Arbitrary Choice of Basic Variables in Density Functional Theory. I. Formalism

TL;DR

This paper extends the Hohenberg-Kohn theorem in density functional theory to allow arbitrary physical quantities as basic variables, enabling more flexible and efficient descriptions of ground-state properties.

Contribution

It introduces a modified theorem that permits arbitrary basic variables, unifying and generalizing existing density functional theories like SDFT and CDFT.

Findings

The new theorem confirms the validity with examples using spin-density and current-density.

Derived single-particle equations match Kohn-Sham equations for specific basic variables.

The approach improves efficiency in describing ground-state properties.

Abstract

The Hohenberg-Kohn theorem of the density functional theory is extended by modifying the Levy constrained-search formulation. The new theorem allows us to choose arbitrary physical quantities as the basic variables which determine the ground-state properties of the system. Moreover, the theorem establishes a minimum principle with respect to variations in the chosen basic variables as well as with respect to variations in the density. By using this theorem, the self-consistent single-particle equations are derived. N single-particle orbitals introduced reproduce the basic variables. The validity of the theory is confirmed by the examples where the spin-density or paramagnetic current-density is chosen as one of the basic variables. The resulting single-particle equations coincide with the Kohn-Sham equations of the spin-density functional theory (SDFT) or current-density functional theory (CDFT), respectively. By choosing basic variables appropriate to the system, the present theory can describe the ground-state properties more efficiently than the conventional DFT.