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

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.

23 pages, 1 figure, Changed content

Cited by in corpus (12)

• The choice of basic variables in current-density functional theory
• Arbitrary Choice of Basic Variables in Density Functional Theory. II. Illustrative Applications
• Exact-Exchange Spin-Current Density-Functional Theory
• Pair density functional theory by means of the correlated wave function
• The structure of the density-potential mapping. Part I: Standard density-functional theory
• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• Density functional scheme for calculating the pair density
• A local tensor that unifies kinetic energy density and vorticity dependent exchange-correlation functionals
• Basic variables to be reproduced in the first-principles theory for superconductors: Fluctuation of the particle number
• Quantized Hall conductance in graphene by nonperturbative magnetic-field-containing relativistic tight-binding approximation method
• Exposing minimal composition of Kohn-Sham theory and its extendability
• Constrained Search in Imaginary Time