Linear-scaling tight binding from a truncated-moment approach

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Abstract
We present an approximation to the total-energy tight-binding (TB) method based on use of the kernel polynomial method within a truncated subspace. Chebyshev polynomial moments of the Hamiltonian matrix are generated in a stable and efficient manner through recursive matrix-vector multiples. To compute the energy, either the electronic density of states (DOS) or the zero-temperature Fermi function is smeared by convolution with the kernel polynomial, with Jackson damping to minimize Gibbs oscillations while maintaining the positivity of the DOS. These are shown to give approximate lower and upper bounds, respectively, on the exact TB energy, and are averaged to obtain an improved energy estimate. The scaling of the computational work is made linear in the number of atoms by truncating the moment computation at a certain range about each atom. Energy derivatives necessary for molecular dynamics are obtained via a matrix-polynomial derivative relation. The method converges to exact TB as the number of moments and the truncation range are increased. We demonstrate the convergence properties and viability of 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. © 1996 The American Physical Society.