Singularities of Møller-Plesset series: example "bh aug-cc-pVQZ 1.7r_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

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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
0.9333 + 0.0002 i
0.000994 - 0.000993 i
Singularities of quadratic [5, 5, 4] approximant
2
0.9333 - 0.0002 i
0.000994 + 0.000993 i
3
1.4013 + 0.4414 i
0.0257 + 0.136 i
4
1.4013 - 0.4414 i
0.0257 - 0.136 i
5
2.8782
1.02
6
-2.9013
0.051
7
-2.9999
0.0619 i
8
-4.6587
0.121
9
8.0288
0.413 i
10
-16.1005
0.187 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
0.5797 + 1.0685 i
0.00164 - 0.000274 i
Singularities of quadratic [5, 5, 5] approximant
2
0.5797 - 1.0685 i
0.00164 + 0.000274 i
3
0.5808 + 1.0696 i
0.000274 + 0.00164 i
4
0.5808 - 1.0696 i
0.000274 - 0.00164 i
5
1.4041 + 0.4326 i
0.0624 + 0.132 i
6
1.4041 - 0.4326 i
0.0624 - 0.132 i
7
2.6065
0.857
8
-3.265
65.4
9
-4.7302
0.193 i
10
81.3671
0.214 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
0.3168 + 1.0472 i
0.000572 + 0.000328 i
Singularities of quadratic [6, 5, 5] approximant
2
0.3168 - 1.0472 i
0.000572 - 0.000328 i
3
0.3165 + 1.0477 i
0.000328 - 0.000572 i
4
0.3165 - 1.0477 i
0.000328 + 0.000572 i
5
1.4031 + 0.4315 i
0.0627 + 0.131 i
6
1.4031 - 0.4315 i
0.0627 - 0.131 i
7
2.671
0.934
8
-3.3162
24.
9
-5.0643
0.142 i
10
13.1736 + 32.2699 i
0.053 + 0.329 i
11
13.1736 - 32.2699 i
0.053 - 0.329 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
1.0812
0.00581
Singularities of quadratic [6, 6, 5] approximant
2
1.0838
0.00583 i
3
1.3969 + 0.4403 i
0.0262 + 0.134 i
4
1.3969 - 0.4403 i
0.0262 - 0.134 i
5
-1.5471 + 1.8361 i
0.000768 + 0.00855 i
6
-1.5471 - 1.8361 i
0.000768 - 0.00855 i
7
-1.594 + 1.8313 i
0.00856 - 0.000721 i
8
-1.594 - 1.8313 i
0.00856 + 0.000721 i
9
3.2403
2.13
10
-3.3954
1.39
11
6.1518
0.561 i
12
-9.1811
0.103 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
1.4116
0.0692
Singularities of quadratic [6, 6, 6] approximant
2
1.4539
0.0776 i
3
1.4014 + 0.452 i
0.00524 - 0.171 i
4
1.4014 - 0.452 i
0.00524 + 0.171 i
5
-1.8366 + 0.0046 i
0.00406 + 0.00406 i
6
-1.8366 - 0.0046 i
0.00406 - 0.00406 i
7
2.6407 + 1.236 i
0.153 + 0.283 i
8
2.6407 - 1.236 i
0.153 - 0.283 i
9
-3.1329 + 0.0758 i
0.109 + 0.0587 i
10
-3.1329 - 0.0758 i
0.109 - 0.0587 i
11
5.4895
0.345
12
-7.7585
0.284
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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
0.0309
0
Singularities of quadratic [7, 6, 6] approximant
2
0.0309
0
3
1.3781 + 0.447 i
0.0241 + 0.0852 i
4
1.3781 - 0.447 i
0.0241 - 0.0852 i
5
-1.7615
0.00118
6
-1.778
0.00121 i
