Singularities of Møller-Plesset series: example "bh cc-pvtz 1.5re"

Molecule X 1^Sigma+ State of BH. Basis CC-PVTZ. 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
1.0105
0.00187
Singularities of quadratic [5, 5, 4] approximant
2
1.0134
0.00188 i
3
1.409 + 0.4356 i
0.0124 + 0.0693 i
4
1.409 - 0.4356 i
0.0124 - 0.0693 i
5
-2.9035
0.0165
6
-3.257
0.0195 i
7
3.2788
2.8
8
-7.0103 + 3.1517 i
0.0464 + 0.0757 i
9
-7.0103 - 3.1517 i
0.0464 - 0.0757 i
10
24.7247
0.241 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
1.0634
0.0027
Singularities of quadratic [5, 5, 5] approximant
2
1.0678
0.00272 i
3
1.4107 + 0.4391 i
0.00806 + 0.0716 i
4
1.4107 - 0.4391 i
0.00806 - 0.0716 i
5
-3.1512
0.0272
6
3.2161
2.22
7
-3.9459
0.0409 i
8
-5.3866 + 4.1494 i
0.0525 + 0.0763 i
9
-5.3866 - 4.1494 i
0.0525 - 0.0763 i
10
91.0823
0.156 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
1.4238
0.0337
Singularities of quadratic [6, 5, 5] approximant
2
1.4795
0.0404 i
3
1.4275 + 0.4709 i
0.0446 - 0.0918 i
4
1.4275 - 0.4709 i
0.0446 + 0.0918 i
5
-2.4742
0.0159
6
-2.5239
0.0162 i
7
3.2271 + 1.0378 i
0.596 + 0.806 i
8
3.2271 - 1.0378 i
0.596 - 0.806 i
9
-4.5799
7.8
10
5.7274
0.601
11
-9.7376
0.2 i
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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
1.4611 + 0.5165 i
0.147 - 0.0364 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4611 - 0.5165 i
0.147 + 0.0364 i
3
1.6715 + 0.284 i
0.281 + 0.054 i
4
1.6715 - 0.284 i
0.281 - 0.054 i
5
1.8507 + 0.558 i
0.573 - 0.554 i
6
1.8507 - 0.558 i
0.573 + 0.554 i
7
-2.6798
0.0149
8
-2.8138
0.0155 i
9
2.9104
2.68
10
-5.7181
0.296
11
-8.987
0.104 i
12
83.933
0.441 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
1.4582 + 0.4875 i
0.129 - 0.128 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4582 - 0.4875 i
0.129 + 0.128 i
3
1.8178 + 0.0952 i
0.144 - 0.0767 i
4
1.8178 - 0.0952 i
0.144 + 0.0767 i
5
2.3614
2.68
6
2.2598 + 0.7262 i
1.09 - 0.407 i
7
2.2598 - 0.7262 i
1.09 + 0.407 i
8
-2.7458
0.0221
9
-2.8788
0.0228 i
10
-5.8522 + 0.9418 i
0.0107 + 0.281 i
11
-5.8522 - 0.9418 i
0.0107 - 0.281 i
12
-25.4217
8.56
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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
1.4589 + 0.4851 i
0.127 - 0.141 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4589 - 0.4851 i
0.127 + 0.141 i
3
1.8799 + 0.0225 i
0.0591 - 0.0527 i
4
1.8799 - 0.0225 i
0.0591 + 0.0527 i
5
2.186
0.794
6
2.2641 + 0.7658 i
0.946 - 0.212 i
7
2.2641 - 0.7658 i
0.946 + 0.212 i
8
-2.7464
0.0253
9
-2.8654
0.026 i
10
-5.7637 + 0.725 i
0.00254 + 0.38 i
