Singularities of Møller-Plesset series: example "BH aug-cc-pVQZ 1.6r_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
1.141
0.191
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
1.0283
0.156
Singularities of quadratic [1, 1, 0] approximant
2
400.566
3.07 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
1.4552
0.672
Singularities of quadratic [1, 1, 1] approximant
2
-3.5359
0.326
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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
1.5574
1.03
Singularities of quadratic [2, 1, 1] approximant
2
-4.6125
0.406
3
8.8986
0.394 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
2.022
5.59
Singularities of quadratic [2, 2, 1] approximant
2
-2.0437
0.0576
3
-4.1823
0.0749 i
4
5.7748
0.212 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
1.7144 + 0.6576 i
0.532 - 0.0116 i
Singularities of quadratic [2, 2, 2] approximant
2
1.7144 - 0.6576 i
0.532 + 0.0116 i
3
-3.0853
0.173
4
3.6999
2.33
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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
1.2057 + 0.088 i
0.0494 - 0.0377 i
Singularities of quadratic [3, 2, 2] approximant
2
1.2057 - 0.088 i
0.0494 + 0.0377 i
3
2.7695
0.305
4
-3.5035 + 1.4553 i
0.197 + 0.0453 i
5
-3.5035 - 1.4553 i
0.197 - 0.0453 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
1.5739 + 0.4336 i
0.453 - 0.915 i
Singularities of quadratic [3, 3, 2] approximant
2
1.5739 - 0.4336 i
0.453 + 0.915 i
3
1.9684
0.494
4
-2.8683
0.156
5
-12.0677
0.203 i
6
28.1525
0.397 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
1.5029 + 0.559 i
0.273 - 0.0834 i
Singularities of quadratic [3, 3, 3] approximant
2
1.5029 - 0.559 i
0.273 + 0.0834 i
3
1.8338
0.382
4
-2.7938
0.117
5
4.0953
0.581 i
6
18.458
1.15
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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
1.5629 + 0.462 i
0.409 - 0.675 i
Singularities of quadratic [4, 3, 3] approximant
2
1.5629 - 0.462 i
0.409 + 0.675 i
3
2.0403
0.488
4
-2.9893
0.212
5
-7.2883
0.271 i
6
8.7326
0.554 i
7
85.5599
55.9
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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
-0.6641 + 0.e-4 i
0.000432 + 0.000432 i
Singularities of quadratic [4, 4, 3] approximant
2
-0.6641 - 0.e-4 i
0.000432 - 0.000432 i
3
1.5733 + 0.5059 i
0.597 - 0.163 i
4
1.5733 - 0.5059 i
0.597 + 0.163 i
5
1.8543
0.447
6
-3.0066
0.269
7
-9.1279
0.183 i
8
23.479
0.361 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
1.0837
0.0147
Singularities of quadratic [4, 4, 4] approximant
2
1.0983
0.0148 i
3
1.5967
0.205
4
1.6598 + 0.5521 i
0.208 + 0.515 i
5
1.6598 - 0.5521 i
0.208 - 0.515 i
6
-3.1604
0.477
7
-5.4642
0.269 i
8
-31.4043
3.81
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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
1.3832
0.0391
Singularities of quadratic [5, 4, 4] approximant
2
1.4341
0.0455 i
3
1.4274 + 0.4729 i
0.0437 - 0.12 i
4
1.4274 - 0.4729 i
0.0437 + 0.12 i
5
-3.0175
0.211
6
3.7722 + 0.88 i
0.068 - 1.52 i
7
3.7722 - 0.88 i
0.068 + 1.52 i
8
-5.95
0.422 i
9
99.335
6.63
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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
0.8201
0.000464
Singularities of quadratic [5, 5, 4] approximant
2
0.8203
0.000464 i
3
1.4255 + 0.4367 i
0.0311 + 0.107 i
4
1.4255 - 0.4367 i
0.0311 - 0.107 i
5
-2.0037
0.00642
6
-2.04
0.00658 i
7
2.9583
1.34
8
-3.512
2.27
9
8.7742
0.333 i
10
-10.157
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
0.8062
0.000423
Singularities of quadratic [5, 5, 5] approximant
2
0.8064
0.000423 i
3
1.4253 + 0.4363 i
0.0321 + 0.106 i
4
1.4253 - 0.4363 i
0.0321 - 0.106 i
5
-1.9632
0.00576
6
-1.9946
0.00589 i
7
2.9676
1.37
8
-3.4933
2.85
9
8.6738
0.335 i
10
-10.2115
0.134 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
0.919
0.000989
Singularities of quadratic [6, 5, 5] approximant
2
0.9196
0.00099 i
3
1.4249 + 0.4403 i
0.0227 + 0.107 i
4
1.4249 - 0.4403 i
0.0227 - 0.107 i
5
-1.7475
0.00392
6
-1.7585
0.00395 i
7
2.969
1.26
8
-3.3111
11.5
9
7.7127
0.457 i
10
-8.2157
0.158 i
11
-6412.2289
856.
