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

Molecule H- ion. 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

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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
1.3245 + 0.0463 i
0.0052 - 0.0044 i
Singularities of quadratic [5, 5, 4] approximant
2
1.3245 - 0.0463 i
0.0052 + 0.0044 i
3
1.533 + 0.5798 i
0.00623 - 0.0211 i
4
1.533 - 0.5798 i
0.00623 + 0.0211 i
5
1.4799 + 2.1056 i
0.000668 - 0.0212 i
6
1.4799 - 2.1056 i
0.000668 + 0.0212 i
7
1.4164 + 2.5555 i
0.026 + 0.00427 i
8
1.4164 - 2.5555 i
0.026 - 0.00427 i
9
-11.507 + 7.3539 i
0.373 + 0.643 i
10
-11.507 - 7.3539 i
0.373 - 0.643 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
1.4964 + 0.2976 i
0.0207 - 0.0629 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4964 - 0.2976 i
0.0207 + 0.0629 i
3
1.9055 + 0.8803 i
0.0418 + 0.0268 i
4
1.9055 - 0.8803 i
0.0418 - 0.0268 i
5
1.8017 + 2.1756 i
0.0275 - 0.013 i
6
1.8017 - 2.1756 i
0.0275 + 0.013 i
7
1.9859 + 3.6028 i
0.0044 + 0.0325 i
8
1.9859 - 3.6028 i
0.0044 - 0.0325 i
9
-4.6853 + 0.163 i
0.00949 + 0.00919 i
10
-4.6853 - 0.163 i
0.00949 - 0.00919 i
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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
1.4874 + 0.3084 i
0.0229 - 0.0496 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4874 - 0.3084 i
0.0229 + 0.0496 i
3
1.8808 + 1.0048 i
0.0223 + 0.035 i
4
1.8808 - 1.0048 i
0.0223 - 0.035 i
5
1.8771 + 2.3326 i
0.0293 + 0.00716 i
6
1.8771 - 2.3326 i
0.0293 - 0.00716 i
7
1.9781 + 4.5004 i
0.0266 - 0.0303 i
8
1.9781 - 4.5004 i
0.0266 + 0.0303 i
9
-8.6175 + 4.6438 i
0.457 - 0.0398 i
10
-8.6175 - 4.6438 i
0.457 + 0.0398 i
11
-10.0294
0.188
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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
1.4808 + 0.3021 i
0.00997 - 0.0445 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4808 - 0.3021 i
0.00997 + 0.0445 i
3
1.8978 + 1.1154 i
0.00657 - 0.0324 i
4
1.8978 - 1.1154 i
0.00657 + 0.0324 i
5
-2.8578 + 0.2027 i
0.000128 + 0.000198 i
6
-2.8578 - 0.2027 i
0.000128 - 0.000198 i
7
1.5187 + 2.6894 i
0.00287 - 0.0146 i
8
1.5187 - 2.6894 i
0.00287 + 0.0146 i
9
-3.1518 + 0.4103 i
0.000353 - 0.0000607 i
10
-3.1518 - 0.4103 i
0.000353 + 0.0000607 i
11
4.1195
0.127
12
5.6531
0.0557 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
1.5016 + 0.3139 i
0.0532 - 0.0539 i
Singularities of quadratic [6, 6, 6] approximant
2
1.5016 - 0.3139 i
0.0532 + 0.0539 i
3
1.8306 + 0.8659 i
