Comment on the exchange-energy formula of Ghosh and Parr: A new derivation applicable to molecules

Recently Ghosh and Parr [S. K. Ghosh and R. G. Parr, Phys. Rev. A 34, 785 (1986)] have developed a new nonlocal exchange functional given by K(ρ)=(π/2) F ${\rho }^2$(r)β(r)dr. Using the spherical average of the exchange hole, we redefine β(r) using $t_s$(r,ρ)=Tr(t→) where t→ is the kinetic energy density tensor matrix. We then obtain the same formula whatever the symmetry of the system.