Functionals of the Electron Density
The electron density is the fundamental variable in our approach to the quantum-classical correspondence (see Recent Work, below). In our approach, all purely quantum terms are expressed as functionals of the electron density.
- One goal is to extend and generalize our approach to (i) Strengthen the relevance of our work to the connection between quantum mechanics and Information Theory. (ii) Strengthen the relevance of our work to the construction of direct (orbital-free) kinetic-energy functionals. This is a collaboration with Luigi Delle Site, Free University, Germany and Luca Ghiringhelli, Fritz Haber Institute, Berlin.
- Another goal is to understand and predict chemical bonding and reactivity using the quantum potential, Q, and other functionals of the electron density such as the Laplacian and the Electron Localization Function. In regions where Q is negative, the kinetic energy is positive and the electron is classically allowed. This is a collaboration with Cherif Matta, Mount Saint Vincent University and SeyedAbdolreza Sadjadi, University of Hong Kong.
- We have explored formal aspects of the electron density (with Ricardo Mosna, Universidade Estadual de Campinas, Brazil and Luigi Delle Site, Free University, Berlin). We proposed an approach to the quantum-classical correspondence based on deformations of the momentum and kinetic operators of quantum mechanics. In our approach, the quantum potential (of Bohm) appears naturally, as it does in the hydrodynamic formulation of quantum mechanics. We constructed classical versions of momentum and kinetic operators which, in addition to the standard quantum expressions, contain terms that are functionals of the electron density. In our approach the kinetic energy is decomposed as the sum of a classical term and a purely quantum term which is essentially identical to the Fisher information.
- Postdoctoral fellow Wai-To Chan examined valence shell structures in distributions of the quantum potential and the Laplacian of the electron density for a variety of diatomics. We proposed an alternative definition of the valence shell charge concentration as the outermost region for which the one-electron potential is negative. Also, for a series of amines we examined the correspondence between the quantum potential and the Laplacian of the electron density as indicators of proton affinity. Proton affinities for a series of amines and phosphines are shown to exhibit linear correlation with valence minima of N and P.