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# OUR RESEARCH

## 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.

## DENSITY RESONANCE THEORY

We like all kinds of resonances. In particular, we want to understand as best as possible the nature of metastable negative-ion resonances, and develop first-principle techniques to calculate their energies and lifetimes. In spite of being ubiquitous in chemistry, there is no formal theory based on DFT to predict these properties of resonant states. The negative electron affinities measured for many molecules by electron transmission spectroscopy cannot always be accurately calculated via standard DFT. Their importance has been highlighted in recent years due mainly to the role they tend to play as intermediate species during the fragmentation of large molecules upon electron impact at low energies. Efficient treatment of electron correlation effects is essential in such cases, and although this is the specialty of DFT, unbound negative ions lie beyond its current capabilities.