Scaling the spin densities separately in density functional theory
  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. 
R.J. Magyar, T.K. Whittingham, K. Burke