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Using principles of asymptotic analysis, we derive the exact leadingcorrection to the Thomas-Fermi kinetic energy approximation for Kohn-Shamelectrons for slabs. This asymptotic expansion approximation includes crucialquantum oscillations missed by standard semilocal density functionals. Becausethese account for the derivative discontinuity, chemical accuracy is achievedat fourth-order. The implications for both orbital-free electronic structureand exchange-correlation approximations are discussed.

Orbital-free functional with sub-milliHartree errors for slabs