Fundamental study of kinetic energy and exchange-correlation densities: density matrices as starting point for new functionals in DFT.

Quantum chemists make use of the laws of quantum mechanics to describe chemical systems. These laws assign a certain probability to every particle configuration, which leads to information overload. This renders any chemical interpretation nearly impossible.
However, by averaging over certain subsets of probabilities, we can compute lower dimensional densities, which are more amenable to analysis in terms of chemical concepts. The electron density, for example, gives the probability that an electron can be found at a certain position and can be obtained by averaging over the positions of all other electrons. Similarly, one can derive property densities that combine the idea of a density with the value of a property at that position. Experience has shown, however, that when defining appropriate property densities, there are obstacles of both chemical, physical and mathematical nature. These ambiguities are particularly relevant for Density Functional Theory (DFT), which tries to frame all of chemistry in terms of
functionals of chemically relevant densities. In this project, we propose to resolve these problems by studying the underlying kinetic energy and exchange-correlation densities from a matrix perspective. By uncovering the important information hidden in the eigenvectors and eigenvalues of these matrices, we aim to extend the chemical understanding of these property densities and to contribute novel ideas to the field of DFT.