.0913 - 6.0706 i
0.175 - 0.0431 i
18
4.4363 + 5.47 i
0.491 - 0.0779 i
19
4.4363 - 5.47 i
0.491 + 0.0779 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
-1.3039 + 0.e-4 i
2.41e-6 + 2.41e-6 i
Singularities of quadratic [10, 10, 9] approximant
2
-1.3039 - 0.e-4 i
2.41e-6 - 2.41e-6 i
3
-0.2944 + 1.2876 i
7.61e-6 - 4.37e-6 i
4
-0.2944 - 1.2876 i
7.61e-6 + 4.37e-6 i
5
-0.2944 + 1.2876 i
4.37e-6 + 7.61e-6 i
6
-0.2944 - 1.2876 i
4.37e-6 - 7.61e-6 i
7
1.4249 + 0.1924 i
0.0625 + 0.0651 i
8
1.4249 - 0.1924 i
0.0625 - 0.0651 i
9
1.5163 + 0.3052 i
0.179 + 0.0105 i
10
1.5163 - 0.3052 i
0.179 - 0.0105 i
11
1.5899 + 0.3232 i
1.24 - 0.814 i
12
1.5899 - 0.3232 i
1.24 + 0.814 i
13
-2.3765
0.000949
14
2.4377
1.01
15
-3.4935
0.00447 i
16
5.824
23.7 i
17
-6.0674 + 0.3871 i
0.0896 + 0.0849 i
18
-6.0674 - 0.3871 i
0.0896 - 0.0849 i
19
-0.036 + 13.182 i
0.0479 - 0.164 i
20
-0.036 - 13.182 i
0.0479 + 0.164 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
0.158 + 0.852 i
1.71e-7 + 4.27e-9 i
Singularities of quadratic [10, 10, 10] approximant
2
0.158 - 0.852 i
1.71e-7 - 4.27e-9 i
3
0.158 + 0.852 i
4.27e-9 - 1.71e-7 i
4
0.158 - 0.852 i
4.27e-9 + 1.71e-7 i
5
1.3347 + 0.2141 i
0.00146 + 0.00323 i
6
1.3347 - 0.2141 i
0.00146 - 0.00323 i
7
1.406 + 0.444 i
0.0011 + 0.00219 i
8
1.406 - 0.444 i
0.0011 - 0.00219 i
9
1.8323
0.0868
10
1.7547 + 0.7953 i
0.0018 + 0.00441 i
11
1.7547 - 0.7953 i
0.0018 - 0.00441 i
12
-1.8949 + 0.7577 i
0.0000499 - 0.0000372 i
13
-1.8949 - 0.7577 i
0.0000499 + 0.0000372 i
14
-1.9004 + 0.7644 i
0.0000376 + 0.00005 i
15
-1.9004 - 0.7644 i
0.0000376 - 0.00005 i
16
2.3502
0.041 i
17
-2.3592
0.000987
18
-4.4189
0.0113 i
19
3.9103 + 2.9694 i
0.0589 + 0.0227 i
20
3.9103 - 2.9694 i
0.0589 - 0.0227 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
0.0462 + 0.7959 i
1.45e-7 + 7.22e-8 i
Singularities of quadratic [11, 10, 10] approximant
2
0.0462 - 0.7959 i
1.45e-7 - 7.22e-8 i
3
0.0462 + 0.7959 i
7.22e-8 - 1.45e-7 i
4
0.0462 - 0.7959 i
7.22e-8 + 1.45e-7 i
5
1.4238 + 0.1069 i
0.0291 + 0.0316 i
6
1.4238 - 0.1069 i
0.0291 - 0.0316 i
7
1.4072 + 0.2915 i
0.00889 + 0.0127 i
8
1.4072 - 0.2915 i
0.00889 - 0.0127 i
9
1.5981 + 0.4558 i
0.0203 + 0.0207 i
10
1.5981 - 0.4558 i
0.0203 - 0.0207 i
11
