PARTITION DENSITY FUNCTIONAL THEORY
We want to understand how chemical concepts arise from basic quantum mechanics. What is the electronegativity of a part of a molecule? What is its chemical hardness? What makes a bond covalent or ionic, and what does that really mean? We are investigating these and other essential questions of theoretical chemistry via a recently-developed Partition Theory, which provides a rigorous way based on Density Functional Theory to divide a molecule into smaller parts.
We impose the constraint that the sum of the electron densities of the parts must be identical to the true density of the entire system. We then minimize the sum of the energies of the parts subject to such density constraint. In the process, an interesting potential (the partition potential) appears as the Lagrange multiplier that guarantees the satisfaction of the density constraint. In work that requires of both, development of formal theory as well as numerical experiments, we are currently investigating general properties of the partition potential, efficient ways to calculate it, implications of the theory, and possible time-dependent extensions.