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Download fileGrassmann Extrapolation of Density Matrices for Born–Oppenheimer Molecular Dynamics
journal contribution
posted on 08.10.2021, 16:42 authored by Étienne Polack, Geneviève Dusson, Benjamin Stamm, Filippo LippariniBorn–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 nonlinear constraint that an idempotent density needs to satisfy
makes 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 BOMD simulations,
showing that sizeable performance gains can be achieved, especially
when a tighter convergence to the KS equations is required.
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sizeable performance gainslocally bijective mapkohn – shamcorrect physical propertiesmm bomd simulationsidempotent density needsvector spacetighter convergencetangent spacesatisfy makesprevious pointspolarizable qmnonlinear constraintmain bottlenecklinear extrapolationiterative proceduregrassmann extrapolationexpensive techniquedirect usedensity matrixdensity matricesconverged densities