Dirk Heinemann

All-electron Dirac—Fock—Slater SCF calculations of the Au2 molecule

Abstract All-electron Dirac—Fock—Slater SCF clculations of the Au 2 molecule have been carried out using relativistic numerical atomic basis functions. In order to get a numerically accurate potential energy curve an improved calculation of the direct Coulomb potential has been taken into account. The relativistic effect inthe binding energy, the bond distance and the vibration frequency of the ground state potential energy curve have been studied in comparison with consistent non-relativistic results.

H2 solved by the finite element method

Abstract We report on the solution of the Hartree-Fock equations for the ground state of the H 2 molecule using the finite element method. Both the Hartree-Fock and the Poisson equations are solved with this method to an accuracy of 10 −8 using only 26 × 11 grid points in two dimensions. A 41 × 16 grid gives a new Hartree-Fock benchmark to ten-figure accuracy.

Accurate Hartree-Fock-Slater calculations on small diatomic molecules with the finite-element method

We report on the self-consistent field solution of the Hartree-Fock-Slater equations using the finite-element method for the three small diatomic molecules N2, BH and CO as examples. The quality of the results is not only better by two orders of magnitude than the fully numerical finite difference method of Laaksonen et al. but the method also requires a smaller number of grid points.

Relativistic self-consistent calculations for small diatomic molecules by the finite element method

Abstract A two-dimensional, fully numerical approach to the four-component first-order Dirac equation using the finite element method is employed for diatomic systems. Using the Dirac—Fock approximation with only 2116 grid points we achieve for H 2 an absolute accuracy of about 10 −10 au for the ground-state total energy. For the many-electron systems Li 2 and BH, we obtain a similar accuracy within the Dirac—Fock—Slater approximation which allows us to determine the relativistic contribution to the total as well as orbital energies very precisely.

An accurate solution of the two-centre Dirac equation for H+2 by the finite-element method

Abstract A two-dimensional, fully numerical approach to the four-component Dirac equation using the finite-element method (FEM) is employed for a diatomic system. For H + 2 , an absolute accuracy of about 10 −10 au for the 1σ g orbital energy is obtained by using only 2601 grid points. Using a difference method, the relativistic energy correction can be calculated with an accuracy of about 10 −13 au.

Influence of the interaction potential on simulated sputtering and reflection data

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 (Molière, 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.

Solution of the one-electron Dirac equation for the heavy diatomic quasi-molecule NiPb109+ by the finite element method

Abstract A two-dimensional, fully numerical approach to the four-component first-order Dirac equation using the finite element method is employed for diatomic systems. Using the Dirac-Fock approximation with only 2601 grid points we achieve for the heavy quasi-molecule NiPb 109+ at R = 0.002 au a relative accuracy better than 10 −8 for orbital energies (nuclear repulsion energies ignored).

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

Abstract A fully numerical two-dimensional solution of the Schrodinger equation is presented for the linear polyatomic molecule H 3 2+ using the finite element method (FEM). The Coulomb singularities at the nuclei are rectified by using both a condensed element distribution around the singularities and special elements. The accuracy of the results for the lσ and 2σ orbitals is of the order of 10 −7 au.

Dirac–Fock–Slater calculations for diatomic molecules with a finite element defect correction method (FEM-DKM)

Abstract The finite element method (FEM) has been developed into an accurate tool for non-relativistic and relativistic single-particle type descriptions of atoms and diatomic molecules, which has become quite fast. Nevertheless, the efficiency remained unsatisfactory in that most of the FEM points were used up in the core regions even though the molecular orbitals there are atomic-like and simply structured. The joint functional set consisting of atomic orbitals used for an LCAO trial wavefunction and the finite element basis for good convergence, employed as a defect correction method (DKM), remedies this deficiency; the computational effort scales basically linearly with the number of FEM points. Using the DKM we reached the same accuracy about an order faster than with pure FEM.

Total differential scattering cross section of Ar+-Ar at 15 to 400 keV

Abstract We report on the measurement of the total differential scattering cross section of Ar+-Ar at laboratory energies between 15 and 400 keV. Using an ab initio relativistic molecular program which calculates the interatomic potential energy curve with high accuracy, we are able to reproduce the detailed structure found in the experiment.