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We generalise the non-affine theory of viscoelasticity for use with large,well-sampled systems of arbitrary chemical complexity. Having in mindpredictions of mechanical and vibrational properties of amorphous systems withatomistic resolution, we propose an extension of the Kernel Polynomial Method(KPM) for the computation of the vibrational density of states (VDOS) and theeigenmodes, including the $\Gamma$-correlator of the affine force-field, whichis a key ingredient of lattice-dynamic calculations of viscoelasticity. We showthat the results converge well to the solution obtained by directdiagonalization (DD) of the Hessian (dynamical) matrix. As is well known, theDD approach has prohibitively high computational requirements for systems with$N=10^4$ atoms or larger. Instead, the KPM approach developed here allows oneto scale up lattice dynamic calculations of real materials up to $10^6$ atoms,with a hugely more favorable (linear) scaling of computation time and memoryconsumption with $N$.

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