Rigorous formulation of Slater’s transition-state theory for excited states

Abstract

Slater's transition-state equations, which are used for calculating electronic properties of excited states of atoms, molecules, and solids, are similar to the Kohn-Sham (KS) equations, apart from the fact that the former involve fractional occupation numbers. The subspace density functional theory (SDFT) was introduced by one of us [A. K. Theophilou, J. Phys. C 12, 5419 (1979)] for the development of an excited-state DFT. The lowest-order approximation of SDFT coincides with Slater's transition-state theory. However SDFT shares the mathematical deficiencies of the initial Kohn-Sham DFT for the ground state. In this paper a rigorous derivation of SDFT equations is presented, which lacks these mathematical deficiencies and, in particular, bypasses the v-representability problem. The present formalism makes use of density functionals for subspaces similar to those defined by Levy and Lieb. The procedure followed is along the same lines as the recent developments in the rigorous derivation of the KS theory [N. Hadjisavvas and A. K. Theophilou, Phys. Rev. A 30, 2138 (1984); M. Levy and J. P. Perdiew, in Density Functional Methods in Physics, edited by R. M. Dreizler and X. da Providencia (Plenum, New York, 1985)].