Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 1.5r_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 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 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-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 [1, 0, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.1703
0.193
Singularities of quadratic [1, 0, 0] approximant
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Table 2. Singularities with their weights for the quadratic approximant [1, 1, 0]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.0722
0.163
Singularities of quadratic [1, 1, 0] approximant
2
584.5263
3.8 i
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Table 3. Singularities with their weights for the quadratic approximant [1, 1, 1]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4833
0.631
Singularities of quadratic [1, 1, 1] approximant
2
-3.8947
0.358
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Table 4. Singularities with their weights for the quadratic approximant [2, 1, 1]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.569
0.879
Singularities of quadratic [2, 1, 1] approximant
2
-5.1211
0.453
3
10.0816
0.408 i
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Table 5. Singularities with their weights for the quadratic approximant [2, 2, 1]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.9292
112.
Singularities of quadratic [2, 2, 1] approximant
2
-2.1913
0.0618
3
-4.3172
0.0779 i
4
7.4162
0.231 i
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Table 6. Singularities with their weights for the quadratic approximant [2, 2, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.792 + 0.6109 i
0.642 - 0.0462 i
Singularities of quadratic [2, 2, 2] approximant
2
1.792 - 0.6109 i
0.642 + 0.0462 i
3
-3.3875
0.192
4
3.6774
2.17
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Table 7. Singularities with their weights for the quadratic approximant [3, 2, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.1573 + 0.0605 i
0.0343 - 0.0291 i
Singularities of quadratic [3, 2, 2] approximant
2
1.1573 - 0.0605 i
0.0343 + 0.0291 i
3
2.5199
0.396
4
-3.9014 + 1.5658 i
0.23 + 0.0424 i
5
-3.9014 - 1.5658 i
0.23 - 0.0424 i
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Table 8. Singularities with their weights for the quadratic approximant [3, 3, 2]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5929 + 0.418 i
0.421 - 0.806 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5929 - 0.418 i
0.421 + 0.806 i
3
1.8993
0.481
4
-3.0555
0.153
5
-12.5846
0.205 i
6
25.4153
0.381 i
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Table 9. Singularities with their weights for the quadratic approximant [3, 3, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5811 + 0.4668 i
0.468 - 0.369 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5811 - 0.4668 i
0.468 + 0.369 i
3
1.8703
0.438
4
-3.0271
0.136
5
10.1923
0.367 i
6
-28.1768
0.198 i
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Table 10. Singularities with their weights for the quadratic approximant [4, 3, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.5864 + 0.4483 i
0.47 - 0.534 i
Singularities of quadratic [4, 3, 3] approximant
2
1.5864 - 0.4483 i
0.47 + 0.534 i
3
1.9004
0.458
4
-3.0672
0.153
5
11.6179
0.395 i
6
-13.2196
0.221 i
7
91.058
3.82
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Table 11. Singularities with their weights for the quadratic approximant [4, 4, 3]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.4704
0.000497
Singularities of quadratic [4, 4, 3] approximant
2
0.4704
0.000497 i
3
1.6021 + 0.4646 i
0.666 - 0.262 i
4
1.6021 - 0.4646 i
0.666 + 0.262 i
5
1.8156
0.418
6
-3.1115
0.181
7
-10.9811
0.197 i
8
25.6846
0.382 i
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Table 12. Singularities with their weights for the quadratic approximant [4, 4, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.7506
0.00354
Singularities of quadratic [4, 4, 4] approximant
2
0.7509
0.00354 i
3
1.6123 + 0.4647 i
