A computational algorithm for densities of states

In this article we introduce the differential-area method for producing accurate phonon or electron density-of-states spectra. Its inherent advantages are that (1) the energy or frequency variable can be preset to any desired interval range; (2) no root-searching or gradient computations are required; (3) it is independent of any force model employed in deriving the matrix elements of a phonon-dynamical or electron-connectivity matrix; and (4) its numerical algorithm is totally crystal-symmetry independent. Model density-of-phonon-states calculations are performed for the next-nearest-neighbor cubic lattices and compared to an exact technique, the root surface method.