Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon

We present a density-functional-based scheme for determining the necessary parameters of common nonorthogonal tight-binding (TB) models within the framework of the linear-combination-of-atomic-orbitals formalism using the local-density approximation (LDA). By only considering two-center integrals the Hamiltonian and overlap matrix elements are calculated out of suitable input densities and potentials rather than fitted to experimental data. We can derive analytical functions for the C-C, C-H, and H-H Hamiltonian and overlap matrix elements. The usual short-range repulsive potential appearing in most TB models is fitted to self-consistent calculations performed within the LDA. The calculation of forces is easy and allows an application of the method to molecular-dynamics simulations. Despite its extreme simplicity, the method is transferable to complex carbon and hydrocarbon systems. The determination of equilibrium geometries, total energies, and vibrational modes of carbon clusters, hydrocarbon molecules, and solid-state modifications of carbon yield results showing an overall good agreement with more sophisticated methods.