Dimensional crossover of the exchange-correlation energy at the semilocal level

Abstract

Commonly used semilocal density functional approximations for the exchange-correlation energy fail badly when the true two dimensional limit is approached. We show, using a quasi-two-dimensional uniform electron gas in the infinite barrier model, that the semilocal level can correctly recover the exchange-correlation energy of the two-dimensional uniform electron gas. We derive new exact constraints at the semilocal level for the dimensional crossover of the exchange-correlation energy and we propose a method to incorporate them in any exchange-correlation density functional approximation.

6 pages, 5 figures

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• Gaussian approximations for the exchange-energy functional of current-carrying states: Applications to two-dimensional systems
• Generalized gradient approximation correlation energy functionals based on the uniform electron gas with gap model
• Three- to two-dimensional crossover in time-dependent density-functional theory
• Improving the applicability of the Pauli kinetic energy density based semilocal functional for solids
• Laplacian-level density functionals for the exchange-correlation energy of low-dimensional nanostructures
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• Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas
• Exchange-correlation potentials for inhomogeneous electron systems in two dimensions from exact diagonalization: comparison with the local-spin-density approximation
• Stability of spin droplets in realistic quantum Hall devices
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