Order-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>method for a nonorthogonal tight-binding Hamiltonian

Abstract

We have developed an order-$N$ method to calculate the total energy and atomic forces for a nonorthogonal tight-binding Hamiltonian. We have first confirmed the validity of our approach by comparing our results with the exact calculation for a small silicon cluster. The efficiency of our approach for a large system is demonstrated by determining the equilibrium configuration of a ${\mathrm{Si}}_{1000}$ cluster using quenching and annealing techniques based on molecular dynamics.