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We test local and semi-local density functionals for the electronic exchangefor a variety of systems including atoms, molecules, and atomic chains. Inparticular, we focus on a recent universal extension of the Becke-Johnsonexchange potential [E. R\"as\"anen, S. Pittalis, and C. R. Proetto, J. Chem.Phys. 132, 044112 (2010)]. It is shown that when this potential is usedtogether with the Becke-Roussel approximation to the Slater potential [A. D.Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)], a good overallagreement is obtained with experimental and numerically exact results forseveral systems, and with a moderate computational cost. Thus, thisapproximation is a very promising candidate in the quest for a simple andall-round semi-local potential.

Toward an all-round semi-local potential for the electronic exchange