7
2.0667
0.736
8
2.3104
0.529 i
9
2.6707 + 2.7179 i
0.0496 + 0.0269 i
10
2.6707 - 2.7179 i
0.0496 - 0.0269 i
11
-5.0504
0.0659
12
1.7264 + 4.8203 i
0.0394 - 0.0123 i
13
1.7264 - 4.8203 i
0.0394 + 0.0123 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
1.3435 + 0.0058 i
0.0099 - 0.00956 i
Singularities of quadratic [7, 7, 6] approximant
2
1.3435 - 0.0058 i
0.0099 + 0.00956 i
3
1.3889 + 0.4755 i
0.0563 - 0.0961 i
4
1.3889 - 0.4755 i
0.0563 + 0.0961 i
5
-2.1133
0.00819
6
-2.1623
0.00841 i
7
2.227 + 0.4432 i
1.62 - 0.25 i
8
2.227 - 0.4432 i
1.62 + 0.25 i
9
2.462
10.9
10
-3.699 + 1.0706 i
0.0155 + 0.102 i
11
-3.699 - 1.0706 i
0.0155 - 0.102 i
12
-6.6498 + 1.6772 i
0.0722 - 0.227 i
13
-6.6498 - 1.6772 i
0.0722 + 0.227 i
14
14.4066
0.271 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
1.277 + 0.0031 i
0.00551 - 0.00542 i
Singularities of quadratic [7, 7, 7] approximant
2
1.277 - 0.0031 i
0.00551 + 0.00542 i
3
1.3872 + 0.4743 i
0.05 - 0.0918 i
4
1.3872 - 0.4743 i
0.05 + 0.0918 i
5
-2.0773
0.00561
6
-2.1263
0.00578 i
7
2.2769 + 0.5509 i
0.984 - 0.555 i
8
2.2769 - 0.5509 i
0.984 + 0.555 i
9
2.6935
23.1
10
-3.6852 + 1.717 i
0.0203 + 0.0415 i
11
-3.6852 - 1.717 i
0.0203 - 0.0415 i
12
-4.1071 + 3.2445 i
0.0362 - 0.0478 i
13
-4.1071 - 3.2445 i
0.0362 + 0.0478 i
14
84.2535
0.301 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
1.4059 + 0.4802 i
0.127 - 0.157 i
Singularities of quadratic [8, 7, 7] approximant
2
1.4059 - 0.4802 i
0.127 + 0.157 i
3
1.5991 + 0.3546 i
0.243 + 0.0686 i
4
1.5991 - 0.3546 i
0.243 - 0.0686 i
5
1.66 + 0.3428 i
0.0795 - 0.559 i
6
1.66 - 0.3428 i
0.0795 + 0.559 i
7
-2.2035 + 0.0141 i
0.028 + 0.0286 i
8
-2.2035 - 0.0141 i
0.028 - 0.0286 i
9
2.5494
0.639
10
-3.1168 + 0.3487 i
0.253 - 0.194 i
11
-3.1168 - 0.3487 i
0.253 + 0.194 i
12
-5.4657
0.197
13
5.5651
1.26 i
14
-21.2317
0.41 i
15
25.827
9.44
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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
1.402 + 0.4786 i
0.102 - 0.142 i
Singularities of quadratic [8, 8, 7] approximant
2
1.402 - 0.4786 i
0.102 + 0.142 i
3
1.6572 + 0.2962 i
0.177 - 0.0555 i
4
1.6572 - 0.2962 i
0.177 + 0.0555 i
5
1.6991 + 0.2784 i
0.153 + 0.207 i
6
1.6991 - 0.2784 i
0.153 - 0.207 i
7
-2.2358 + 0.0388 i
0.00914 + 0.0098 i
8
-2.2358 - 0.0388 i
0.00914 - 0.0098 i
9
2.45
0.626
10
-2.8437 + 0.2503 i
0.0535 + 0.00213 i
11
-2.8437 - 0.2503 i
0.0535 - 0.00213 i
12
-6.1721
0.136
13
7.4051
0.429 i
14
-13.025
2.1 i
15
-5.3574 + 12.0139 i
0.242 + 0.11 i
16
-5.3574 - 12.0139 i
0.242 - 0.11 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
1.3999 + 0.4786 i
0.0943 - 0.129 i
