4RTH-ORDER GRADIENT CORRECTIONS TO THE EXCHANGE-ONLY ENERGY FUNCTIONAL IMPORTANCE OF DEL(2)N CONTRIBUTIONS

The pertinence of fourth-order gradient corrections to the exchange-only energy functional E(x)[n] for producing accurate exchange potentials upsilon(x)(r) is examined utilizing the exact upsilon(x)(r)'s obtained from the optimized-potential model (OPM) for spherical atoms and jellium spheres (whose inner regions have slowly varying densities for which the gradient expansion should be valid). It is found that the fourth-order contributions containing del(2)n represent important ingredients of E(x)[n] which should be included in gradient-based nonlocal extensions of the local-density approximation. In accordance with this observation the upsilon(x)(r)'s resulting from the fourth-order gradient expansion are closer to the exact upsilon(x)(OPM)(r)'s than those from generalized gradient approximations which do not contain del(2)n contributions.