Direct energy minimization based on exponential transformation in density functional calculations of finite and extended systems

The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality orbitals. system is then represented as a function elements skew-Hermitian matrix optimized directly unconstrained methods. An implementation based on limited memory Broyden-Fletcher-Goldfarb-Shanno approach with inexact line search and preconditioner presented performance compared commonly used self-consistent field approach. Results are for G2 set 148 molecules, liquid water configurations up to 576 molecules some insulating crystals. A general applicable fractional orbital occupation is, example, needed k-point sampling periodic systems. This direct found outperform standard all converge same parameter values it requires less computational effort average. formulation gradients here quite applied functionals not unitary invariant such self-interaction corrected functionals.