KERNEL POLYNOMIAL METHOD FOR A NONORTHOGONAL ELECTRONIC-STRUCTURE CALCULATION OF AMORPHOUS DIAMOND

The Kernel polynomial method (KPM) has been successfully applied to ti ght-binding electronic-structure calculations as an O(N) method. Here we extend this method to nonorthogonal basis sets with a sparse overla p matrix S and a sparse Hamiltonian H. Since the KPM method utilizes m atrix vector multiplications it is necessary to apply S-1H onto a vect or. The multiplication of S-1 is performed using a preconditioned conj ugate-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-struc ture calculation of amorphous diamond.