Scaling the spin densities separately in density functional theory

TL;DR

This paper explores separate spin density scaling in density functional theory, deriving related theorems and formulas, and evaluates various functionals on atomic and electron gas models to understand their behavior under spin scaling.

Contribution

It introduces a framework for separate spin density scaling, deriving a virial theorem and adiabatic connection formula specific to spin scaling, and assesses popular functionals in this context.

Findings

Virial theorem relates spin-scaled correlation energy and potentials.

Adiabatic connection formula expresses energies at different spin interactions.

Evaluation of functionals on atoms and electron gas reveals differences from uniform scaling.

Abstract

Coordinate scaling of each spin density separately is considered in spin density functional theory. A virial theorem relates the spin-scaled correlation energy to the spin-scaled correlation potentials. An adiabatic connection formula expresses energies at different spin interaction strengths in terms of spin scaling. Several popular approximate functionals are evaluated on the spin-scaled densities of atoms and of the uniform electron gas. The differences between this and uniform scaling are discussed.