Self-consistent finite-difference electronic structure calculations

Abstract

We present an accurate and efficient self-consistent method of solving the time-independent Schrödinger equation to find the electronic structure of materials. We use a finite-difference grid, which has the flexibility to cope with difficult geometry. The atomic cores are replaced with an embedded potential with a small muffin-tin radius allowing the full potential outside the muffin-tin. The resulting Hamiltonian matrix is sparse and can be diagonalized with computer time of O(N) using the Lanczos algorithm. For a larger number of atoms, the electronic properties of the system are found with greater efficiency than the Lanczos algorithm, using the calculation of the Green function of the system. Poisson's equation is solved using the multigrid method and the new potential in each self-consistent iteration is constructed within local density functional theory. The self-consistent electronic structure properties are shown for fcc copper.