Maximum entropy approach for linear scaling in the electronic structure problem

Abstract

We present a method for obtaining the band-structure energy and density of states for large, sparse Hamiltonian matrices as occur in electronic structure problems. The computation scales linearly with the dimension of the matrix. We use a statistical approach using random vectors along with the principle of maximum entropy to obtain highly accurate estimates for integrals over the density of states. We offer several tests of the approach using tight-binding Hamiltonians and apply the scheme to large icosahedral fullerenes with 720 and 2160 atoms.