0.765 - 0.153 i
4
1.6123 - 0.4647 i
0.765 + 0.153 i
5
1.7867
0.398
6
-3.1258
0.19
7
-9.9054
0.199 i
8
36.4271
0.386 i
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Table 13. Singularities with their weights for the quadratic approximant [5, 4, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
1.4166
0.0465
Singularities of quadratic [5, 4, 4] approximant
2
1.3716 + 0.5541 i
0.0381 - 0.0214 i
3
1.3716 - 0.5541 i
0.0381 + 0.0214 i
4
2.4222
0.746 i
5
1.9089 + 1.9271 i
0.0249 - 0.0736 i
6
1.9089 - 1.9271 i
0.0249 + 0.0736 i
7
-2.994
0.105
8
3.638
0.125
9
-9.6549
0.4 i
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Table 14. 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
1.2439
0.00883
Singularities of quadratic [5, 5, 4] approximant
2
1.2635
0.0092 i
3
1.4154 + 0.4464 i
0.0119 - 0.0699 i
4
1.4154 - 0.4464 i
0.0119 + 0.0699 i
5
-2.3417
0.017
6
-2.5006
0.0186 i
7
2.9629
1.34
8
-3.91
1.16
9
9.7441
0.321 i
10
-9.9547
0.133 i
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Table 15. 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
1.2231
0.00789
Singularities of quadratic [5, 5, 5] approximant
2
1.2424
0.0082 i
3
1.4111 + 0.445 i
0.00902 - 0.0664 i
4
1.4111 - 0.445 i
0.00902 + 0.0664 i
5
-2.2632
0.0141
6
-2.3811
0.0151 i
7
3.0442
1.62
8
-3.7605
3.14
9
8.631
0.343 i
10
-11.2299
0.141 i
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Table 16. 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
1.375
0.0233
Singularities of quadratic [6, 5, 5] approximant
2
1.4221
0.0267 i
3
1.4251 + 0.459 i
0.0321 - 0.08 i
4
1.4251 - 0.459 i
0.0321 + 0.08 i
5
-2.1137
0.0178
6
-2.1542
0.0184 i
7
3.2504
1.73
8
-3.346
0.638
9
5.7403
1.16 i
10
-8.3498
0.227 i
11
77.0705
48.2
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Table 17. 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
1.4997 + 0.5201 i
0.228 + 0.0433 i
Singularities of quadratic [6, 6, 5] approximant
2
1.4997 - 0.5201 i
0.228 - 0.0433 i
3
1.6162 + 0.3759 i
0.599 + 0.529 i
4
1.6162 - 0.3759 i
0.599 - 0.529 i
5
1.7755 + 0.6003 i
0.355 - 0.207 i
6
1.7755 - 0.6003 i
0.355 + 0.207 i
7
-2.2035
0.017
8
-2.2751
0.0177 i
9
2.6023
1.18
10
-3.5503
9.9
11
-9.4054
0.151 i
12
12.9438
0.292 i
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Table 18. 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
1.4553 + 0.4648 i
0.0706 - 0.145 i
Singularities of quadratic [6, 6, 6] approximant
2
1.4553 - 0.4648 i
0.0706 + 0.145 i
3
1.6343
0.12
4
1.79
0.235 i
5
-2.2388
0.138
6
-2.2572
0.145 i
7
2.5819 + 1.2124 i
0.272 + 0.221 i
8
2.5819 - 1.2124 i
0.272 - 0.221 i
9
-3.3762
0.4
10
3.9932
0.375
11
-6.0539
0.303 i
12
-39.2805
8.06
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Table 19. 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
1.4501 + 0.4876 i
0.0945 - 0.0678 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4501 - 0.4876 i
0.0945 + 0.0678 i
3
1.592 + 0.0578 i
0.0639 - 0.0396 i
4
1.592 - 0.0578 i
0.0639 + 0.0396 i
5
-2.2336
0.012
6
-2.3514
0.0128 i
7
2.3799 + 0.5612 i
0.394 - 0.794 i
8
2.3799 - 0.5612 i
0.394 + 0.794 i
9
3.6406
1.66
10
-3.9315
0.672
11
-6.5589 + 14.3927 i
0.00828 + 0.111 i
12
-6.5589 - 14.3927 i
0.00828 - 0.111 i
13
35.7689
0.257 i
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Table 20. 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
1.4561 + 0.4832 i
0.108 - 0.088 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4561 - 0.4832 i
0.108 + 0.088 i
3
1.6533 + 0.0627 i
0.0849 - 0.0508 i
4
1.6533 - 0.0627 i
0.0849 + 0.0508 i
5
-2.2404
0.0129
6
-2.3574
0.0135 i
7
2.3797 + 0.659 i
0.682 - 0.658 i
8
2.3797 - 0.659 i
0.682 + 0.658 i
9
3.0317
8.21
10
-4.1397
0.284
11
-6.5999
0.1 i
12
-6.653 + 3.9815 i
0.0537 - 0.115 i
13
-6.653 - 3.9815 i
0.0537 + 0.115 i
14
18.6218
0.281 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 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 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-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

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Designed by A. Sergeev.