11
-5.7637 - 0.725 i
0.00254 - 0.38 i
12
-31.9013
3.24
13
56.2779
0.405 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
1.4609 + 0.4811 i
0.119 - 0.167 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4609 - 0.4811 i
0.119 + 0.167 i
3
1.8483
0.21
4
1.9912 + 0.3296 i
0.437 - 0.218 i
5
1.9912 - 0.3296 i
0.437 + 0.218 i
6
2.2352 + 0.7579 i
0.925 + 0.0074 i
7
2.2352 - 0.7579 i
0.925 - 0.0074 i
8
-2.8111 + 0.0458 i
0.0277 + 0.0298 i
9
-2.8111 - 0.0458 i
0.0277 - 0.0298 i
10
-4.4382 + 0.3556 i
0.156 + 0.0344 i
11
-4.4382 - 0.3556 i
0.156 - 0.0344 i
12
-10.0515
0.118
13
-26.5844
0.151 i
14
47.5992
0.325 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
1.4603 + 0.4817 i
0.118 - 0.162 i
Singularities of quadratic [7, 7, 7] approximant
2
1.4603 - 0.4817 i
0.118 + 0.162 i
3
1.8535
0.196
4
2.0087 + 0.2942 i
0.377 - 0.288 i
5
2.0087 - 0.2942 i
0.377 + 0.288 i
6
2.2412 + 0.7476 i
1.03 - 0.0219 i
7
2.2412 - 0.7476 i
1.03 + 0.0219 i
8
-2.4351
0.00176
9
-2.5313 + 0.0405 i
0.000825 - 0.00111 i
10
-2.5313 - 0.0405 i
0.000825 + 0.00111 i
11
-2.9362
0.00666 i
12
-7.3318 + 1.059 i
0.0564 + 0.0739 i
13
-7.3318 - 1.059 i
0.0564 - 0.0739 i
14
-59.8434
1.72
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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
1.4601 + 0.4826 i
0.123 - 0.156 i
Singularities of quadratic [8, 7, 7] approximant
2
1.4601 - 0.4826 i
0.123 + 0.156 i
3
1.8212
0.173
4
2.0279 + 0.2434 i
0.314 - 0.364 i
5
2.0279 - 0.2434 i
0.314 + 0.364 i
6
2.2484 + 0.7904 i
0.832 - 0.0979 i
7
2.2484 - 0.7904 i
0.832 + 0.0979 i
8
-2.7995
0.0471
9
-2.8948
0.0528 i
10
-3.5633 + 0.0697 i
0.0667 + 0.0854 i
11
-3.5633 - 0.0697 i
0.0667 - 0.0854 i
12
-5.242
1.49
13
-6.7355
0.262 i
14
23.4408
0.514 i
15
-105.2813
7.63
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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
-0.339
1.78e-8
Singularities of quadratic [8, 8, 7] approximant
2
-0.339
1.78e-8 i
3
1.461 + 0.4835 i
0.135 - 0.155 i
4
1.461 - 0.4835 i
0.135 + 0.155 i
5
1.7849
0.161
6
2.0189 + 0.2322 i
0.322 - 0.371 i
7
2.0189 - 0.2322 i
0.322 + 0.371 i
8
2.2593 + 0.8275 i
0.651 - 0.0333 i
9
2.2593 - 0.8275 i
0.651 + 0.0333 i
10
-2.7599 + 0.18 i
0.00293 + 0.00393 i
11
-2.7599 - 0.18 i
0.00293 - 0.00393 i
12
-3.4357 + 0.1836 i
0.00657 + 0.00299 i
13
-3.4357 - 0.1836 i
0.00657 - 0.00299 i
14
-11.6156
0.0907
15
-28.9612
0.139 i
16
30.7552
0.309 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
1.4319 + 0.437 i
0.0494 + 0.0413 i
Singularities of quadratic [8, 8, 8] approximant
2
1.4319 - 0.437 i
0.0494 - 0.0413 i
3
1.5372 + 0.46 i
