Relaxation of atomic orbitals in a plane-wave basis

We present a first-principles calculation scheme for crystals that diagonalizes an effective Hamiltonian in a small atomic orbital basis set which is expanded in plane waves, yielding initial trial wave functions. A simple relaxation procedure applied to the trial wave functions expanded in a plane-wave basis can be used to generate a set of correction wave functions. We show that a subsequent diagonalization of the effective Hamiltonian in the subspace of the trial and correction wave functions is sufficient to obtain results quite close from a full converged calculation on the plane-wave basis set used for the projection. The proposed method should be simple to implement in other plane-wave computer programs and leads to substantial gains in computation speed while maintaining reasonable accuracy.