We investigate methods to calculate projected density of states from a finite set of recursion coefficients. We consider tight-binding Hamiltonians describing the diamond-structure semiconductors α-Sn, Ge, Si, and C. Coefficients for about 110 levels of recursion are available for these Hamiltonians. Thus, we have coefficients for a sufficient number of recursion levels so that their asymptotic behavior is apparent. We first extrapolate the calculated coefficients using a linear predictive analysis suggested by Allan. This extrapolation is based on a perturbation theory that assumes that band gaps are small compared to the bandwidth. For α-Sn, Ge, and Si, which have band gap to bandwidth ratios (for the model Hamiltonians) of less than 0.05, the extrapolation procedure is found to be very successful. For C, however, with a band gap to bandwidth ratio of 0.106, large spurious features, which can be clearly associated with second-order perturbation terms, appear in the calculated density of states. We modify the extrapolation procedure using nonperturbative results for the asymptotic behavior of the recursion coefficients. The new extrapolation procedure gives good densities of states for C. Also, the calculated Green’s function has the correct analytic structure.

• Received 6 February 1987

DOI:https://doi.org/10.1103/PhysRevB.36.1725