Calculations of the polycentric linear molecule H32+ with the finite element method

Hackel, Siegfried; Heinemann, Dirk; Kolb, D.; Fricke, B.

doi:10.1016/0009-2614(93)85522-p

Cited by 25 publications

(8 citation statements)

References 15 publications

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“…An ab initio calculation using a finite-element molecular self-consistent field Hartree-Fock-Slater (SCF-HFS) code [9] gives the interaction between two silicon atoms [10]. This pointwise determined interaction potential is approximated by The approximation is based on the Moli6re potential with additional terms to account for the zero crossing and the attractive potential well.…”

Section: Interaction Potentialsmentioning

confidence: 99%

Influence of the interaction potential on simulated sputtering and reflection data

Eckstein

Hackel

Heinemann

et al. 1992

Z Phys D - Atoms, Molecules and Clusters

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Atoms, Molecules zo, ts0. r, , and ClustersAbstract. The TRIM.SP program which is based on the binary collision approximation was changed to handle not only repulsive interaction potentials, but also potentials with an attractive part. Sputtering yields, average depth and reflection coefficients calculated with four different potentials are compared. Three purely repulsive potentials (Moli6re, Kr-C and ZBL) are used and an ab initio pair potential, which is especially calculated for silicon bombardment by silicon. The general trends in the calculated results are similar for all potentials applied, but differences between the repulsive potentials and the ab initio potential occur for the reflection coefficients and the sputtering yield at large angles of incidence.

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Section: Interaction Potentialsmentioning

confidence: 99%

Influence of the interaction potential on simulated sputtering and reflection data

Eckstein

Hackel

Heinemann

et al. 1992

Z Phys D - Atoms, Molecules and Clusters

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“…The lack of a suitable coordinate system makes the application of finite difference methods 9–13 to arbitrary polyatomic molecules computationally intractable with contemporary computing machines. Of the approaches using basis set expansions, the vast majority employ global basis functions rather than the piece‐wise functions, which are characteristic of the finite element method 14–17. What is more, of the global basis sets suggested over the years the Gaussian‐type function 18–20 has assumed a dominant position because of the ease and accuracy with which the associated molecular integrals can be evaluated 21.…”

Section: Introductionmentioning

confidence: 99%

Generation of systematic sequences of even‐tempered basis sets: Empirical generating formulae

Kryachko

Wilson

2003

Int J of Quantum Chemistry

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“…Over the past decade, fully numerical Hartree-Fock calculations for diatomic molecules have been reported using first finite difference methods [47][48][49][50] and then finite element techniques [51][52][53][54]. Most of these calculations have been formulated within the framework of non-relativistic quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

On the accuracy of the algebraic approximation in molecular electronic structure calculations: V. Electron correlation in the ground state of the nitrogen molecule

Moncrieff

Wilson

1996

J. Phys. B: At. Mol. Opt. Phys.

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Many-body perturbation theory, formulated within the algebraic approximation, is used to determine the correlation energy of the ground state of the nitrogen molecule. Systematically constructed even-tempered basis sets of Gaussian-type functions, which have been shown to achieve an accuracy approaching Hartree in matrix Hartree - Fock calculations, have been developed to afford basis sets suitable for electron correlation studies using the second-order many-body perturbation expansion. Over 98% of an empirical estimate of the ground-state correlation energy of the molecule at its equilibrium geometry is recovered by using a basis set constructed from even-tempered sets centred on the atoms and on the bond midpoint and containing functions of s, p, d, f, g and h symmetry. The importance of functions with i symmetry is also assessed. It is estimated that the calculated correlation energy corresponds to 99.1% of the exact second-order energy. The correlation energy obtained in the present study is compared with second-order energies obtained by using previously reported basis sets, which are shown to recover, at best, about 10% less of the empirical correlation energy estimate.

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Calculations of the polycentric linear molecule H32+ with the finite element method

Cited by 25 publications

References 15 publications

Influence of the interaction potential on simulated sputtering and reflection data

Influence of the interaction potential on simulated sputtering and reflection data

Generation of systematic sequences of even‐tempered basis sets: Empirical generating formulae

On the accuracy of the algebraic approximation in molecular electronic structure calculations: V. Electron correlation in the ground state of the nitrogen molecule

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