Correlated Spin-Density-Wave Theory

Federico E. Zahariev, Mark S. Gordon, Mel Levy

It has recently been shown how to replace spin-wave functions with purely spatial wave functions in the formulation of spin-density functional theory (SDFT), without any change to the resultant density functional expressions [F. Zahariev and M. Levy, Phys. Rev. A 100, 062507 (2019)]. The purely spatial wave functions that are obtained are much more convenient to use and thus allow for a relatively easy decomposition and manipulation of terms in the constrained-search formulation of SDFT. All the essential ingredients of SDFT, including the kinetic, exchange, and correlation contributions, are explicitly defined in terms of the universal functional expressed in this spin-free manner. Constrained-search derivations of the Oliver-Perdew relations for the kinetic and exchange terms are presented. The up-down spin component of the correlation term is found to contain the up-down spin component of the Hartree term. A spin-dependent generalization of the adiabatic connection is put forth and a connection with spin-dependent coordinate scaling is established for the correlation energy.

Federico Becca, Sandro Sorella

S. Caprara, M. Avignon, Oracio Navarro

Federico E. Zahariev, Mel Levy

It is proven that entirely spin-free wave functions can be utilized in the basic definitions of the universal functionals in density-functional theory and spin-density-functional theory. Then, for the purpose of approximating these functionals, it is shown that the knowledge of certain properties of the functionals, such as those involving the coordinate scaling of just one of the spin densities, is made feasible precisely because the wave functions in the functional definitions are free of explicit spins. Among the examples, a conjectured spin-density scaling relation for the correlation energy is studied.

A. I. Solomon, Joseph L. Birman

M J Morris, J. F. Cornwell

The Green function theory formulated in I is generalized to give a higher-order approximation to the correlation problem. The spin-density-wave stability in this approximation is compared in detail with the Hartree-Fock approximation results of I and are found to be in conflict in several respects.