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

K. SCHWARZ (*) and F. HERMAN 

IBM Research Laboratory, San Jose, California 95114, USA




Abstract. 

The optimized Xa method has the drawback that the optimum value of a for isolated atoms is 2-dependent, a consequence of the fact that VX~ has to represent inhomogeneous as well as homogeneous exchange effects. In treating polyatomic molecules and crystals by the Xa 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 Xab method, which treats homogeneous and inhomogeneous exchange effects separately, and attempt to find optimum 2-independent values for the two parameters a and b. In this paper, such a universal (2-independent) X@ exchange potential is constructed, and it is shown that except for the very lightest atoms (He and Li), the choice a = 213 and ll = 0.003 leads to an exchange model which is superior to the optimized Xu model, at least on the basis of the Hartree-Fock total energy criterion. The choice a = 213, suggested by theoretical considerations, is supported by empirical studies. The choice = 0.003 is not particularly critical. The universal optimized Xab exchange potential described here should prove particularly useful in applications to polyatomic molecules and crystals, including self-consistent electronic structure calculations. 

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