Singularities of quadratic [8, 8, 8] approximant
2
1.3999 - 0.4786 i
0.0943 + 0.129 i
3
1.6959 + 0.2053 i
0.0984 - 0.123 i
4
1.6959 - 0.2053 i
0.0984 + 0.123 i
5
1.8641 + 0.0432 i
0.0544 - 0.0477 i
6
1.8641 - 0.0432 i
0.0544 + 0.0477 i
7
2.0524
0.17
8
-2.2216 + 0.0212 i
0.0185 + 0.0195 i
9
-2.2216 - 0.0212 i
0.0185 - 0.0195 i
10
-2.99 + 0.2892 i
0.14 - 0.0167 i
11
-2.99 - 0.2892 i
0.14 + 0.0167 i
12
-5.3297
0.145
13
5.1123 + 3.1385 i
0.33 + 0.266 i
14
5.1123 - 3.1385 i
0.33 - 0.266 i
15
11.3833 + 4.0629 i
0.434 - 1.33 i
16
11.3833 - 4.0629 i
0.434 + 1.33 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
1.3995 + 0.4789 i
0.094 - 0.126 i
Singularities of quadratic [9, 8, 8] approximant
2
1.3995 - 0.4789 i
0.094 + 0.126 i
3
1.6999
0.0916
4
1.6963 + 0.1859 i
0.0799 - 0.13 i
5
1.6963 - 0.1859 i
0.0799 + 0.13 i
6
2.0335 + 0.2136 i
0.166 + 0.459 i
7
2.0335 - 0.2136 i
0.166 - 0.459 i
8
-2.2214 + 0.0182 i
0.023 + 0.0244 i
9
-2.2214 - 0.0182 i
0.023 - 0.0244 i
10
-3.0001 + 0.2881 i
0.156 - 0.0155 i
11
-3.0001 - 0.2881 i
0.156 + 0.0155 i
12
-5.2291
0.139
13
5.3104 + 3.2716 i
0.236 + 0.347 i
14
5.3104 - 3.2716 i
0.236 - 0.347 i
15
9.0768
2.66 i
16
14.3653 + 18.7943 i
0.438 + 0.491 i
17
14.3653 - 18.7943 i
0.438 - 0.491 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
1.3986 + 0.4792 i
0.0912 - 0.12 i
Singularities of quadratic [9, 9, 8] approximant
2
1.3986 - 0.4792 i
0.0912 + 0.12 i
3
1.5973
0.0663
4
1.7136 + 0.1018 i
0.00559 + 0.121 i
5
1.7136 - 0.1018 i
0.00559 - 0.121 i
6
2.049 + 0.3819 i
1.01 + 0.906 i
7
2.049 - 0.3819 i
1.01 - 0.906 i
8
-2.2222 + 0.0155 i
0.0294 + 0.0319 i
9
-2.2222 - 0.0155 i
0.0294 - 0.0319 i
10
-2.9974 + 0.2804 i
0.161 - 0.00561 i
11
-2.9974 - 0.2804 i
0.161 + 0.00561 i
12
4.2763
0.818 i
13
-5.1829
0.131
14
5.2017 + 1.9406 i
0.132 + 0.433 i
15
5.2017 - 1.9406 i
0.132 - 0.433 i
16
-0.7254 + 16.9538 i
0.258 + 0.206 i
17
-0.7254 - 16.9538 i
0.258 - 0.206 i
18
-111.5683
6.85 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
-0.0469
0
Singularities of quadratic [9, 9, 9] approximant
2
-0.0469
0
3
1.3993 + 0.4791 i
0.0943 - 0.124 i
4
1.3993 - 0.4791 i
0.0943 + 0.124 i
5
1.657
0.0807
6
1.7002 + 0.164 i
0.0547 - 0.132 i
7
1.7002 - 0.164 i
0.0547 + 0.132 i
8
2.0515 + 0.2631 i
0.286 + 0.618 i
9
2.0515 - 0.2631 i
0.286 - 0.618 i
10
-2.2211 + 0.0228 i
0.0167 + 0.0174 i
11
-2.2211 - 0.0228 i
0.0167 - 0.0174 i
12
-2.9911 + 0.2926 i
0.137 - 0.0206 i
13
-2.9911 - 0.2926 i
0.137 + 0.0206 i
14
-5.3476
0.149
15
4.9684 + 2.9007 i
0.349 + 0.305 i
16
4.9684 - 2.9007 i
0.349 - 0.305 i
17
8.1711
0.857 i
18
18.4865
83.5
