Generalized generalized gradient approximation:An improved density-functional theory for accurate orbital eigenvalues

TL;DR: The generalized gradient approximation (GGA) for the exchange functional in conjunction with accurate expressions for the correlation functional have led to numerous applications in which density-functional theory (DFT) provides structures, bond energies, and reaction activation energies in excellent agreement with the most accurate ab initio calculations and with the experiment.

Abstract: The generalized gradient approximation (GGA) for the exchange functional in conjunction with accurate expressions for the correlation functional have led to numerous applications in which density-functional theory (DFT) provides structures, bond energies, and reaction activation energies in excellent agreement with the most accurate ab initio calculations and with the experiment. However, the orbital energies that arise from the Kohn-Sham auxiliary equations of DFT may differ by a factor of 2 from the ionization potentials, indicating that excitation energies and properties involving sums over excited states (nonlinear-optical properties, van der Waals attraction) may be in serious error.mWe propose herein a generalization of the GGA in which the changes in the functionals due to virtual changes in the orbitals are allowed to differ from the functional used to map the exact density onto the exact energy. Using the simplest version of this generalized GGA we show that orbital energies are within ∼5% of the correct values and the long-range behavior has the correct form.