CONSTRUCTION OF AN OPTIMIZED Z-INDEPENDENT STATISTICAL EXCHANGE POTENTIAL FOR ATOMIC, MOLECULAR, AND SOLID STATE CALCULATIONS

Abstract

The optimized Xα method has the drawback that the optimum value of α for isolated atoms is Z-dependent, a consequence of the fact that Vxα has to represent inhomogeneous as well as homogeneous exchange effects. In treating polyatomic molecules and crystals by the Xα method, one is obliged to use spatially discontinuous exchange potentials (muffin-tin approximation) or arbitrarily smoothed versions of these. A simple way of avoiding such difficulties is to adopt the Xαβ method, which treats homogeneous and inhomogeneous exchange effects separately, and attempt to find optimum Z-independent values for the two parameters αand β. In this paper, such a universal (Z-independent) Xαβ exchange potential is constructed, and it is shown that except for the very lightest atoms (He and Li), the choice α = 2/3 and β = 0.003 leads to an exchange model which is superior to the optimized Xα model, at least on the basis of the Hartree-Fock total energy criterion. The choice α = 2/3, suggested by theoretical considerations, is supported by empirical studies. The choice β = 0.003 is not particularly critical. The universal optimized Xαβ exchange potential described here should prove particularly useful in applications to polyatomic molecules and crystals, including self-consistent electronic structure calculations.