A general terminator for the recursion method

A general method is presented for approximating continuous densities of states, and wavefunctions over infinite regions, within the recursion method by means of a terminator which is an infinite set of approximate basis states and their Hamiltonian matrix elements. This is an analytical and computational solution to the problem of approximating the projected density of states for a Hamiltonian having an arbitrary number of bands with van Hove singularities. It also enables calculation of charge densities and other quantities related to the wavefunctions. The method is applied to many-band problems. Criteria are developed for the convergence of densities of states, and the asymptotic convergence of the terminator is related to singularities in the spectrum.