Diagonalization of large matrices in pseudopotential band-structure calculations: Dual-space formalism

Combining iterative methods of calculating the eigenvectors of a Hermitian matrix with a matrix-multiplication technique using the fast-Fourier-transform algorithm, we present an efficient method of performing total-energy and band-structure calculations in crystals with the plane-wave local-pseudopotential formalism. The method can be viewed as a dual-space formalism where part of the calculations is performed in momentum space and another part in coordinate space. Significant savings in both computer time and memory are obtained. Results of calculations for molecular hydrogen with matrix sizes as large as 7200 are presented as an example.