0.0337 - 0.00116 i
4
1.8306 - 0.8659 i
0.0337 + 0.00116 i
5
1.649 + 1.8667 i
0.00424 - 0.01 i
6
1.649 - 1.8667 i
0.00424 + 0.01 i
7
0.822 + 3.5013 i
0.00402 + 0.00476 i
8
0.822 - 3.5013 i
0.00402 - 0.00476 i
9
-6.1426 + 2.1283 i
0.0102 + 0.00144 i
10
-6.1426 - 2.1283 i
0.0102 - 0.00144 i
11
-0.9194 + 9.9324 i
0.011 - 0.00232 i
12
-0.9194 - 9.9324 i
0.011 + 0.00232 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
1.5008 + 0.3108 i
0.0363 - 0.0542 i
Singularities of quadratic [7, 6, 6] approximant
2
1.5008 - 0.3108 i
0.0363 + 0.0542 i
3
1.9329 + 0.0815 i
0.212 - 0.0021 i
4
1.9329 - 0.0815 i
0.212 + 0.0021 i
5
1.9638 + 1.0933 i
0.0131 + 0.0598 i
6
1.9638 - 1.0933 i
0.0131 - 0.0598 i
7
2.0364 + 2.403 i
0.0367 + 0.0238 i
8
2.0364 - 2.403 i
0.0367 - 0.0238 i
9
2.2971 + 5.2207 i
0.0596 - 0.0221 i
10
2.2971 - 5.2207 i
0.0596 + 0.0221 i
11
-6.1386 + 5.7875 i
0.105 - 0.00376 i
12
-6.1386 - 5.7875 i
0.105 + 0.00376 i
13
-20.6511
0.25
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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
1.5035 + 0.3184 i
0.0545 - 0.042 i
Singularities of quadratic [7, 7, 6] approximant
2
1.5035 - 0.3184 i
0.0545 + 0.042 i
3
1.9775 + 0.7138 i
0.0655 - 0.0608 i
4
1.9775 - 0.7138 i
0.0655 + 0.0608 i
5
2.2726
0.104
6
1.9837 + 1.5712 i
0.0278 + 0.0326 i
7
1.9837 - 1.5712 i
0.0278 - 0.0326 i
8
1.7053 + 3.1847 i
0.0282 - 0.00837 i
9
1.7053 - 3.1847 i
0.0282 + 0.00837 i
10
-5.0239 + 4.2737 i
0.0205 + 0.0292 i
11
-5.0239 - 4.2737 i
0.0205 - 0.0292 i
12
-5.7869 + 7.425 i
0.0233 - 0.0326 i
13
-5.7869 - 7.425 i
0.0233 + 0.0326 i
14
17.2344
0.0723 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
1.5063 + 0.3264 i
0.0635 - 0.0251 i
Singularities of quadratic [7, 7, 7] approximant
2
1.5063 - 0.3264 i
0.0635 + 0.0251 i
3
1.8969 + 0.7053 i
0.0334 - 0.056 i
4
1.8969 - 0.7053 i
0.0334 + 0.056 i
5
2.1418
0.0815
6
1.9027 + 1.6502 i
0.0112 + 0.023 i
7
1.9027 - 1.6502 i
0.0112 - 0.023 i
8
1.5012 + 3.3813 i
0.0178 + 0.00654 i
9
1.5012 - 3.3813 i
0.0178 - 0.00654 i
10
5.5747
0.161 i
11
-5.0574 + 3.4056 i
0.0153 - 0.0133 i
12
-5.0574 - 3.4056 i
0.0153 + 0.0133 i
13
-4.9349 + 5.0403 i
0.0194 + 0.00783 i
14
-4.9349 - 5.0403 i
0.0194 - 0.00783 i
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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
-0.9647 + 0.e-5 i
6.66e-6 + 6.66e-6 i
Singularities of quadratic [8, 7, 7] approximant
2
-0.9647 - 0.e-5 i
6.66e-6 - 6.66e-6 i
3
1.4997 + 0.3096 i
0.0351 - 0.0542 i
4
1.4997 - 0.3096 i
