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Register a new userIdeal regularization of the Coulomb singularity in exact exchange by Wigner-Seitz truncated interactions: towards chemical accuracy in non-trivial systems
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Added by
Ravishankar Sundararaman
Publication date
2013
fields
Physics
and research's language is
English
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Hybrid density functionals show great promise for chemically-accurate first principles calculations, but their high computational cost limits their application in non-trivial studies, such as exploration of reaction pathways of adsorbents on periodic surfaces. One factor responsible for their increased cost is the dense Brillouin-zone sampling necessary to accurately resolve an integrable singularity in the exact exchange energy. We analyze this singularity within an intuitive formalism based on Wannier-function localization and analytically prove Wigner-Seitz truncation to be the ideal method for regularizing the Coulomb potential in the exchange kernel. We show that this method is limited only by Brillouin-zone discretization errors in the Kohn-Sham orbitals, and hence converges the exchange energy exponentially with the number of k-points used to sample the Brillouin zone for all but zero-temperature metallic systems. To facilitate the implementation of this method, we develop a general construction for the plane-wave Coulomb kernel truncated on the Wigner-Seitz cell in one, two or three lattice directions. We compare several regularization methods for the exchange kernel in a variety of real systems including low-symmetry crystals and low-dimensional materials. We find that our Wigner-Seitz truncation systematically yields the best k-point convergence for the exchange energy of all these systems and delivers an accuracy to hybrid functionals comparable to semi-local and screened-exchange functionals at identical k-point sets.
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Exchange interactions are a manifestation of the quantum mechanical nature of the electrons and play a key role in predicting the properties of materials from first principles. In density functional theory (DFT), a widely used approximation to the exchange energy combines fractions of density-based and Hartree-Fock (exact) exchange. This so-called hybrid DFT scheme is accurate in many materials, for reasons that are not fully understood. Here we show that a 1/4 fraction of exact exchange plus a 3/4 fraction of density-based exchange is compatible with a correct quantum mechanical treatment of the exchange energy of an electron pair in the unpolarized electron gas. We also show that the 1/4 exact-exchange fraction mimics a correlation interaction between doubly-excited electronic configurations. The relation between our results and trends observed in hybrid DFT calculations is discussed, along with other implications.
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