Density functional theory formalism

Abstract

A derivation and formulation of density functional theory, which eliminates the formal and practical inconsistencies and limitations of previous theories and allows its extension to stationary states other than the ground state, is given. The theory presented here can also be stated as a series of three theorems that define a family of its mathematical forms, as far as the physical content of the third theorem can either be implicitly incorporated in the density functional or explicitly in the procedure to find a solution to the equations. Examples of both cases are discussed, including the statement of configuration interaction procedure in density functional form.

A formal definition of carriers

“…It has been argued that this constraint is enough for the development and use of the theory, but recent evidence indicates that other constraints are needed [7,8,9,10], this is in accordance with our present approach.…”

Energy Density Functional Theory of Many-Electron Systems

“…Also, it has been shown Keller and Ludeiia 1987) that when N = 2, the Euler-Lagrange equation (6.7-H) may be put in the form…”

“…(6.7-75) may be put as . We make the following conjecture: lIb] has an explicit functio'1al dependence upon Ti = A so that we may write The plausibility of this conjecture comes about from the fact that the two-electron is just a particular instance of a more general formulation where some vectors formed by occupation numbers playa preponderant role (Ludeiia,1985;Ludeiia, 1987;Keller and Ludeiia, 1987). (5-101) and (5-99)).…”

Geometric Formulation of the Many-Electron Theory

“…16) describes the time evolution of the auxiliary function φ i as a weighted addition of the auxiliary function φ j .…”