0.0351 + 0.0542 i
5
2.1167 + 0.142 i
0.159 - 0.0519 i
6
2.1167 - 0.142 i
0.159 + 0.0519 i
7
2.0244 + 1.1398 i
0.0043 - 0.0824 i
8
2.0244 - 1.1398 i
0.0043 + 0.0824 i
9
2.1721 + 2.6284 i
0.0245 + 0.0593 i
10
2.1721 - 2.6284 i
0.0245 - 0.0593 i
11
4.3922 + 5.5327 i
0.116 + 0.103 i
12
4.3922 - 5.5327 i
0.116 - 0.103 i
13
-6.3771 + 5.315 i
0.0851 + 0.0777 i
14
-6.3771 - 5.315 i
0.0851 - 0.0777 i
15
189.0209
1.59
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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
-1.1453 + 0.e-5 i
0.0000138 + 0.0000138 i
Singularities of quadratic [8, 8, 7] approximant
2
-1.1453 - 0.e-5 i
0.0000138 - 0.0000138 i
3
1.499 + 0.3065 i
0.0285 - 0.0573 i
4
1.499 - 0.3065 i
0.0285 + 0.0573 i
5
2.0141 + 0.1244 i
0.235 + 0.0234 i
6
2.0141 - 0.1244 i
0.235 - 0.0234 i
7
1.9536 + 1.1213 i
0.00613 + 0.0535 i
8
1.9536 - 1.1213 i
0.00613 - 0.0535 i
9
2.0258 + 2.4606 i
0.028 + 0.0297 i
10
2.0258 - 2.4606 i
0.028 - 0.0297 i
11
2.2648 + 5.3929 i
0.0775 - 0.0176 i
12
2.2648 - 5.3929 i
0.0775 + 0.0176 i
13
-7.4475 + 5.2884 i
0.115 + 0.217 i
14
-7.4475 - 5.2884 i
0.115 - 0.217 i
15
-4.9407 + 29.3673 i
0.265 + 0.0485 i
16
-4.9407 - 29.3673 i
0.265 - 0.0485 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
1.5054 + 0.3141 i
0.0587 - 0.0543 i
Singularities of quadratic [8, 8, 8] approximant
2
1.5054 - 0.3141 i
0.0587 + 0.0543 i
3
-1.7731
0.0000195
4
-1.7736
0.0000195 i
5
1.9184 + 0.8049 i
0.0502 - 0.00859 i
6
1.9184 - 0.8049 i
0.0502 + 0.00859 i
7
1.8492 + 1.539 i
0.0364 + 0.019 i
8
1.8492 - 1.539 i
0.0364 - 0.019 i
9
1.3002 + 2.5332 i
0.00248 + 0.00464 i
10
1.3002 - 2.5332 i
0.00248 - 0.00464 i
11
-0.2423 + 3.7578 i
0.00166 - 0.000794 i
12
-0.2423 - 3.7578 i
0.00166 + 0.000794 i
13
-5.4279
0.0032
14
0.5474 + 6.9665 i
0.000921 + 0.00285 i
15
0.5474 - 6.9665 i
0.000921 - 0.00285 i
16
7.8011
0.0096
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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
-1.0195 + 0.7601 i
3.12e-6 + 6.88e-6 i
Singularities of quadratic [9, 8, 8] approximant
2
-1.0195 - 0.7601 i
3.12e-6 - 6.88e-6 i
3
-1.0195 + 0.7601 i
6.88e-6 - 3.12e-6 i
4
-1.0195 - 0.7601 i
6.88e-6 + 3.12e-6 i
5
1.5018 + 0.3115 i
0.0436 - 0.0544 i
6
1.5018 - 0.3115 i
0.0436 + 0.0544 i
7
2.2699 + 0.7286 i
0.183 - 0.0504 i
8
2.2699 - 0.7286 i
0.183 + 0.0504 i
9
2.4708
0.138
10
2.1316 + 1.2999 i
0.125 - 0.109 i
11
2.1316 - 1.2999 i
0.125 + 0.109 i
12
1.8121 + 2.8439 i
0.00479 - 0.0248 i
13
1.8121 - 2.8439 i
0.00479 + 0.0248 i
14
-5.5746 + 4.2288 i
