A generalized gradient approximation (GGA) for the exchange energy functional of relativistic many-electron systems, including both a longitudinal and a transverse contribution, is presented. The resulting longitudinal exchange energies for atoms reproduce the corresponding exact values, obtained via the relativistic optimized-potential method, with the same accuracy that has been found for GGAs in the nonrelativistic context. In addition, it is shown that transverse contributions to the self-consistent exchange potential should not be neglected in the case of gradient-corrected functionals. {} 1996 The American Physical Society.
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Engel et al. (1996) studied this question.
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