An Alternative Approach to Extend Levy Constrained Search in Fock Spaceto No Integer Electron Number in Density Functional Theory

The Hohenberg-Kohn theorem in density functional theory,as originally formulated,states that if an electron density,ρ_0(r),is the nondegenerate ground state density of an N-electron system with external potential v_0(r),where N is a

Levy Constrained Search in Fock Space：An Alternative Approach to Noninteger Electron Number

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.