0.00255 - 0.0216 i
15
-5.5746 - 4.2288 i
0.00255 + 0.0216 i
16
-1.2277 + 7.2675 i
0.00421 - 0.0187 i
17
-1.2277 - 7.2675 i
0.00421 + 0.0187 i
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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
-0.1921
0
Singularities of quadratic [9, 9, 8] approximant
2
-0.1921
0
3
1.5097 + 0.3067 i
0.062 - 0.0946 i
4
1.5097 - 0.3067 i
0.062 + 0.0946 i
5
-0.8977 + 1.7534 i
2.32e-6 + 0.0000116 i
6
-0.8977 - 1.7534 i
2.32e-6 - 0.0000116 i
7
-0.9017 + 1.759 i
0.0000116 - 2.25e-6 i
8
-0.9017 - 1.759 i
0.0000116 + 2.25e-6 i
9
1.9371 + 1.0485 i
0.00463 + 0.0326 i
10
1.9371 - 1.0485 i
0.00463 - 0.0326 i
11
2.1368 + 1.7188 i
0.0814 - 0.00108 i
12
2.1368 - 1.7188 i
0.0814 + 0.00108 i
13
-3.259 + 0.1771 i
0.000036 + 0.0000289 i
14
-3.259 - 0.1771 i
0.000036 - 0.0000289 i
15
0.8705 + 3.4283 i
0.00138 + 0.00225 i
16
0.8705 - 3.4283 i
0.00138 - 0.00225 i
17
-3.9001 + 1.9956 i
0.0000638 + 0.000306 i
18
-3.9001 - 1.9956 i
0.0000638 - 0.000306 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
0.8572 + 0.e-5 i
3.77e-6 - 3.77e-6 i
Singularities of quadratic [9, 9, 9] approximant
2
0.8572 - 0.e-5 i
3.77e-6 + 3.77e-6 i
3
1.5109 + 0.303 i
0.0468 - 0.12 i
4
1.5109 - 0.303 i
0.0468 + 0.12 i
5
-0.9961 + 1.3015 i
7.17e-6 + 3.85e-6 i
6
-0.9961 - 1.3015 i
7.17e-6 - 3.85e-6 i
7
-0.9957 + 1.3019 i
3.85e-6 - 7.17e-6 i
8
-0.9957 - 1.3019 i
3.85e-6 + 7.17e-6 i
9
1.9494 + 1.0657 i
0.000352 - 0.0398 i
10
1.9494 - 1.0657 i
0.000352 + 0.0398 i
11
2.1284 + 1.7978 i
0.0605 + 0.0521 i
12
2.1284 - 1.7978 i
0.0605 - 0.0521 i
13
1.1239 + 3.5044 i
0.00364 + 0.00461 i
14
1.1239 - 3.5044 i
0.00364 - 0.00461 i
15
-3.7933 + 2.7726 i
0.0013 - 0.0000789 i
16
-3.7933 - 2.7726 i
0.0013 + 0.0000789 i
17
-4.8001 + 1.6699 i
0.0012 - 0.000661 i
18
-4.8001 - 1.6699 i
0.0012 + 0.000661 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
-0.7014 + 1.1179 i
2.13e-6 - 8.3e-6 i
Singularities of quadratic [10, 9, 9] approximant
2
-0.7014 - 1.1179 i
2.13e-6 + 8.3e-6 i
3
-0.7015 + 1.1179 i
8.3e-6 + 2.13e-6 i
4
-0.7015 - 1.1179 i
8.3e-6 - 2.13e-6 i
5
1.4964 + 0.3085 i
0.026 - 0.0505 i
6
1.4964 - 0.3085 i
0.026 + 0.0505 i
7
1.8921 + 0.0753 i
0.237 + 0.0199 i
8
1.8921 - 0.0753 i
0.237 - 0.0199 i
9
-2.0207 + 0.0005 i
0.0000283 + 0.0000282 i
10
-2.0207 - 0.0005 i
0.0000283 - 0.0000282 i
11
2.0229 + 1.1503 i
0.027 - 0.0763 i
12
2.0229 - 1.1503 i
0.027 + 0.0763 i
13
2.3554 + 2.3505 i
0.13 + 0.0117 i
14
2.3554 - 2.3505 i
0.13 - 0.0117 i
15
2.2868 + 4.3704 i
