A thermal orbital-free density functional approach

A generating function σ is defined for spherically symmetric systems. Compared to the density, the generating functional has two extra variables and reduces to the density if these variables are equal to zero. It is proved that σ satisfies a differential equation that contains only the derivatives of σ and the Kohn-Sham potential. A Schrödinger-like equation for the square root of σ is also derived. The effective potential of this equation is the sum of the Kohn-Sham potential and a term that is expressed with an integral containing the derivatives of σ. The noninteracting kinetic energy can be calculated in the knowledge of σ. The theory is valid in case of zero and nonzero temperatures as well. For nonspherically symmetric systems, the muffin-tin approximation can be applied.