Non-local exchange-correlation effects on the spin susceptibility and thermal density of states of Cu

A variational-principle–spin-density-functional approach has been used to investigate the importance of non-local exchange-correlation effects on the spin magnetic susceptibility χp, of Cu. These effects are contained in two functionals, one of which gives the exchange-correlation part of the effective single-particle potential while the other gives an effective spin–spin interaction. For the former functional we have compared two empirically based choices with the commonly used local approximation. The differences between these single-particle potentials are shown to be of the same magnitude as the lowest order density gradient corrections to the local approximation and produce appreciable (~ 5%) effects on the single-particle density of states at the Fermi surface and on the density functional analog of the Stoner parameter I through changes in the single particle spin magnetization. To assess the importance of these non-local corrections, we have calculated the exchange-correlation contributions to the electronic thermal density of states by the density functional theory and find that they are necessary to bring theory and experiment into agreement. The non-local effects of the spin–spin interaction functional on I are investigated by using several non-local approximations based on calculations of the wave vector dependent spin susceptibility for the uniform electron gas system. On the basis of these investigations we conclude that non-local exchange-correlation effects on χp will be significant for d-band metals, especially those with a highly enhanced χp. Numerical techniques useful for finding Fourier series representations of translationally invariant functions with cubic symmetry, important in this work, are discussed in an Appendix.