Singularities of Møller-Plesset series: example "hf aug-cc-pVDZ 1.5r_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

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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
-0.6642 + 0.0152 i
0.00258 + 0.00407 i
Singularities of quadratic [5, 5, 4] approximant
2
-0.6642 - 0.0152 i
0.00258 - 0.00407 i
3
-0.6928
0.00519
4
1.6408 + 0.0805 i
0.058 - 0.0467 i
5
1.6408 - 0.0805 i
0.058 + 0.0467 i
6
-2.1422
0.253 i
7
2.7952
0.871
8
-1.0412 + 2.9184 i
0.292 - 0.0865 i
9
-1.0412 - 2.9184 i
0.292 + 0.0865 i
10
128.3564
58.3 i
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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
-0.6714 + 0.0185 i
0.00283 + 0.00521 i
Singularities of quadratic [5, 5, 5] approximant
2
-0.6714 - 0.0185 i
0.00283 - 0.00521 i
3
-0.6973
0.00567
4
1.8169 + 0.1574 i
0.164 - 0.0918 i
5
1.8169 - 0.1574 i
0.164 + 0.0918 i
6
-2.198
0.251 i
7
2.5856
0.998
8
-1.2605 + 2.8409 i
0.375 - 0.0416 i
9
-1.2605 - 2.8409 i
0.375 + 0.0416 i
10
-14.3086
1.29
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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
-0.6683 + 0.0172 i
0.00258 + 0.00457 i
Singularities of quadratic [6, 5, 5] approximant
2
-0.6683 - 0.0172 i
0.00258 - 0.00457 i
3
-0.6939
0.00514
4
1.8829 + 0.2455 i
0.247 - 0.0492 i
5
1.8829 - 0.2455 i
0.247 + 0.0492 i
6
-2.2281
0.23 i
7
-1.0723 + 2.6974 i
0.258 - 0.0323 i
8
-1.0723 - 2.6974 i
0.258 + 0.0323 i
9
3.0312
0.391
10
3.7068
0.709 i
11
11.0655
0.907
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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
-0.6536 + 0.0112 i
0.00186 + 0.00257 i
Singularities of quadratic [6, 6, 5] approximant
2
-0.6536 - 0.0112 i
0.00186 - 0.00257 i
3
-0.683
0.00398
4
-1.714
0.203 i
5
-1.6736 + 0.449 i
0.278 - 0.0532 i
6
-1.6736 - 0.449 i
0.278 + 0.0532 i
7
1.7527 + 0.1326 i
0.0908 - 0.057 i
8
1.7527 - 0.1326 i
0.0908 + 0.057 i
9
2.9999
0.581
10
-1.5589 + 2.6832 i
0.254 + 0.165 i
11
-1.5589 - 2.6832 i
0.254 - 0.165 i
12
23.0475
1.34e3 i
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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
-0.6517 + 0.0105 i
0.00184 + 0.00246 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.6517 - 0.0105 i
0.00184 - 0.00246 i
3
-0.6826
0.00407
4
-1.4109
0.33 i
5
-1.6092 + 0.2291 i
0.708 - 0.0333 i
6
-1.6092 - 0.2291 i
0.708 + 0.0333 i
7
1.765 + 0.138 i
0.1 - 0.0612 i
8
1.765 - 0.138 i
0.1 + 0.0612 i
9
2.9086
0.635
10
-1.519 + 2.7368 i
0.303 + 0.159 i
11
-1.519 - 2.7368 i
0.303 - 0.159 i
12
56.1709
13.2 i
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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
-0.6521 + 0.0106 i
