Functional form of the generalized gradient approximation for exchange: The PBE$\alpha$ functional

TL;DR

This paper introduces a flexible, physically transparent exchange functional form within density functional theory, allowing systematic variation and reliability estimation while maintaining key exact conditions of the PBE functional.

Contribution

A new one-parameter exchange functional form for GGA that satisfies PBE constraints and can be tuned for specific problems, improving reliability and simplicity.

Findings

Functional form obeys PBE constraints

Parameter tuning adjusts accuracy for different systems

Avoids oscillating exchange potential terms

Abstract

A new functional form for the exchange enhancement in the generalized gradient approximation within density functional theory is given. The functional form satisfies the constraints used to construct the Perdew-Burke-Ernzerhof (PBE) functional but can be systematically varied using one parameter. This gives the possibility to estimate the reliability of a computational result or to fit the parameter for a certain problem. Compared to other semi-empirical functionals, the present has the advantage that only one physically transparent parameter is used and that the fitted functional will obey the same exact conditions as PBE functional. Furthermore the simple form of the exchange enhancement means that oscillating terms in the exchange potential are avoided.