0.034 - 0.0536 i
16
2.2868 - 4.3704 i
0.034 + 0.0536 i
17
-6.7473 + 4.5104 i
0.0211 + 0.0682 i
18
-6.7473 - 4.5104 i
0.0211 - 0.0682 i
19
-28.297
0.298
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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
-0.6434 + 1.2073 i
8.49e-7 - 3.7e-6 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.6434 - 1.2073 i
8.49e-7 + 3.7e-6 i
3
-0.6434 + 1.2074 i
3.7e-6 + 8.49e-7 i
4
-0.6434 - 1.2074 i
3.7e-6 - 8.49e-7 i
5
1.5021 + 0.3118 i
0.0453 - 0.0528 i
6
1.5021 - 0.3118 i
0.0453 + 0.0528 i
7
2.0733 + 0.8059 i
0.0594 + 0.00808 i
8
2.0733 - 0.8059 i
0.0594 - 0.00808 i
9
2.1928 + 1.269 i
0.175 - 0.139 i
10
2.1928 - 1.269 i
0.175 + 0.139 i
11
-2.5348 + 0.0112 i
0.0000217 + 0.0000215 i
12
-2.5348 - 0.0112 i
0.0000217 - 0.0000215 i
13
1.5812 + 2.2756 i
0.00594 - 0.000825 i
14
1.5812 - 2.2756 i
0.00594 + 0.000825 i
15
2.5664 + 1.884 i
0.0119 - 0.0244 i
16
2.5664 - 1.884 i
0.0119 + 0.0244 i
17
0.2849 + 4.1672 i
0.00316 - 0.000292 i
18
0.2849 - 4.1672 i
0.00316 + 0.000292 i
19
-5.107 + 2.2138 i
0.00126 - 0.00154 i
20
-5.107 - 2.2138 i
0.00126 + 0.00154 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
-0.5609 + 1.1667 i
3.5e-7 - 3.18e-7 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.5609 - 1.1667 i
3.5e-7 + 3.18e-7 i
3
-0.561 + 1.1668 i
3.18e-7 + 3.5e-7 i
4
-0.561 - 1.1668 i
3.18e-7 - 3.5e-7 i
5
1.53
0.0257
6
1.5074 + 0.3122 i
0.0828 - 0.0652 i
7
1.5074 - 0.3122 i
0.0828 + 0.0652 i
8
1.5434
0.0327 i
9
1.8688 + 1.2106 i
0.00471 - 0.0131 i
10
1.8688 - 1.2106 i
0.00471 + 0.0131 i
11
-1.664 + 2.2236 i
5.8e-6 + 0.0000145 i
12
-1.664 - 2.2236 i
5.8e-6 - 0.0000145 i
13
-1.8859 + 2.176 i
0.0000145 - 2.41e-6 i
14
-1.8859 - 2.176 i
0.0000145 + 2.41e-6 i
15
2.7438 + 1.3049 i
0.0528 - 0.101 i
16
2.7438 - 1.3049 i
0.0528 + 0.101 i
17
-3.006 + 1.5218 i
0.0000312 - 0.0000215 i
18
-3.006 - 1.5218 i
0.0000312 + 0.0000215 i
19
0.3772 + 3.9505 i
0.000598 - 0.000542 i
20
0.3772 - 3.9505 i
0.000598 + 0.000542 i
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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
0.0455
0
Singularities of quadratic [11, 10, 10] approximant
2
0.0455
0
3
-0.549 + 1.2095 i
4.79e-8 + 2.54e-7 i
4
-0.549 - 1.2095 i
4.79e-8 - 2.54e-7 i
5
-0.5492 + 1.2096 i
2.54e-7 - 4.79e-8 i
6
-0.5492 - 1.2096 i
2.54e-7 + 4.79e-8 i
7
1.4997 + 0.315 i
0.0442 - 0.0363 i
8
1.4997 - 0.315 i
0.0442 + 0.0363 i
9
1.8422 + 1.0794 i
0.00848 + 0.00753 i
10
1.8422 - 1.0794 i
0.00848 - 0.00753 i
11
0.0645 + 2.4341 i
