Analytical representation of the Becke–Roussel exchange functional

The unique meta-GGA (generalized gradient approximation) exchange functional of Becke and Roussel (BR89) and the correlation functional of Becke related to it (B94) are represented for the first time in an analytical form. All functional derivatives are then obtained analytically, which allows an efficient self-consistent implementation. A brief assessment of this ‘BR89B94’ meta-GGA scheme is made considering molecular atomization energies and equilibrium geometries, with the latter being reported for the first time. The hybrid version of it yields one of the most accurate atomization energies to date, but its bond distances are less satisfactory. Some interesting features of the BR exchange hole are discussed.