Local temperature in an electronic system

It is argued that the most appropriate definition of the local temperature T(r) for the ground state of an electronic system is provided by the formula 3/2ρ(r)kT(r)=1/8${\sum }_{\mathit{i}}$[(∇ ${\mathrm{\rho }}_{\mathit{i}}$⋅∇ ${\mathrm{\rho }}_{\mathit{i}}$)/${\mathrm{\rho }}_{\mathit{i}}$], where ρ(r) is the total electron density and the ${\mathrm{\rho }}_{\mathit{i}}$ are Kohn-Sham orbital densities. T(r) is everywhere non-negative. For atoms, T(r) is nearly stepwise constant. T(r) behaves very much like the Politzer average local ionization energy index. Accordingly, T(r) measures reactivity toward attack by an electron-attracting reagent. Exchange energies and Compton profiles are calculated for several atoms using this definition of the local temperature. © 1996 The American Physical Society.