0.123 - 0.0757 i
4
1.5372 - 0.46 i
0.123 + 0.0757 i
5
1.5322 + 0.5885 i
0.11 - 0.0168 i
6
1.5322 - 0.5885 i
0.11 + 0.0168 i
7
1.9571 + 1.3606 i
0.0459 + 0.000713 i
8
1.9571 - 1.3606 i
0.0459 - 0.000713 i
9
2.2151 + 1.3129 i
0.00451 - 0.0614 i
10
2.2151 - 1.3129 i
0.00451 + 0.0614 i
11
-2.7924 + 0.1247 i
0.00614 + 0.00612 i
12
-2.7924 - 0.1247 i
0.00614 - 0.00612 i
13
-4.1421 + 0.3404 i
0.0424 + 0.0069 i
14
-4.1421 - 0.3404 i
0.0424 - 0.0069 i
15
4.1924
1.94
16
-16.5482
0.315
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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
1.4674 + 0.4462 i
0.164 + 0.117 i
Singularities of quadratic [9, 8, 8] approximant
2
1.4674 - 0.4462 i
0.164 - 0.117 i
3
1.5955 + 0.3862 i
0.272 + 0.348 i
4
1.5955 - 0.3862 i
0.272 - 0.348 i
5
1.5821 + 0.5091 i
0.291 + 0.174 i
6
1.5821 - 0.5091 i
0.291 - 0.174 i
7
2.2334 + 1.3363 i
0.0895 + 0.0525 i
8
2.2334 - 1.3363 i
0.0895 - 0.0525 i
9
-2.8029 + 0.0997 i
0.00892 + 0.00881 i
10
-2.8029 - 0.0997 i
0.00892 - 0.00881 i
11
2.8499 + 1.398 i
0.116 - 0.0924 i
12
2.8499 - 1.398 i
0.116 + 0.0924 i
13
-4.3274 + 0.4127 i
0.0865 - 0.000388 i
14
-4.3274 - 0.4127 i
0.0865 + 0.000388 i
15
5.659
0.531
16
-12.5856
0.271
17
-38.8143
0.362 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
1.4625 + 0.4569 i
0.0918 + 0.177 i
Singularities of quadratic [9, 9, 8] approximant
2
1.4625 - 0.4569 i
0.0918 - 0.177 i
3
1.6433 + 0.4045 i
1.35 + 1.14 i
4
1.6433 - 0.4045 i
1.35 - 1.14 i
5
1.6249 + 0.5311 i
0.199 + 0.16 i
6
1.6249 - 0.5311 i
0.199 - 0.16 i
7
2.1786 + 1.4126 i
0.0701 + 0.0429 i
8
2.1786 - 1.4126 i
0.0701 - 0.0429 i
9
-2.8036 + 0.0983 i
0.00912 + 0.00907 i
10
-2.8036 - 0.0983 i
0.00912 - 0.00907 i
11
2.5764 + 1.495 i
0.0728 - 0.0755 i
12
2.5764 - 1.495 i
0.0728 + 0.0755 i
13
-4.3016 + 0.3985 i
0.0818 + 0.00369 i
14
-4.3016 - 0.3985 i
0.0818 - 0.00369 i
15
4.6467
1.09
16
-11.7515
0.214
17
-37.9349
0.279 i
18
742.5618
1.4 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
-0.1683
0
Singularities of quadratic [9, 9, 9] approximant
2
-0.1683
0
3
1.4611 + 0.4778 i
0.093 - 0.189 i
4
1.4611 - 0.4778 i
0.093 + 0.189 i
5
1.9373 + 0.2959 i
0.362 - 0.0709 i
6
1.9373 - 0.2959 i
0.362 + 0.0709 i
7
1.9671 + 0.5261 i
2.01 + 1.04 i
8
1.9671 - 0.5261 i
2.01 - 1.04 i
9
1.3586 + 2.0887 i
0.00115 + 0.0104 i
10
1.3586 - 2.0887 i
0.00115 - 0.0104 i
11
1.3479 + 2.1033 i
0.0103 - 0.00105 i
12
1.3479 - 2.1033 i
0.0103 + 0.00105 i
13
2.6515
1.19
14
-2.7886 + 0.1321 i
0.00565 + 0.00536 i
15
-2.7886 - 0.1321 i
0.00565 - 0.00536 i
16
-4.2278 + 0.3665 i
0.0508 + 0.00323 i
17
-4.2278 - 0.3665 i
