Generalized Kohn-Sham theory for electronic excitations in realistic systems

Instead of expressing the total energy of an interacting electron system as a functional of the one-particle density as in the Hohenberg-Kohn-Sham theory, we use a conventional approach in determining total energies by forming the expectation value 〈scrH〉 of the N-electron Hamiltonian with the true wave function {Ψ}(q₁,q₂,...,qN). We introduce a new concept of partitioning {Ψ}(q₁,q₂,...,qN) into two components such that the one-particle density is connected with the first component only. If one requires 〈scrH〉 to be stationary against variation of {Ψ}(q₁,q₂,...,qN) , this first component turns out to be one Slater determinant in terms of one-particle states which obey Kohn-Sham--type one-particle equations. Hence, the expression for the one-particle density becomes identical to that of the Kohn-Sham theory. The virtues of the new approach, particularly its capability of describing thermal excitation in solids, optical transitions, etc., are discussed in detail. We also address the so-called gap problem which has recently been an extensively debated subject within the one-particle description of N-electron systems.