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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
0.7544 + 0.3204 i
0.000253 + 0.000477 i
Singularities of quadratic [6, 6, 5] approximant
2
0.7544 - 0.3204 i
0.000253 - 0.000477 i
3
0.7545 + 0.3204 i
0.000477 - 0.000253 i
4
0.7545 - 0.3204 i
0.000477 + 0.000253 i
5
1.4248 + 0.4329 i
0.0392 + 0.103 i
6
1.4248 - 0.4329 i
0.0392 - 0.103 i
7
-1.9083
0.00524
8
-1.9328
0.00533 i
9
2.9555
1.38
10
-3.4523
6.03
11
8.9436
0.324 i
12
-9.8932
0.134 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
1.4795
0.0695
Singularities of quadratic [6, 6, 6] approximant
2
1.4364 + 0.4612 i
0.0307 - 0.158 i
3
1.4364 - 0.4612 i
0.0307 + 0.158 i
4
1.5338
0.0827 i
5
-2.1091 + 0.0165 i
0.0108 + 0.0109 i
6
-2.1091 - 0.0165 i
0.0108 - 0.0109 i
7
2.7641 + 1.2451 i
0.163 + 0.331 i
8
2.7641 - 1.2451 i
0.163 - 0.331 i
9
-3.0734
0.121
10
-4.0579
769. i
11
5.9422
0.379
12
-9.5671
0.431
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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
1.1645 + 0.0017 i
0.00206 - 0.00204 i
Singularities of quadratic [7, 6, 6] approximant
2
1.1645 - 0.0017 i
0.00206 + 0.00204 i
3
1.4114 + 0.4746 i
0.0278 - 0.0719 i
4
1.4114 - 0.4746 i
0.0278 + 0.0719 i
5
-2.1683
0.00774
6
-2.2649
0.0083 i
7
2.3602 + 0.3197 i
0.434 - 0.729 i
8
2.3602 - 0.3197 i
0.434 + 0.729 i
9
-4.2734
0.128
10
4.711
0.329
11
-0.3816 + 8.7254 i
0.0408 + 0.0595 i
12
-0.3816 - 8.7254 i
0.0408 - 0.0595 i
13
12.8066
0.118 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
1.4267 + 0.0096 i
0.0155 - 0.0145 i
Singularities of quadratic [7, 7, 6] approximant
2
1.4267 - 0.0096 i
0.0155 + 0.0145 i
3
1.4287 + 0.4813 i
0.0676 - 0.0954 i
4
1.4287 - 0.4813 i
0.0676 + 0.0954 i
5
-2.2019
0.0108
6
-2.2961
0.0114 i
7
2.3919 + 0.5698 i
1.01 - 0.493 i
8
2.3919 - 0.5698 i
1.01 + 0.493 i
9
2.8619
13.5
10
-4.3398 + 0.9171 i
0.0332 + 0.0851 i
11
-4.3398 - 0.9171 i
0.0332 - 0.0851 i
12
-6.4233 + 3.2725 i
0.0728 - 0.126 i
13
-6.4233 - 3.2725 i
0.0728 + 0.126 i
14
16.768
0.274 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

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