Linear Scaling Method for Phonon Calculations from Electronic Structure

We present a method for phonon spectrum calculations from electronic structure calculations that scales linearly with system size. It allows computation of the dynamical matrix and phonon structure of systems of unprecedented size. The method is based on (i) use of localized wave functions to describe the electronic states, (ii) truncation of the dynamical matrix beyond a cutoff, and (iii) reconstruction of the spectrum of the sparse dynamical matrix by the maximum entropy approach of Drabold and Sankey. We test the method with a tight-binding Hamiltonian for carbon, on a 216 atom supercell in the diamond structure, and in fullerene balls of up to 3840 atoms.