A real-space pseudopotential method for computing the electronic properties of periodic systems

We present a real space method for electronic structure calculations of periodic systems. Our method is based on self-consistent solution of the Kohn-Sham equations on a uniform threedimensional grid. A higher-order finite difference method is combined with ab initio pseudopotentials. The kinetic energy operator, the non-local term of the ionic pseudopotential and the Hartree and exchange-correlation potentials are set up directly on the real-space grid. The local contribution to the ionic pseudopotential is initially obtained in reciprocal space and is then transferred to the real-space grid by Fourier transform. Our method enjoys the main advantages of real-space grid techniques over traditional plane wave representations for density-functional calculations, i.e. improved scaling and easier implementation on parallel computers. We illustrate the method by application to liquid silicon.