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