Semilocal density functional theory with correct surface asymptotics

摘要

Semilocal density functional theory is the most used computational method forelectronic structure calculations in theoretical solid-state physics andquantum chemistry of large systems, providing good accuracy with a veryattractive computational cost. Nevertheless, because of the non-locality of theexchange-correlation hole outside a metal surface, it was always consideredinappropriate to describe the correct surface asymptotics. Here, we derive,within the semilocal density functional theory formalism, an exact conditionfor the image-like surface asymptotics of both the exchange-correlation energyper particle and potential. We show that this condition can be easilyincorporated into a practical computational tool, at the simplemeta-generalized-gradient approximation level of theory. Using this tool, wealso show that the Airy-gas model exhibits asymptotic properties that areclosely related to the ones at metal surfaces. This result highlights therelevance of the linear effective potential model to the metal surfaceasymptotics.