The V-electron Hamiltonian

The //-electron wave function T is an antisymmetric function of N sets of spatial and spin coordinates r,, v, for individual electrons, all evaluated at a common timer. In postulating a time-dependent Schrodinger equation of the form 

Spin indices and summations will be suppressed in the notation here, but are to be understood in connection with coordinate indices and integrations over coordinates. Thus / d3 r is intended to imply an implicit summation over a spin index. The energy functional for an antisymmetric wave function T( 1. AT) is ( b // T) = f1d3ri fN d3rN i H i and the normalization integral is (fi l b) = 

The Schrodinger variational principle requires (T //1T) to be stationary subject to constant normalization ( ). Introducing a Lagrange multiplier, the variational condition is 

---

The /V-electron Hamiltonian is H = f + U + V, where T is kinetic energy, U, the interelectronic Coulomb interaction, and V. the external potential term. A system of N interacting electrons is modeled by a system of N noninteracting electrons moving in a self-consistent mean field. This requires a postulated mapping rule by... 

Given the V-electron Hamiltonian H = T + U + V, and postulating some rule 1fr— that determines a reference state, this defines an orbital functional E=T+U+V + EC, where T + U + V = (P H 4>) is explicit, as defined previously, and Ec — /iexac( — (

orbital functional defined for a particular approximate model. It is assumed that E is minimized in the ground state of the model. V = Y,i nfilvli) if v is a general nonlocal external potential. 

The mathematical issues relevant to the definition of density functional derivatives can be considered in the simple model of noninteracting electrons. As in the KSC [4], this singles out the kinetic energy. The /V-electron Hamiltonian operator is H = T + V. Orbital functional derivatives determine the noninteracting OEL equations... 

---