0.00186 + 0.0025 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.6521 - 0.0106 i
0.00186 - 0.0025 i
3
-0.6829
0.0041
4
-1.4164
0.327 i
5
-1.6083 + 0.2382 i
0.689 + 0.0304 i
6
-1.6083 - 0.2382 i
0.689 - 0.0304 i
7
1.7699 + 0.1389 i
0.105 - 0.0643 i
8
1.7699 - 0.1389 i
0.105 + 0.0643 i
9
2.844
0.688
10
-1.5924 + 2.7652 i
0.332 + 0.2 i
11
-1.5924 - 2.7652 i
0.332 - 0.2 i
12
-12.6494 + 20.1422 i
5.49 - 0.197 i
13
-12.6494 - 20.1422 i
5.49 + 0.197 i
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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
0.0387
0
Singularities of quadratic [7, 7, 6] approximant
2
0.0387
0
3
-0.6507 + 0.0104 i
0.0017 + 0.00226 i
4
-0.6507 - 0.0104 i
0.0017 - 0.00226 i
5
-0.6811
0.00379
6
-1.6233
0.226 i
7
-1.6584 + 0.4006 i
0.314 - 0.0926 i
8
-1.6584 - 0.4006 i
0.314 + 0.0926 i
9
1.7706 + 0.1349 i
0.109 - 0.0695 i
10
1.7706 - 0.1349 i
0.109 + 0.0695 i
11
2.8407
0.686
12
-1.4651 + 2.7851 i
0.298 + 0.102 i
13
-1.4651 - 2.7851 i
0.298 - 0.102 i
14
34.0991
316. i
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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
-0.2669
3.11e-7
Singularities of quadratic [7, 7, 7] approximant
2
-0.2669
3.11e-7 i
3
-0.6411 + 0.0089 i
0.00103 + 0.00123 i
4
-0.6411 - 0.0089 i
0.00103 - 0.00123 i
5
-0.6719
0.00255
6
1.2285 + 0.0061 i
0.00128 - 0.00128 i
7
1.2285 - 0.0061 i
0.00128 + 0.00128 i
8
1.6398 + 0.1967 i
0.0214 + 0.000641 i
9
1.6398 - 0.1967 i
0.0214 - 0.000641 i
10
-2.7058
0.244 i
11
-2.5606 + 2.5603 i
20.4 + 8.31 i
12
-2.5606 - 2.5603 i
20.4 - 8.31 i
13
4.8685
1.14
14
-7.377
0.441
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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
-0.3112 + 0.e-5 i
8.68e-7 + 8.68e-7 i
Singularities of quadratic [8, 7, 7] approximant
2
-0.3112 - 0.e-5 i
8.68e-7 - 8.68e-7 i
3
-0.6405 + 0.0088 i
0.000994 + 0.00118 i
4
-0.6405 - 0.0088 i
0.000994 - 0.00118 i
5
-0.6714
0.00249
6
1.4171 + 0.0382 i
0.00291 - 0.00295 i
7
1.4171 - 0.0382 i
0.00291 + 0.00295 i
8
1.591 + 0.2394 i
0.0116 + 0.0078 i
9
1.591 - 0.2394 i
0.0116 - 0.0078 i
10
-2.6149
0.25 i
11
-2.3206 + 2.4994 i
3.96 - 4. i
12
-2.3206 - 2.4994 i
3.96 + 4. i
13
6.4704 + 3.1384 i
0.651 - 2.14 i
14
6.4704 - 3.1384 i
0.651 + 2.14 i
15
-7.4631
0.504
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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
-0.642 + 0.0088 i
0.00112 + 0.00136 i
Singularities of quadratic [8, 8, 7] approximant
2
-0.642 - 0.0088 i
0.00112 - 0.00136 i
3
-0.6732
0.00275
4
0.3782 + 0.8813 i
1.56e-6 + 0.000127 i
5
0.3782 - 0.8813 i
1.56e-6 - 0.000127 i
6
0.3784 + 0.8813 i
0.000127 - 1.6e-6 i
7
0.3784 - 0.8813 i
0.000127 + 1.6e-6 i
8
1.5052 + 0.2611 i
0.00521 - 0.0023 i
9
1.5052 - 0.2611 i