1.03e-6 + 0.0000249 i
12
0.0645 - 2.4341 i
1.03e-6 - 0.0000249 i
13
0.1844 + 2.4759 i
0.0000321 - 2.05e-6 i
14
0.1844 - 2.4759 i
0.0000321 + 2.05e-6 i
15
2.3384 + 0.9293 i
0.0674 - 0.0439 i
16
2.3384 - 0.9293 i
0.0674 + 0.0439 i
17
-3.1048 + 1.1243 i
0.0000306 + 3.33e-6 i
18
-3.1048 - 1.1243 i
0.0000306 - 3.33e-6 i
19
-0.6472 + 3.2762 i
0.0000394 + 0.0000793 i
20
-0.6472 - 3.2762 i
0.0000394 - 0.0000793 i
21
-4.2394
0.0000617
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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
-0.553 + 0.e-5 i
0
Singularities of quadratic [11, 11, 10] approximant
2
-0.553 - 0.e-5 i
0
3
-0.7015 + 1.165 i
1.14e-7 + 3.12e-7 i
4
-0.7015 - 1.165 i
1.14e-7 - 3.12e-7 i
5
-0.7018 + 1.1652 i
3.12e-7 - 1.14e-7 i
6
-0.7018 - 1.1652 i
3.12e-7 + 1.14e-7 i
7
1.4439 + 0.0021 i
0.00219 - 0.0021 i
8
1.4439 - 0.0021 i
0.00219 + 0.0021 i
9
1.5101 + 0.3224 i
0.0951 + 0.00633 i
10
1.5101 - 0.3224 i
0.0951 - 0.00633 i
11
-1.7606 + 0.0015 i
2.86e-7 + 2.85e-7 i
12
-1.7606 - 0.0015 i
2.86e-7 - 2.85e-7 i
13
1.791 + 1.2112 i
0.00245 - 0.00818 i
14
1.791 - 1.2112 i
0.00245 + 0.00818 i
15
3.06
0.888
16
2.9538 + 1.8225 i
0.0129 - 0.0383 i
17
2.9538 - 1.8225 i
0.0129 + 0.0383 i
18
0.2448 + 3.7162 i
0.000457 - 0.00069 i
19
0.2448 - 3.7162 i
0.000457 + 0.00069 i
20
-3.5608 + 2.2647 i
0.0000387 + 0.000179 i
21
-3.5608 - 2.2647 i
0.0000387 - 0.000179 i
22
9.1863
0.0179 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
-0.9781 + 0.1889 i
2.3e-8 - 6.34e-9 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.9781 - 0.1889 i
2.3e-8 + 6.34e-9 i
3
-0.9781 + 0.1889 i
6.34e-9 + 2.3e-8 i
4
-0.9781 - 0.1889 i
6.34e-9 - 2.3e-8 i
5
0.6324 + 1.0614 i
1.09e-6 + 1.44e-6 i
6
0.6324 - 1.0614 i
1.09e-6 - 1.44e-6 i
7
0.6324 + 1.0615 i
1.44e-6 - 1.09e-6 i
8
0.6324 - 1.0615 i
1.44e-6 + 1.09e-6 i
9
-0.7773 + 1.1408 i
2.83e-7 - 1.43e-7 i
10
-0.7773 - 1.1408 i
2.83e-7 + 1.43e-7 i
11
-0.7776 + 1.141 i
1.43e-7 + 2.83e-7 i
12
-0.7776 - 1.141 i
1.43e-7 - 2.83e-7 i
13
1.5011 + 0.3156 i
0.0489 - 0.0349 i
14
1.5011 - 0.3156 i
0.0489 + 0.0349 i
15
1.8157 + 1.1348 i
0.00242 + 0.00756 i
16
1.8157 - 1.1348 i
0.00242 - 0.00756 i
17
2.3408 + 1.1974 i
0.0376 + 0.029 i
18
2.3408 - 1.1974 i
0.0376 - 0.029 i
19
0.1609 + 3.9985 i
0.000862 - 0.000138 i
20
0.1609 - 3.9985 i
0.000862 + 0.000138 i
21
-3.5162 + 2.0153 i
0.0000593 - 0.000149 i
22
-3.5162 - 2.0153 i
0.0000593 + 0.000149 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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