Investigation of Crystalline Quartz and Molecular Silicon-Oxygen Compounds with a Simplified Lcao-Lda Method
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other calculations and with experiments. We will show that the quality of the results can be improved for solid as well as molecular systems if the 3d valence states of Si are considered. Finally a summary is given. METHOD AND PRACTICAL REALIZATION The method is based on an LCAO ansatz of the Kohn-Sham wave functions. Atomiclike wave functions - centered at the atomic sites - as linear combinations of Slater-type orbitals are used as basis functions. They are obtained by self-consistent atomic calculations within the local density approximation (LDA). The effective Kohn-Sham potential in a next step is approximated as a simple superposition of the potentials of the neutral atoms. Consistent with this approximation - see [10] - , only two-centre Hamiltonian matrix elements are considered. All these two-centre terms h,•, and the overlap matrix elements S,,, are calculated using potentials and wave functions from LDA-density functional theory (DFT) rather than fitted as in parametrized empirical schemes. This consideration of only two-center terms leads to a Hamiltonian matrix similar to empirically parametrized non-orthogonal TB. To impove the quality of the results, we use instead of free atoms slightly "compressed" atoms, which are achieved by using an additional confinement potential of the form (r/ro)n in the atomic scf calculations. Such potential originally was introduced by Eschrig [11] in favor of an optimization of LCAO-LDA band structure calculations in metals. The confinement radius r0 is related to the covalent radius of the particular atom type. The corresponding contracted valence electron orbitals are then used as a basis set to represent the wavefunctions for the extended systems. After solving the general eigenvalue problem for the determination of the single particle energies and eigenstates of the system, the total energy is written as the sum of a "bandstructure energy" (sum of occupied Kohn-Sham energies) and a repulsive two-particle interaction [6, 12]. Following Ref. [5], the repulsive energies for the different atom-type combinations are derived as universal short range pair potentials from fitting the differences between the bandstructure energies of proper molecular and crystalline reference systems and the corresponding scf-LDA cohesive energy curves. The presented scheme can be viewed as a "hybrid" between an ab initio method - based on density functional theory - and the usage of purely empirical schemes. The results for Si-Si, H-H and Si-H have been presented recently [13]. For the construction of the 0-0 and 0-H repulsive potentials, again as reference structures the dimers 02 and OH were chosen. For Si-O, instead of the dimer a tetrahedral SiO0- cluster - with the Si atom in the center - has been used. This cluster anion is a "closed-shell" system and appears as structural unit in the Si0 2 crystals as quartz and stishovite and in Silicates as well. The SiO4- cluster was embedded in the potential of four neutralizing positive point charges surrounding the system, which simulates the s
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