Semiclassical Correlation Energies of Atoms and Molecules

1. Semiclassical Correlation Energies of Atoms and Molecules Eric J Heller, Harvard University Presently, Density functional theory is a hugely popular method for estimating atomic and molecular electronic energies, a crucial step in understanding matter of importance to chemistry and physics. The predecessor of density functional theory is Thomas Fermi theory. Both of these approaches attempt to estimate the electronic energy by treating the electrons as a self consistent fluid. However, explicit electron interactions are ignored in favor of a mean field approach. The basic premise of this project is that explicit interactions can be included by statistical means, that is, by assuming that the electrons ergodically explore their available phase space. In the mean field approaches, Fermi statistics is handled at an early stage, since it governs the energy – density relationships of the electron fluid. Not so the method developed under this grant – the available phase space for classical particles must be corrected to allow for Fermi statistics. The problem boils down to knowing which of the quantum states starting from the Bosonic ground state, is the first totally anti-symmetric fermi state (e.g. the 21st etc.). We have demonstrated that the energies so obtained are much superior to any mean field approach in the strongly correlated regime. However, we are still investigating the question “Which is the first Fermi state?”, which is a new question in the field. We are looking at the permuation group of N identical particles and their eigenstates in this pursuit. Random waves for interacting particles, like this one, are the basis for a new “Correlated Thomas Fermi” theory of atoms and molecules