-1.5833 + 0.9707 i
0.0000336 + 5.37e-6 i
12
-1.5833 - 0.9707 i
0.0000336 - 5.37e-6 i
13
-1.583 + 0.9726 i
5.32e-6 - 0.0000337 i
14
-1.583 - 0.9726 i
5.32e-6 + 0.0000337 i
15
-2.3485
0.000698
16
2.7071
35.7
17
-3.791
0.00663 i
18
-0.3224 + 7.6309 i
0.0405 - 0.0174 i
19
-0.3224 - 7.6309 i
0.0405 + 0.0174 i
20
15.7499 + 4.1415 i
0.0545 + 0.0597 i
21
15.7499 - 4.1415 i
0.0545 - 0.0597 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
-0.046 + 0.7081 i
1.04e-8 + 2.23e-9 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.046 - 0.7081 i
1.04e-8 - 2.23e-9 i
3
-0.046 + 0.7081 i
2.23e-9 - 1.04e-8 i
4
-0.046 - 0.7081 i
2.23e-9 + 1.04e-8 i
5
1.3157 + 0.2261 i
0.000318 + 0.00188 i
6
1.3157 - 0.2261 i
0.000318 - 0.00188 i
7
1.3765 + 0.4898 i
7.79e-6 - 0.00098 i
8
1.3765 - 0.4898 i
7.79e-6 + 0.00098 i
9
-1.5818 + 0.849 i
4.78e-6 - 8.85e-6 i
10
-1.5818 - 0.849 i
4.78e-6 + 8.85e-6 i
11
-1.581 + 0.8516 i
8.88e-6 + 4.74e-6 i
12
-1.581 - 0.8516 i
8.88e-6 - 4.74e-6 i
13
1.6116 + 0.8966 i
0.000355 + 0.00119 i
14
1.6116 - 0.8966 i
0.000355 - 0.00119 i
15
1.7566 + 0.6307 i
0.00119 - 0.00267 i
16
1.7566 - 0.6307 i
0.00119 + 0.00267 i
17
-2.3877
0.00155
18
-4.7082
0.0135 i
19
3.704 + 3.458 i
0.0205 + 0.02 i
20
3.704 - 3.458 i
0.0205 - 0.02 i
21
-17.5296 + 6.1893 i
0.0557 + 0.037 i
22
-17.5296 - 6.1893 i
0.0557 - 0.037 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
-0.0244 + 0.8237 i
5.61e-8 + 1.71e-8 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.0244 - 0.8237 i
5.61e-8 - 1.71e-8 i
3
-0.0244 + 0.8237 i
1.71e-8 - 5.61e-8 i
4
-0.0244 - 0.8237 i
1.71e-8 + 5.61e-8 i
5
1.3343 + 0.2158 i
0.00125 + 0.00322 i
6
1.3343 - 0.2158 i
0.00125 - 0.00322 i
7
-1.3472 + 0.5106 i
2.36e-6 + 1.1e-6 i
8
-1.3472 - 0.5106 i
2.36e-6 - 1.1e-6 i
9
-1.3474 + 0.5106 i
1.1e-6 - 2.36e-6 i
10
-1.3474 - 0.5106 i
1.1e-6 + 2.36e-6 i
11
1.4089 + 0.4494 i
0.000818 + 0.00232 i
12
1.4089 - 0.4494 i
0.000818 - 0.00232 i
13
1.8123
0.119
14
1.7892 + 0.8162 i
0.000642 + 0.00507 i
15
1.7892 - 0.8162 i
0.000642 - 0.00507 i
16
-2.4301
0.0022
17
2.6396
0.102 i
18
-2.786
0.00715 i
19
-3.0254
0.00578
20
-4.4129
0.0131 i
21
4.0485 + 3.3972 i
0.0354 + 0.0444 i
22
4.0485 - 3.3972 i
0.0354 - 0.0444 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.