Comparison of two O(N) methods for total-energy semi-empirical tight-binding calculation

摘要

We compare two O(N) methods, to calculate the total energy of a system, based on a local evaluation of the density matrix (DM) via the Lanczos-Haydock recursion scheme. We have recently introduced the first method, in which an approximated DM is directly computed from the local tridiagonalized hamiltionian (LTH). In the second method, the DM is obtained from the diagonalized LTH without any further approximation. The use of the first method is restricted to temperatures higher than 1000 K, but there is no limitation for the second one. The methods are compared when applied to a grain boundary in silicon and germanium.