Exchange functionals and potentials

The commonly used exchange-correlation functionals of density functional theory and their potentials are examined numerically following the first such investigation by Perdew. They are also investigated for Ne and Kr. Their behaviour for large gradients of the density and for large distances is not satisfactory. In particular, the correct asymptotic r -1 behaviour is difficult to achieve. Following van Leeuwen and Baerends, this is linked to the energy ϵmax of the highest occupied orbital arising from the Kohn-Sham equations. This deficiency is linked also with the poor prediction of molecular polarizabilities. The Becke-Roussel (BR) exchange functional is examined, which is derived by assuming a hydrogen-like exchange hole at all spatial points, and it has the attraction of being dependent on both the kinetic energy density and the Laplacian of the density and has no adjustable parameters. Becke has presented encouraging results using this functional in a hybrid manner. Fully self-consistent Kohn-Sham ca...

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