A Selfconsistent-Charge Density-Functional Tight-Binding Scheme
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ABSTRACT We present an extension to the tight-binding (TB) approach to improve total energies, forces and transferability in the presence of considerable long-range Coulomb interactions. We derive an approximate energy expression in terms of charge density fluctuations 6n at a reference (input) density no, which is a second order approximation to the total energy expression in density functional theory (DFT). With the choice of no as a superposition of densities of neutral atomic fragments, we can define a repulsive potential as in standard TB theory, which is pairwise, short ranged and transferable. The zero order terms in the total energy expression are recoverd as the standard terms of our density-functional based tight-binding (DF-TB). For the second order terms, the charge density fluctuations 6n are approximated by the total charge fluctuation Aq, at atom a, which is qualitatively estimated by employing the Mullikan charge analysis. Within this approximations the total energy expression contains new parameters, which are related to ab-intio DFT calculations. Finally, by introducing localized basis functions and applying the variational principle we arrive at the Hamilton matrix elements, wich themselves depend on the charge fluctuations and, therefore, the general eigenvalue problem has to be solved self-consistently. To obtain forces for efficient geometry relaxation and molecular-dyamics, we calculated analytical derivatives of the total energy with respect to the atomic sites. In order to demonstrate the strenghts of our self-consistent-charge tight-binding (SCC-TB), we calculated reaction energies, geometries and vibrational frequencies for a large set of molecules and compare the results to semi-empirical methods, density-functional calculations and experiment. I. INTRODUCTION It has been shown that the TB-approach in general may be understood as a stationary approximation to density-functional theory (DFT) (1, 2, 3, 4, 5]. Central features of the common methodology, namely, non-selfconsistent treatment of the Kohn-Sham equations and the exploitation of pairwise repulsive interactions are strongly related to an appropriate "educated guess" for the inital charge density of the system. In standard tight-binding theory, the calculated total energy differs from the true ground state energy in second order of the charge density fluctuations, which can be shown to be small for a properly chosen input density. For an input density, which is the superposition of the electronic density of neutral atomic fragments, a repulsive part in the total energy expression can be defined, which is pairwise, short ranged and depends only on the chosen input density [2]. In heteronuclear systems with considerable charge transfer, where the groundstate density may not be representable as a superposition of neutral atomic fragment densities, i.e. the initial charge density is not close to the ground state density, the second order corrections may become important. On the other hand, choosing an input density close to the true gr
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