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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
1.401 + 0.4767 i
0.0848 - 0.146 i
Singularities of quadratic [10, 9, 9] approximant
2
1.401 - 0.4767 i
0.0848 + 0.146 i
3
-1.1091 + 1.2057 i
0.0000518 - 0.0000832 i
4
-1.1091 - 1.2057 i
0.0000518 + 0.0000832 i
5
-1.1092 + 1.2058 i
0.0000832 + 0.0000519 i
6
-1.1092 - 1.2058 i
0.0000832 - 0.0000519 i
7
1.6755 + 0.3016 i
0.213 - 0.0149 i
8
1.6755 - 0.3016 i
0.213 + 0.0149 i
9
1.7154 + 0.3157 i
0.034 + 0.347 i
10
1.7154 - 0.3157 i
0.034 - 0.347 i
11
-2.1995 + 0.125 i
0.00145 + 0.00123 i
12
-2.1995 - 0.125 i
0.00145 - 0.00123 i
13
2.3655
0.577
14
-2.6965 + 0.3858 i
0.00591 - 0.00648 i
15
-2.6965 - 0.3858 i
0.00591 + 0.00648 i
16
5.6643
2.99 i
17
-5.203 + 4.1312 i
0.076 + 0.0166 i
18
-5.203 - 4.1312 i
0.076 - 0.0166 i
19
18.3289
0.529
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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
-0.8903 + 0.e-5 i
6.79e-7 + 6.79e-7 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.8903 - 0.e-5 i
6.79e-7 - 6.79e-7 i
3
1.4034 + 0.4777 i
0.109 - 0.157 i
4
1.4034 - 0.4777 i
0.109 + 0.157 i
5
1.6657 + 0.2644 i
0.223 + 0.102 i
6
1.6657 - 0.2644 i
0.223 - 0.102 i
7
1.6569 + 0.3301 i
0.238 - 0.12 i
8
1.6569 - 0.3301 i
0.238 + 0.12 i
9
-2.1656 + 0.1267 i
0.000951 + 0.000715 i
10
-2.1656 - 0.1267 i
0.000951 - 0.000715 i
11
2.6112
0.889
12
-2.7997 + 0.5338 i
0.00105 - 0.00767 i
13
-2.7997 - 0.5338 i
0.00105 + 0.00767 i
14
-1.6923 + 2.7769 i
0.000665 - 0.00179 i
15
-1.6923 - 2.7769 i
0.000665 + 0.00179 i
16
-1.8264 + 2.784 i
0.00172 + 0.000743 i
17
-1.8264 - 2.784 i
0.00172 - 0.000743 i
18
-3.1324 + 4.5988 i
0.00464 - 0.0145 i
19
-3.1324 - 4.5988 i
0.00464 + 0.0145 i
20
13.7268
0.184 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
-0.0427
0
Singularities of quadratic [10, 10, 10] approximant
2
-0.0427
0
3
-1.0714
2.14e-6
4
-1.0714
2.14e-6 i
5
1.4044 + 0.4789 i
0.13 - 0.155 i
6
1.4044 - 0.4789 i
0.13 + 0.155 i
7
1.6523 + 0.2203 i
0.173 + 0.0381 i
8
1.6523 - 0.2203 i
0.173 - 0.0381 i
9
1.6549 + 0.3036 i
0.183 - 0.143 i
10
1.6549 - 0.3036 i
0.183 + 0.143 i
11
-2.1028
0.0011
12
-2.5264 + 0.1291 i
0.000675 - 0.00214 i
13
-2.5264 - 0.1291 i
0.000675 + 0.00214 i
14
2.6625
1.09
15
-3.3643 + 1.1393 i
0.0158 + 0.0106 i
16
-3.3643 - 1.1393 i
0.0158 - 0.0106 i
17
-0.3189 + 5.7446 i
0.0258 - 0.000901 i
18
-0.3189 - 5.7446 i
0.0258 + 0.000901 i
19
1.8767 + 7.7297 i
0.00614 + 0.0488 i
20
1.8767 - 7.7297 i
0.00614 - 0.0488 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
-0.8089 + 0.4013 i
1.87e-7 - 4.71e-7 i
Singularities of quadratic [11, 10, 10] approximant