0.00521 + 0.0023 i
10
1.9987
0.0268
11
-2.2789
0.412 i
12
2.3082 + 0.6399 i
0.0165 - 0.0576 i
13
2.3082 - 0.6399 i
0.0165 + 0.0576 i
14
-1.9919 + 2.0587 i
0.307 - 0.134 i
15
-1.9919 - 2.0587 i
0.307 + 0.134 i
16
5.3562
0.336 i
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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
0.1993 + 0.5797 i
7.87e-6 - 0.0000111 i
Singularities of quadratic [8, 8, 8] approximant
2
0.1993 - 0.5797 i
7.87e-6 + 0.0000111 i
3
0.1993 + 0.5797 i
0.0000111 + 7.87e-6 i
4
0.1993 - 0.5797 i
0.0000111 - 7.87e-6 i
5
-0.6418 + 0.0088 i
0.0011 + 0.00133 i
6
-0.6418 - 0.0088 i
0.0011 - 0.00133 i
7
-0.6729
0.0027
8
1.4098
0.00447
9
1.4742 + 0.1174 i
0.000813 - 0.00713 i
10
1.4742 - 0.1174 i
0.000813 + 0.00713 i
11
1.813
0.155 i
12
-2.3926
0.342 i
13
-2.1595 + 2.2006 i
0.666 - 0.31 i
14
-2.1595 - 2.2006 i
0.666 + 0.31 i
15
3.708
0.411
16
40.7648
2.42 i
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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
-0.4193
0.0000113
Singularities of quadratic [9, 8, 8] approximant
2
-0.4193
0.0000113 i
3
-0.6417 + 0.0093 i
0.00102 + 0.00121 i
4
-0.6417 - 0.0093 i
0.00102 - 0.00121 i
5
-0.672
0.00248
6
-1.3931
0.667 i
7
-1.435
8.1
8
1.6316 + 0.4039 i
0.00795 - 0.0258 i
9
1.6316 - 0.4039 i
0.00795 + 0.0258 i
10
1.7819 + 0.1214 i
0.0189 - 0.00891 i
11
1.7819 - 0.1214 i
0.0189 + 0.00891 i
12
-2.1203
0.32 i
13
-1.6821 + 2.4846 i
0.241 + 0.493 i
14
-1.6821 - 2.4846 i
0.241 - 0.493 i
15
2.5017 + 2.6811 i
0.0402 - 0.241 i
16
2.5017 - 2.6811 i
0.0402 + 0.241 i
17
330.5047
17.8
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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
-0.561 + 0.1552 i
0.00011 + 0.000145 i
Singularities of quadratic [9, 9, 8] approximant
2
-0.561 - 0.1552 i
0.00011 - 0.000145 i
3
-0.5611 + 0.1552 i
0.000145 - 0.00011 i
4
-0.5611 - 0.1552 i
0.000145 + 0.00011 i
5
-0.6438 + 0.0066 i
0.00178 + 0.00261 i
6
-0.6438 - 0.0066 i
0.00178 - 0.00261 i
7
-0.6779
0.00404
8
1.6392
0.0104
9
1.5934 + 0.4605 i
0.00718 - 0.011 i
10
1.5934 - 0.4605 i
0.00718 + 0.011 i
11
-2.228
0.39 i
12
2.524 + 0.3146 i
0.237 + 0.0411 i
13
2.524 - 0.3146 i
0.237 - 0.0411 i
14
2.0587 + 1.9021 i
0.0109 + 0.0587 i
15
2.0587 - 1.9021 i
0.0109 - 0.0587 i
16
-1.9063 + 2.2412 i
0.263 - 0.345 i
17
-1.9063 - 2.2412 i
0.263 + 0.345 i
18
9.3229
1.11 i
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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
0.0893
0
Singularities of quadratic [9, 9, 9] approximant
2
0.0893
0
3
-0.5998 + 0.0011 i
0.000216 + 0.000218 i
4
-0.5998 - 0.0011 i
0.000216 - 0.000218 i
5
-0.6457
0.00181
6
-0.6693
0.00722 i
7
-0.6932
0.0132
8
1.2225
0.000227
9
1.24
0.000232 i
