Wu, Q; Yang, W, *A direct optimization method for calculating density functionals and exchange-correlation potentials from electron densities*,
Journal of Chemical Physics, vol. 118 no. 6
(2003),
pp. 2498-2509 [doi] .
**Abstract:**

*A direct optimization method for carrying out the computation of implicit density functionals from given electron densities was developed. The analytic first and second derivatives of the vibrational functional with respect to the linear basis set expansion coefficients and also the nonlinear parameters in the basis set were derived. The accuracy and the efficiency of the method were demonstrated in the case of the Kohn-Sham kinetic energies, HOMO energies, and exchange-correlation potentials.*