Unfortunately, however, given only the density, the current methodology comprising density functional theory provides no procedure that determines the potential and the wave function of the ground state of a system, even if it is assumed that the density does describe the ground state of a potential. Most importantly, the theory cannot decide as to whether or not a given density corresponds to the ground state of a potential.

In this presentation, I show how the constrained search coupled with the process of differentiation with respect to the density leads to a complete theory that determines whether or not a given density corresponds to the ground state of a potential, and if it does allows the unique determination (within a constant) of that potential as well as the ground state energy and wave function of an interacting many-particle system under that potential. These developments evolve from knowledge of the density alone with no reference to potential. In the new formulation, the theorems of Hohenberg and Kohn are replaced with generalized versions applicable to any density, a quantity that is the sole independent variable of the theory.

Furthermore, I demonstrate how the derivatives with respect to the density measure the rate of change with respect to the density of a wave function in the Hilbert space defined by the density and are applicable not only to functionals of the density but also to general expectation values of operators, such as the kinetic and Coulomb interaction operators, determined with respect to wave functions that lead to the density. I also show how differentiation with respect to the density provides a rigorous solution of the self-interaction problem in a Kohn-Sham implementation of the theory. The methodology is illustrated with numerical calculations including those of ground-state energies of atomic systems with results compared to those of other methods. An assessment of the formal and computational significance of the new formalism is given.

Host: John Wills