Thermodynamic extension of density-functional theory. II. Finite-temperature ensemble spin-density functional theory

TL;DR

This paper extends density-functional theory to finite-temperature systems with spin considerations, providing a rigorous mathematical foundation and exploring equilibrium conditions and the applicability of the Hohenberg-Kohn theorem.

Contribution

It develops a thermodynamic extension of spin-density functional theory, including formalism for systems with global and local observables, and discusses conditions for system equivalence.

Findings

Extended Hohenberg-Kohn theorem to thermodynamic spin systems

Defined equilibrium characteristics for systems with multiple observables

Provided a rigorous mathematical foundation for future zero-temperature limits

Abstract

The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable (the internal electron energy) and two local (position-dependent) observables (the total electron density and the spin density). The two-component potential of the many-electron system of interest is constructed of a scalar external potential and a collinear magnetic field (coupled only with the spin operator). Various equilibrium characteristics of two systems are defined and investigated. Conditions for the equivalence between two systems (the same equilibrium density matrix demanded) are derived and thoroughly discussed. The applicability of the Hohenberg-Kohn theorem is extended to the thermodynamic spin-density functional theory. Obtained results provide a rigorous mathematical foundation for future derivation of the zero-temperature limit of this theory and determination of its chemical reactivity indices.