Abstract
Hohenberg and Kohn have dealt with the ground state of an interacting electron gas in an external potential and show that there exists a universal functional of the electron density n ( r ), G [ n ( r )], independent of an external potential. This functional plays a central role in a theory of inhomogeneous electron gas. In this paper, a formal theory for deriving the form of this functional is developed. The method of this derivation is based on the use of a nonlinear response theory. Our analysis shows that G [ n ] can be expressed entirely in terms of nonlinear response functions. We derive the full expression of G [ n ] which is written explicitly by the density n ( r ). Furthermore, we find the generalized form of “compressibility sum rule”.
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