Grassmann extrapolation of density matrices for Born-Oppenheimer\n molecular dynamics

Abstract

Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful but expensive\ntechnique. The main bottleneck in a density functional theory bomd calculation\nis the solution to the Kohn-Sham (KS) equations, that requires an iterative\nprocedure that starts from a guess for the density matrix. Converged densities\nfrom previous points in the trajectory can be used to extrapolate a new guess,\nhowever, the non-linear constraint that an idempotent density needs to satisfy\nmake the direct use of standard linear extrapolation techniques not possible.\nIn this contribution, we introduce a locally bijective map between the manifold\nwhere the density is defined and its tangent space, so that linear\nextrapolation can be performed in a vector space while, at the same time,\nretaining the correct physical properties of the extrapolated density using\nmolecular descriptors. We apply the method to real-life, multiscale polarizable\nQM/MM.\n