Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential.

A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potential behavior. Distinct from them, the new functional provides important improvements in quantities dependent upon response functions, e.g., static and dynamic polarizabilities and hyperpolarizabilities. CAP combined with the Lee-Yang-Parr correlation functional gives roughly equivalent results. Consideration of the computed dynamical polarizabilities in the context of the broad spectrum of other properties considered tips the balance to the non-empirical CAP-PBE combination. Intriguingly, these improvements arise primarily from improvements in the highest occupied and lowest unoccupied molecular orbitals, and not from shifts in the associated eigenvalues. Those eigenvalues do not change dramatically with respect to eigenvalues from other GGA-type functionals that do not provide the correct asymptotic behavior of the potential. Unexpected behavior of the potential at intermediate distances from the nucleus explains this unexpected result and indicates a clear route for improvement.