0.0508 - 0.00323 i
18
-18.742
0.488
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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
-0.6044
8.75e-8
Singularities of quadratic [10, 9, 9] approximant
2
-0.6044
8.75e-8 i
3
1.4622 + 0.4825 i
0.138 - 0.169 i
4
1.4622 - 0.4825 i
0.138 + 0.169 i
5
0.1144 + 1.7836 i
0.000291 + 0.000285 i
6
0.1144 - 1.7836 i
0.000291 - 0.000285 i
7
0.1142 + 1.7837 i
0.000285 - 0.000291 i
8
0.1142 - 1.7837 i
0.000285 + 0.000291 i
9
1.8103
0.171
10
2.003 + 0.2767 i
0.358 - 0.309 i
11
2.003 - 0.2767 i
0.358 + 0.309 i
12
2.2778 + 0.7479 i
0.968 + 0.192 i
13
2.2778 - 0.7479 i
0.968 - 0.192 i
14
-2.7524 + 0.1902 i
0.00298 + 0.00254 i
15
-2.7524 - 0.1902 i
0.00298 - 0.00254 i
16
-4.066 + 0.2718 i
0.0212 + 0.00466 i
17
-4.066 - 0.2718 i
0.0212 - 0.00466 i
18
-33.8873
1.18
19
40.2478
0.481 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
-1.0809
1.2e-6
Singularities of quadratic [10, 10, 9] approximant
2
-1.0809
1.2e-6 i
3
1.4637 + 0.48 i
0.132 - 0.203 i
4
1.4637 - 0.48 i
0.132 + 0.203 i
5
-0.9932 + 1.3927 i
0.000019 + 0.0000285 i
6
-0.9932 - 1.3927 i
0.000019 - 0.0000285 i
7
-0.9936 + 1.3925 i
0.0000285 - 0.000019 i
8
-0.9936 - 1.3925 i
0.0000285 + 0.000019 i
9
1.896 + 0.1871 i
0.268 - 0.0612 i
10
1.896 - 0.1871 i
0.268 + 0.0612 i
11
1.9619 + 0.4461 i
1.14 + 0.0433 i
12
1.9619 - 0.4461 i
1.14 - 0.0433 i
13
-2.6482 + 0.3124 i
0.00108 + 0.000413 i
14
-2.6482 - 0.3124 i
0.00108 - 0.000413 i
15
2.8082 + 1.0781 i
0.112 - 0.351 i
16
2.8082 - 1.0781 i
0.112 + 0.351 i
17
-4.2652
0.0282
18
4.3407
1.49
19
-5.591
1.9 i
20
26.5913
0.227 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
-0.8397 + 0.5545 i
5.72e-7 - 1.41e-6 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.8397 - 0.5545 i
5.72e-7 + 1.41e-6 i
3
-0.8397 + 0.5545 i
1.41e-6 + 5.72e-7 i
4
-0.8397 - 0.5545 i
1.41e-6 - 5.72e-7 i
5
1.4624 + 0.4809 i
0.128 - 0.183 i
6
1.4624 - 0.4809 i
0.128 + 0.183 i
7
1.9114
0.184
8
2.0205 + 0.3163 i
0.307 - 0.338 i
9
2.0205 - 0.3163 i
0.307 + 0.338 i
10
2.2792 + 0.528 i
0.326 + 1.63 i
11
2.2792 - 0.528 i
0.326 - 1.63 i
12
-2.6326
0.00258
13
-3.4351
0.00401 i
14
0.6907 + 3.5363 i
0.00723 - 0.00358 i
15
0.6907 - 3.5363 i
0.00723 + 0.00358 i
16
-3.6371
0.00634
17
0.64 + 3.6306 i
0.00308 + 0.00745 i
18
0.64 - 3.6306 i
0.00308 - 0.00745 i
19
-4.5919
30.5 i
20
-9.6817
0.0909
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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
-0.87 + 0.5465 i
3.45e-7 + 9.87e-7 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.87 - 0.5465 i
3.45e-7 - 9.87e-7 i
3
-0.87 + 0.5466 i
