Efficient modified Jacobi relaxation for minimizing the energy functional

Abstract

We present an efficient scheme of diagonalizing large Hamiltonian matrices in a self-consistent manner. In the framework of the preconditioned conjugate gradient minimization of the energy functional, we replace the modified Jacobi relaxation for preconditioning and use for band-by-band minimization the restricted-block Davidson algorithm, in which only the previous wave functions and the relaxation vectors are included additionally for subspace diagonalization. Our scheme is found to be comparable with the preconditioned conjugate gradient method for both large ordered and disordered Si systems, while it is more rapidly converged for systems with transition-metal elements.