We present a semilocal parametrization of the kinetic-energy density enhancement factor and the associated Pauli potential derived from jellium-slab calculations, within the context of orbital-free density functional theory (OF-DFT). The parametrization is constructed directly from analytical results for slab model systems and exact-exchange Kohn-Sham calculations and is designed to simultaneously satisfy a set of exact constraints, including the correct behavior in both the three-dimensional ($3D$) bulk limit and the two-dimensional ($2D$) extreme quantum limit. In particular, our parametrization reproduces the exact constant value of the Pauli contribution to the noninteracting kinetic energy when only a single slab discrete level is occupied and successfully describes the full dimensional crossover of the noninteracting kinetic energy from the $3D$ bulk limit to the $2D$ extreme quantum limit. The associated orbital-free Pauli potential accurately captures the evolution of surface-induced Friedel oscillations near the bulk-vacuum interface. To our knowledge, this represents the first semilocal kinetic-energy functional and Pauli potential parametrized on the basis of explicit first-principles calculations, with the kinetic-energy density properly capturing the challenging $3D\to 2D$ dimensional crossover.

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• Electronic structure
• Two-dimensional electron gas
• Density functional theory development
• First-principles calculations