9.87e-7 - 3.45e-7 i
4
-0.87 - 0.5466 i
9.87e-7 + 3.45e-7 i
5
1.4579 + 0.4799 i
0.0817 - 0.147 i
6
1.4579 - 0.4799 i
0.0817 + 0.147 i
7
1.7727 + 0.4167 i
0.471 + 0.0451 i
8
1.7727 - 0.4167 i
0.471 - 0.0451 i
9
2.0621 + 0.3942 i
0.298 + 1.67 i
10
2.0621 - 0.3942 i
0.298 - 1.67 i
11
2.3586 + 0.6172 i
0.24 - 0.254 i
12
2.3586 - 0.6172 i
0.24 + 0.254 i
13
-2.7906 + 0.1364 i
0.00641 + 0.00173 i
14
-2.7906 - 0.1364 i
0.00641 - 0.00173 i
15
-1.9493 + 2.5864 i
0.000494 + 0.00102 i
16
-1.9493 - 2.5864 i
0.000494 - 0.00102 i
17
-1.8951 + 2.6272 i
0.001 - 0.000549 i
18
-1.8951 - 2.6272 i
0.001 + 0.000549 i
19
3.9622 + 2.1253 i
0.154 - 0.0965 i
20
3.9622 - 2.1253 i
0.154 + 0.0965 i
21
21.9963
0.22
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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
-0.6361 + 0.8439 i
2.59e-8 - 3.54e-7 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.6361 - 0.8439 i
2.59e-8 + 3.54e-7 i
3
-0.6361 + 0.8439 i
3.54e-7 + 2.59e-8 i
4
-0.6361 - 0.8439 i
3.54e-7 - 2.59e-8 i
5
-1.1917
6.1e-7
6
-1.1917
6.1e-7 i
7
1.4659 + 0.4802 i
0.159 - 0.244 i
8
1.4659 - 0.4802 i
0.159 + 0.244 i
9
0.0965 + 1.7126 i
0.0000176 - 0.0000304 i
10
0.0965 - 1.7126 i
0.0000176 + 0.0000304 i
11
0.0962 + 1.7131 i
0.0000303 + 0.0000177 i
12
0.0962 - 1.7131 i
0.0000303 - 0.0000177 i
13
1.7897 + 0.0359 i
0.0694 - 0.0531 i
14
1.7897 - 0.0359 i
0.0694 + 0.0531 i
15
2.1915 + 0.6521 i
0.539 + 3.39 i
16
2.1915 - 0.6521 i
0.539 - 3.39 i
17
2.677
50.6
18
-2.7181 + 0.2898 i
0.00164 + 0.00002 i
19
-2.7181 - 0.2898 i
0.00164 - 0.00002 i
20
-11.6437
0.0446
21
14.7231
0.691 i
22
-27.7465
0.0883 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
-0.5829 + 0.6653 i
7.95e-8 - 7.76e-8 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.5829 - 0.6653 i
7.95e-8 + 7.76e-8 i
3
-0.5829 + 0.6653 i
7.76e-8 + 7.95e-8 i
4
-0.5829 - 0.6653 i
7.76e-8 - 7.95e-8 i
5
-0.9684
1.39e-7
6
-0.9684
1.39e-7 i
7
1.4644 + 0.4804 i
0.144 - 0.216 i
8
1.4644 - 0.4804 i
0.144 + 0.216 i
9
1.8616
0.0293
10
1.8685
0.0299 i
11
2.2064 + 0.6061 i
7.35 - 5.47 i
12
2.2064 - 0.6061 i
7.35 + 5.47 i
13
-0.0822 + 2.2975 i
0.000229 + 0.000113 i
14
-0.0822 - 2.2975 i
0.000229 - 0.000113 i
15
-0.0879 + 2.2994 i
0.000115 - 0.000227 i
16
-0.0879 - 2.2994 i
0.000115 + 0.000227 i
17
2.4301
2.
18
-2.7413 + 0.2459 i
0.00229 + 0.000365 i
19
-2.7413 - 0.2459 i
0.00229 - 0.000365 i
20
-9.7422 + 3.7063 i
0.0452 + 0.0284 i
21
-9.7422 - 3.7063 i
0.0452 - 0.0284 i
22
85.4807
0.187 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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Designed by A. Sergeev.