Generalized Density Functional Theory

Positionally dependent and positionally independent weighted density approximations of classical density functional theories are each shown to represent limits of a more general approach. The resulting flexibility is used to improve on the results obtained for inhomogeneous systems, the hard-sphere crystal being given as an example. Physical limitations of such mappings are inherent and are shown to arise from the resulting weight functions which remain proportional to the second order direct correlation function. The physical arguments apply also to electronic density functional theory.