The Kernel polynomial method (KPM) has been successfully applied to tight-binding electronic-structure calculations as an O(N) method. Here we extend this method to nonorthogonal basis sets with a sparse overlap matrix S and a sparse Hamiltonian H. Since the KPM method utilizes matrix vector multiplications it is necessary to apply ${\mathbf{S}}^{\mathrm{-}1}$H onto a vector. The multiplication of ${\mathbf{S}}^{\mathrm{-}1}$ is performed using a preconditioned conjugate-gradient method and does not involve the explicit inversion of S. Hence the method scales the same way as the original KPM method, i.e., O(N), although there is an overhead due to the additional conjugate-gradient part. We apply this method to a large scale electronic-structure calculation of amorphous diamond.

• Received 16 September 1996

DOI:https://doi.org/10.1103/PhysRevB.55.15382