2
-0.8089 - 0.4013 i
1.87e-7 + 4.71e-7 i
3
-0.8089 + 0.4013 i
4.71e-7 + 1.87e-7 i
4
-0.8089 - 0.4013 i
4.71e-7 - 1.87e-7 i
5
1.405 + 0.4799 i
0.143 - 0.149 i
6
1.405 - 0.4799 i
0.143 + 0.149 i
7
1.6404 + 0.2157 i
0.171 + 0.0444 i
8
1.6404 - 0.2157 i
0.171 - 0.0444 i
9
1.6397 + 0.3054 i
0.187 - 0.118 i
10
1.6397 - 0.3054 i
0.187 + 0.118 i
11
-2.118
0.00127
12
-2.4962 + 0.1753 i
0.000284 - 0.00295 i
13
-2.4962 - 0.1753 i
0.000284 + 0.00295 i
14
2.8745
2.35
15
-3.8672 + 0.648 i
0.0494 + 0.000725 i
16
-3.8672 - 0.648 i
0.0494 - 0.000725 i
17
2.3465 + 3.7802 i
0.0238 - 0.0126 i
18
2.3465 - 3.7802 i
0.0238 + 0.0126 i
19
1.9906 + 4.4922 i
0.0059 + 0.0233 i
20
1.9906 - 4.4922 i
0.0059 - 0.0233 i
21
-14.8717
9.7 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
0.2028 + 0.8332 i
7.8e-8 + 1.28e-6 i
Singularities of quadratic [11, 11, 10] approximant
2
0.2028 - 0.8332 i
7.8e-8 - 1.28e-6 i
3
0.2028 + 0.8332 i
1.28e-6 - 7.8e-8 i
4
0.2028 - 0.8332 i
1.28e-6 + 7.8e-8 i
5
1.4024 + 0.4769 i
0.0945 - 0.152 i
6
1.4024 - 0.4769 i
0.0945 + 0.152 i
7
1.6552 + 0.3603 i
0.311 - 0.0727 i
8
1.6552 - 0.3603 i
0.311 + 0.0727 i
9
1.674 + 0.3051 i
0.297 + 0.215 i
10
1.674 - 0.3051 i
0.297 - 0.215 i
11
-1.901 + 0.2026 i
0.0000367 + 0.0000674 i
12
-1.901 - 0.2026 i
0.0000367 - 0.0000674 i
13
-2.2092 + 0.2128 i
0.000112 - 6.6e-6 i
14
-2.2092 - 0.2128 i
0.000112 + 6.6e-6 i
15
-2.1788 + 0.8389 i
0.000232 - 7.11e-6 i
16
-2.1788 - 0.8389 i
0.000232 + 7.11e-6 i
17
-2.2701 + 1.0808 i
0.000091 + 0.000416 i
18
-2.2701 - 1.0808 i
0.000091 - 0.000416 i
19
2.6405
0.903
20
-2.8983 + 5.3251 i
0.00228 + 0.0227 i
21
-2.8983 - 5.3251 i
0.00228 - 0.0227 i
22
13.7608
0.176 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
-0.0317 + 0.6927 i
1.18e-7 - 1.71e-7 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.0317 - 0.6927 i
1.18e-7 + 1.71e-7 i
3
-0.0317 + 0.6927 i
1.71e-7 + 1.18e-7 i
4
-0.0317 - 0.6927 i
1.71e-7 - 1.18e-7 i
5
-1.4025
0.0000103
6
-1.4028
0.0000103 i
7
1.4039 + 0.4782 i
0.118 - 0.157 i
8
1.4039 - 0.4782 i
0.118 + 0.157 i
9
1.6597 + 0.2532 i
0.218 + 0.0898 i
10
1.6597 - 0.2532 i
0.218 - 0.0898 i
11
1.6511 + 0.3277 i
0.235 - 0.113 i
12
1.6511 - 0.3277 i
0.235 + 0.113 i
13
-2.0419
0.000417
14
-2.5094 + 0.3054 i
0.000479 + 0.00135 i
15
-2.5094 - 0.3054 i
0.000479 - 0.00135 i
16
2.6661
1.05
17
-2.9328 + 1.3649 i
0.00419 + 0.00257 i
18
-2.9328 - 1.3649 i
0.00419 - 0.00257 i
19
-1.3965 + 5.3019 i
0.0143 + 0.0093 i
20
-1.3965 - 5.3019 i
0.0143 - 0.0093 i
21
-9.9309 + 13.375 i
0.0839 + 0.0148 i
22
-9.9309 - 13.375 i
0.0839 - 0.0148 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.