Quantal Density Functional Theory

Abstract

Quantal density functional theory (Q-DFT) [1–18] is a local effective potential energy theory in which the interacting system as described by the Schrödinger equation is mapped into one of noninteracting fermions with equivalent density ρ(r). The existence of such a model system is an assumption. From the model system, it is then possible to obtain the energy E of the interacting system as well as its first ionization potential I (or electron affinity A). As the fermions of the model system are noninteracting, their effective potential energy v _s(r) is the same. Thus, in the corresponding Hamiltonian, the potential energy operator is multiplicative or local. The model system is referred to as the S system, S being a mnemonic for “single Slater determinant.” For the mapping from any ground or bound excited state, nondegenerate or degenerate pure state of the interacting system, the corresponding state of the S system is arbitrary in that it could be in a ground or excited state. Irrespective of the state of the S system, the energy E, and ionization potential I (or electron affinity A) of the interacting system are once again obtained. Within the framework of Q-DFT, it is also possible to transform any state of the interacting system to one of noninteracting bosons in a ground state such that the density, energy, and ionization potential are obtained. Examples of such mappings as applied to atoms are described in Chap. 11.