Internally Consistent Local Approximation to Density Functional theory

We propose a new non-local functional for the implementation of density functional theory (DFT) within a local approximation. This functional is obtained through the replacement of the conventional form $T_s+\frac{1}{2}\int{\rm d}{\bf r}_1\int{\rm d}{\bf r}_2\frac{n({\bf r}_1)n({\bf r}_2)}{|{\bf r}_1-{\bf r}_2|}$ to represent the kinetic and Coulomb energy of a non-interacting system with the expression $T_s+\frac{1}{2}\int{\rm d}{\bf r}_1\int{\rm d}{\bf r}_2\frac{n_s({\bf r}_1,{\bf r}_2)}{|{\bf r}_1-{\bf r}_2|}$ where $n_s({\bf r}_1,{\bf r}_2)$ is the two-particle density formed from the non-interacting wave function, and $n({\bf r})$ is the single-particle density. Based on this new functional we develop a local approximation and show that it is self-interaction free and also leads to energies that form an upper bound to the exact ground-state energy. We provide a brief comparison with the conventional Kohn-Sham local density approximation and some of the schemes introduced to correct for the presence of self-interaction in the conventional formalism, and comment on our immediate plans for future development.