Electronic structure calculations for plane-wave codes without diagonalization

We present an algorithm to reduce the computational complexity for plane-wa ve codes used in electronic structure calculations. The proposed algorithm avoids the diagonalization of large Hermitian matrices arising in such prob lems. The computational time for the diagonalization procedure typically gr ows as the cube of the number of atoms, or the number of eigenvalues requir ed. To reduce this computational demand, we approximate directly the occupa tion operator corresponding to the eigenvectors associated with the occupie d states in a certain subspace without actually computing these eigenvector s. A smoothed Chebyshev-Jackson expansion of the Heaviside function of the Hamiltonian matrix is used to represent the occupation operator. This proce dure requires only matrix-vector products and is intrinsically parallelizab le. (C) 1999 Elsevier Science B.V.