Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 1.3r_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
1.233
0.199
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
1.1575
0.176
Singularities of quadratic [1, 1, 0] approximant
2
1198.3081
5.65 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
1.5179
0.527
Singularities of quadratic [1, 1, 1] approximant
2
-4.8955
0.463
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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
1.5502
0.587
Singularities of quadratic [2, 1, 1] approximant
2
-5.807
0.54
3
21.7244
0.406 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
1.7143
2.18
Singularities of quadratic [2, 2, 1] approximant
2
-2.7584
0.0952
3
-5.698
0.112 i
4
16.2488
0.33 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
2.0087 + 0.3246 i
1.85 + 0.054 i
Singularities of quadratic [2, 2, 2] approximant
2
2.0087 - 0.3246 i
1.85 - 0.054 i
3
3.7579
3.04
4
-4.0709
0.242
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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
0.8619 + 0.0092 i
0.00917 - 0.00898 i
Singularities of quadratic [3, 2, 2] approximant
2
0.8619 - 0.0092 i
0.00917 + 0.00898 i
3
1.9506
4.34
4
-5.0511 + 1.6464 i
0.403 + 0.00263 i
5
-5.0511 - 1.6464 i
0.403 - 0.00263 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
1.562 + 0.3837 i
0.261 - 0.352 i
Singularities of quadratic [3, 3, 2] approximant
2
1.562 - 0.3837 i
0.261 + 0.352 i
3
1.7574
0.318
4
-3.3813
0.137
5
-13.2423
0.2 i
6
20.8571
0.36 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
1.5624 + 0.3729 i
0.251 - 0.396 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5624 - 0.3729 i
0.251 + 0.396 i
3
1.7447
0.324
4
-3.3836
0.14
5
-11.8995
0.198 i
6
27.0538
0.355 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
1.5395 + 0.4438 i
0.219 - 0.12 i
Singularities of quadratic [4, 3, 3] approximant
2
1.5395 - 0.4438 i
0.219 + 0.12 i
3
1.7587
0.258
4
-3.1824
0.0856
5
-0.3664 + 10.3833 i
0.0782 + 0.163 i
6
-0.3664 - 10.3833 i
0.0782 - 0.163 i
7
19.2967
0.384 i
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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
1.5453 + 0.4359 i
0.236 - 0.139 i
Singularities of quadratic [4, 4, 3] approximant
2
1.5453 - 0.4359 i
0.236 + 0.139 i
3
1.7557
0.265
4
-3.1303
0.0768
5
-3.9659 + 7.343 i
0.0488 + 0.144 i
6
-3.9659 - 7.343 i
0.0488 - 0.144 i
7
-15.2863
0.679 i
8
29.8872
0.395 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
1.3412 + 0.5848 i
0.0185 + 0.00451 i
Singularities of quadratic [4, 4, 4] approximant
2
1.3412 - 0.5848 i
0.0185 - 0.00451 i
3
1.4751
0.0375
4
1.2117 + 1.2064 i
0.00897 - 0.00167 i
5
1.2117 - 1.2064 i
0.00897 + 0.00167 i
6
1.1277 + 1.3325 i
0.0000775 - 0.00962 i
7
1.1277 - 1.3325 i
0.0000775 + 0.00962 i
8
-3.0507
0.0522
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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
1.5061 + 0.5138 i
0.105 + 0.0159 i
Singularities of quadratic [5, 4, 4] approximant
2
1.5061 - 0.5138 i
0.105 - 0.0159 i
3
1.6133
0.13
4
-0.3379 + 1.9366 i
0.00519 - 0.00102 i
5
-0.3379 - 1.9366 i
0.00519 + 0.00102 i
6
-0.2954 + 1.9444 i
0.00117 + 0.00522 i
7
-0.2954 - 1.9444 i
0.00117 - 0.00522 i
8
-2.9532
0.0375
9
-33.1075
