A NEW REPRESENTATION FOR GROUND-STATES AND ITS LEGENDRE TRANSFORMS

The ground-state energy of an electronic system is a functional of the number of electrons (N) and the external potential (upsilon): E = E[N , upsilon], this is the energy representation for ground states. In 19 82, Nalewajski defined the Legendre transforms of this representation, taking advantage of the strict concavity of E with respect to their v ariables (concave respect upsilon and convex respect N), and he also c onstructed a scheme for the reduction of derivatives of his representa tions. Unfortunately, N and the electronic density (rho) were the inde pendent variables of one of these representations, but rho depends exp licitly on N. In this work, this problem is avoided using the energy p er particle (epsilon) as the basic variable. in this case epsilon is a strict concave functional respect to both of his variables, and the L egendre transformations can be defined. A procedure for the reduction of derivatives is generated for the new four representations and, in c ontrast to the Nalewajski's procedure, it only includes derivatives of the four representations. Finally, the reduction of derivatives is us ed to test some relationships between the hardness and softness kernel s. (C) 1994 John Wiley & Sons, Inc.