Efficient Electronic Energy Functionals for Tight-Binding

ABSTRACTGeneralized functionals are constructed from the exchange-correlation energy by a Legendre transformation which makes the new functionals stationary at the electronic charge density, potential, and wave functions for the ground-state. Using generalized functionals, the density, potential, and wave functions can be independently parameterized and varied to determine the ground-state energy-surface for a system of atoms. This eliminates the computationally awkward steps of constructing densities from wave functions or potentials from densities, and is particularly well suited to parameterizations using tight-binding orbitale together with atomic-like densities and potentials. For each choice of parameters, the only quantities which must be computed are the electron-electron energy for the density, the integral of the potential over the density, and the band structure energy for the wave functions. To second order in the density, potential, and wave functions, the energy for a configuration of atoms is given by the generalized functional evaluated at a superposition of atomic densities, a potential made by stitching together the atomic potentials where they are equal, and atomic wave functions. For more accurate stationary energies the densities, potentials, and wave functions can be improved by one or more conjugate gradient steps.