Scaling up the lattice dynamics of amorphous materials by orders of magnitude

We generalize the nonaffine theory of viscoelasticity for use with large, well-sampled systems of arbitrary chemical complexity. Having in mind predictions of mechanical and vibrational properties of amorphous systems with atomistic resolution, we propose an extension of the kernel polynomial method (KPM) for the computation of the vibrational density of states and the eigenmodes, including the Γ correlator of the affine force field, which is a key ingredient of lattice-dynamic calculations of viscoelasticity. We show that the results converge well to the solution obtained by direct diagonalization (DD) of the Hessian (dynamical) matrix. As is well known, the DD approach has prohibitively high computational requirements for systems with N=104 atoms or larger. Instead, the KPM approach developed here allows one to scale up lattice dynamic calculations of real materials up to 106 atoms, with a hugely more favorable (linear) scaling of computation time and memory consumption with N.