0.495 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
1.4701 + 0.4761 i
0.0982 - 0.0434 i
Singularities of quadratic [5, 5, 4] approximant
2
1.4701 - 0.4761 i
0.0982 + 0.0434 i
3
1.664
0.135
4
2.2602
259. i
5
-2.4089
0.0184
6
-2.6326
0.02 i
7
3.2629
4.14
8
-4.9251
0.544
9
-7.6055
0.123 i
10
12.4709
0.295 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
1.4691 + 0.4799 i
0.0954 - 0.0385 i
Singularities of quadratic [5, 5, 5] approximant
2
1.4691 - 0.4799 i
0.0954 + 0.0385 i
3
1.6531
0.132
4
-2.3614
0.0176
5
2.3776
13.3 i
6
-2.5366
0.019 i
7
3.828
1.02e3
8
-4.2944
30.9
9
8.0152
0.329 i
10
-11.3258
0.143 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
1.4832 + 0.4633 i
0.118 - 0.0777 i
Singularities of quadratic [6, 5, 5] approximant
2
1.4832 - 0.4633 i
0.118 + 0.0777 i
3
1.7529
0.191
4
-2.3477
0.145
5
-2.3768
0.172 i
6
2.5782
6.46 i
7
-3.6588
0.2
8
3.6606 + 1.7569 i
0.416 - 0.429 i
9
3.6606 - 1.7569 i
0.416 + 0.429 i
10
-9.122
0.333 i
11
17.8578
1.44
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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
1.49 + 0.4553 i
0.128 - 0.107 i
Singularities of quadratic [6, 6, 5] approximant
2
1.49 - 0.4553 i
0.128 + 0.107 i
3
1.8213
0.229
4
-2.3584
0.0527
5
-2.4267
0.0557 i
6
2.7209 + 1.5545 i
0.194 + 0.31 i
7
2.7209 - 1.5545 i
0.194 - 0.31 i
8
3.2277 + 0.4442 i
0.433 + 0.0792 i
9
3.2277 - 0.4442 i
0.433 - 0.0792 i
10
-3.8526
0.455
11
-8.8754
0.221 i
12
41.3454
0.521 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
1.511 + 0.4826 i
0.181 - 0.00669 i
Singularities of quadratic [6, 6, 6] approximant
2
1.511 - 0.4826 i
0.181 + 0.00669 i
3
1.6581 + 0.2539 i
0.264 + 0.274 i
4
1.6581 - 0.2539 i
0.264 - 0.274 i
5
1.9846
9.22
6
-2.3282
0.0195
7
-2.4593
0.0209 i
8
2.5718
0.942 i
9
-3.9845
2.48
10
4.9357 + 1.7038 i
0.12 + 0.429 i
11
4.9357 - 1.7038 i
0.12 - 0.429 i
12
-16.2518
0.161 i
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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
1.4967 + 0.4414 i
0.106 - 0.172 i
Singularities of quadratic [7, 6, 6] approximant
2
1.4967 - 0.4414 i
0.106 + 0.172 i
3
1.9022
0.338
4
1.9543 + 0.6658 i
0.184 + 0.231 i
5
1.9543 - 0.6658 i
0.184 - 0.231 i
6
-2.3691 + 0.0467 i
0.0203 + 0.0209 i
7
-2.3691 - 0.0467 i
0.0203 - 0.0209 i
8
2.2623 + 0.7576 i
0.412 + 0.0231 i
9
2.2623 - 0.7576 i
0.412 - 0.0231 i
10
-3.5839
0.114
11
5.7119
4.34 i
12
-7.4516
0.556 i
13
27.3161
1.67
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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
1.5043 + 0.4552 i
0.187 - 0.114 i
Singularities of quadratic [7, 7, 6] approximant
2
1.5043 - 0.4552 i
0.187 + 0.114 i
3
1.9971 + 0.238 i
0.31 - 0.0124 i
4
1.9971 - 0.238 i
0.31 + 0.0124 i
5
-2.2792
0.00716
6
-2.5651
0.00669 i
7
2.5083 + 0.9743 i
0.311 - 0.282 i
8
2.5083 - 0.9743 i
0.311 + 0.282 i
9
-3.3994 + 0.9212 i
0.0226 - 0.00537 i
10
-3.3994 - 0.9212 i
0.0226 + 0.00537 i
11
3.5967
1.22
12
-4.6633 + 0.5845 i
0.0772 - 0.119 i
13
-4.6633 - 0.5845 i
0.0772 + 0.119 i
14
30.2916
0.383 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

Plot of singularities Blank Molecule - icon for Allen-dataList of examples Blank Mathematica programs Blank Work in UMassD Blank Waste iconUnpublished reports

Designed by A. Sergeev.