10
1.481 + 0.3773 i
0.000936 + 0.0025 i
11
1.481 - 0.3773 i
0.000936 - 0.0025 i
12
-2.0055
0.802 i
13
1.1151 + 1.7252 i
0.00172 - 0.00309 i
14
1.1151 - 1.7252 i
0.00172 + 0.00309 i
15
1.1796 + 1.8078 i
0.00364 + 0.00189 i
16
1.1796 - 1.8078 i
0.00364 - 0.00189 i
17
-1.6263 + 1.9775 i
0.0795 - 0.0734 i
18
-1.6263 - 1.9775 i
0.0795 + 0.0734 i
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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
-0.6207 + 0.0033 i
0.000463 + 0.000502 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.6207 - 0.0033 i
0.000463 - 0.000502 i
3
-0.6521
0.00166
4
-0.6874
0.0094 i
5
-0.7053
0.0321
6
-1.4666
0.724 i
7
1.3524 + 0.686 i
0.000235 - 0.0017 i
8
1.3524 - 0.686 i
0.000235 + 0.0017 i
9
1.3982 + 0.6874 i
0.00182 + 0.0000945 i
10
1.3982 - 0.6874 i
0.00182 - 0.0000945 i
11
1.5442 + 0.2995 i
0.00485 + 0.000619 i
12
1.5442 - 0.2995 i
0.00485 - 0.000619 i
13
-1.7434
0.141
14
-1.7121 + 1.1244 i
0.0115 - 0.054 i
15
-1.7121 - 1.1244 i
0.0115 + 0.054 i
16
-0.8063 + 2.598 i
0.0213 - 0.036 i
17
-0.8063 - 2.598 i
0.0213 + 0.036 i
18
-0.6777 + 5.1991 i
0.178 - 0.0366 i
19
-0.6777 - 5.1991 i
0.178 + 0.0366 i
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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
-0.6209 + 0.0033 i
0.00046 + 0.000499 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.6209 - 0.0033 i
0.00046 - 0.000499 i
3
-0.6521
0.00162
4
-0.6885
0.00934 i
5
-0.7062
0.0354
6
-1.4249
0.578 i
7
1.3138 + 0.6488 i
0.000071 + 0.00119 i
8
1.3138 - 0.6488 i
0.000071 - 0.00119 i
9
1.3477 + 0.6397 i
0.0012 - 0.000164 i
10
1.3477 - 0.6397 i
0.0012 + 0.000164 i
11
1.5263 + 0.3033 i
0.00386 + 0.000764 i
12
1.5263 - 0.3033 i
0.00386 - 0.000764 i
13
-1.6059
0.228
14
-1.8039 + 1.1503 i
0.00829 - 0.068 i
15
-1.8039 - 1.1503 i
0.00829 + 0.068 i
16
-0.681 + 2.74 i
0.00371 - 0.0425 i
17
-0.681 - 2.74 i
0.00371 + 0.0425 i
18
0.2895 + 4.193 i
0.0598 - 0.0718 i
19
0.2895 - 4.193 i
0.0598 + 0.0718 i
20
-211.658
6.16 i
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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
-0.6226 + 0.0017 i
0.00162 + 0.00159 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.6226 - 0.0017 i
0.00162 - 0.00159 i
3
-0.6643 + 0.0086 i
0.0016 + 0.00672 i
4
-0.6643 - 0.0086 i
0.0016 - 0.00672 i
5
-0.6897
0.00571
6
-0.9323
0.346 i
7
-0.9424
1.08
8
1.66 + 0.2981 i
0.02 - 0.00272 i
9
1.66 - 0.2981 i
0.02 + 0.00272 i
10
1.6219 + 0.7221 i
0.00467 - 0.0146 i
11
1.6219 - 0.7221 i
0.00467 + 0.0146 i
12
-1.9255
0.775 i
13
1.7608 + 0.8295 i
0.0214 + 0.0063 i
14
1.7608 - 0.8295 i
0.0214 - 0.0063 i
15
-2.3963
0.411
16
-2.1953 + 1.2651 i
0.00818 - 0.225 i
17
-2.1953 - 1.2651 i
0.00818 + 0.225 i
18
