LINEAR-SCALING TIGHT-BINDING FROM A TRUNCATED-MOMENT APPROACH

We present an approximation to the total-energy light-binding (TR) met hod based on use of the kernel polynomial method within a truncated su bspace. Chebyshev polynomial moments of the Hamiltonian matrix are gen erated in a stable and efficient manner through recursive matrix-vecto r multiples. To compute the energy, either the electronic density of s tates (DOS) or the zero-temperature Fermi function is smeared by convo lution with the kernel polynomial, with Jackson damping to minimize Gi bbs oscillations while maintaining the positivity of the DOS. These ar e shown to give approximate lower and upper bounds, respectively, on t he exact TB energy, and are averaged to obtain an improved energy esti mate. The scaling of the computational work is made linear in the numb er of atoms by truncating the moment computation at a certain range ab out each atom. Energy derivatives necessary for molecular dynamics are obtained via a matrix-polynomial derivative relation. The method conv erges to exact TB as the number of moments and the truncation range ar e increased. We demonstrate the convergence properties and viability o f the method for materials simulations in an examination of defects in silicon. We also discuss the relative importance of truncation range versus number of moments.