Density Functional Theory (DFT) simulations rely on several numerical
approximations, notably the use of pseudopotentials that reduce the
computational cost by removing core electrons, and the use of finite basis
sets. We describe an all-electron approach used to produce reference results
that can be used to validate pseudopotentials, and provide a systematic
evaluation of the convergence of basis sets. We also address the issue of
accelerating hybrid DFT simulations. Various acceleration schemes have been
proposed to reduce computational cost using localization properties of
orbitals, thus enabling hybrid-DFT first-principles molecular dynamics
simulations. We discuss approaches that allow for error control when truncating
localized orbitals.
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