-1.4229 + 3.0352 i
0.127 - 0.209 i
19
-1.4229 - 3.0352 i
0.127 + 0.209 i
20
11.665
1.79
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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
-0.6217 + 0.0026 i
0.000758 + 0.000799 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.6217 - 0.0026 i
0.000758 - 0.000799 i
3
-0.6573
0.00346
4
-0.6766
0.0228 i
5
-0.6973
0.012
6
-1.1974
0.455 i
7
-1.2589
13.2
8
1.6214 + 0.4531 i
0.00742 - 0.0169 i
9
1.6214 - 0.4531 i
0.00742 + 0.0169 i
10
1.6883
0.0172
11
-1.7552 + 0.8127 i
0.0711 - 0.0271 i
12
-1.7552 - 0.8127 i
0.0711 + 0.0271 i
13
1.6907 + 1.5781 i
0.0187 + 0.0144 i
14
1.6907 - 1.5781 i
0.0187 - 0.0144 i
15
2.5212
0.857 i
16
-1.2733 + 2.1976 i
0.0426 + 0.0398 i
17
-1.2733 - 2.1976 i
0.0426 - 0.0398 i
18
2.1984 + 1.4854 i
0.0115 - 0.0328 i
19
2.1984 - 1.4854 i
0.0115 + 0.0328 i
20
-4.0625 + 2.1196 i
0.306 + 0.138 i
21
-4.0625 - 2.1196 i
0.306 - 0.138 i
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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
-0.6138
0.00028
Singularities of quadratic [11, 11, 10] approximant
2
-0.6257
0.000171 i
3
-0.6416 + 0.0195 i
0.000319 + 0.000262 i
4
-0.6416 - 0.0195 i
0.000319 - 0.000262 i
5
-0.6432
0.000227
6
-0.8451
0.274 i
7
-0.8583
0.312
8
-1.2293
0.8 i
9
-1.2538
1.26
10
1.6714 + 0.2099 i
0.0039 - 0.0263 i
11
1.6714 - 0.2099 i
0.0039 + 0.0263 i
12
1.6158 + 0.5569 i
0.0142 - 0.000473 i
13
1.6158 - 0.5569 i
0.0142 + 0.000473 i
14
1.9477 + 0.7139 i
0.00174 - 0.0214 i
15
1.9477 - 0.7139 i
0.00174 + 0.0214 i
16
-2.243
0.449 i
17
2.6442
158.
18
2.0434 + 1.742 i
0.0109 + 0.0442 i
19
2.0434 - 1.742 i
0.0109 - 0.0442 i
20
-1.9016 + 2.1709 i
0.239 - 0.271 i
21
-1.9016 - 2.1709 i
0.239 + 0.271 i
22
6.8427
0.517 i
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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
-0.6073
0.000127
Singularities of quadratic [11, 11, 11] approximant
2
-0.6159
0.0000842 i
3
-0.6313 + 0.0154 i
0.000139 + 0.000118 i
4
-0.6313 - 0.0154 i
0.000139 - 0.000118 i
5
-0.6345
0.00012
6
-0.7995
2.53e3 i
7
-0.8117
0.0856
8
1.1772 + 0.e-4 i
0.000135 - 0.000135 i
9
1.1772 - 0.e-4 i
0.000135 + 0.000135 i
10
-1.2883
1. i
11
-1.3144
1.12
12
1.6714 + 0.4341 i
0.00391 + 0.0244 i
13
1.6714 - 0.4341 i
0.00391 - 0.0244 i
14
1.9591
0.367
15
1.8242 + 0.8179 i
0.021 + 0.025 i
16
1.8242 - 0.8179 i
0.021 - 0.025 i
17
-2.3707
0.368 i
18
2.2144 + 1.2409 i
0.0825 + 0.00923 i
19
2.2144 - 1.2409 i
0.0825 - 0.00923 i
20
-1.9797 + 2.2441 i
0.344 - 0.416 i
21
-1.9797 - 2.2441 i
0.344 + 0.416 i
22
198.6412
0.933 i
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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

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