Progress at the interface of wave function and density functional theories

Nikitas Gidopoulos
ISIS - STFC, Rutherford Appleton Laboratory, Didcot, Oxon, OX11 0QX, England, U.K.

Mercredi, 15 février 2012 à 11h, bibliothèque LCT, tour 12-13, 4e étage

I shall present my recent work on the border of density functional theory and wave function theory. For example, the Kohn-Sham potential emerges as the minimizing effective local potential in a Rayleigh-Ritz energy minimisation that does not involve fixing the unknown single-electron density. The new variational principle leads to well-behaved approximations for the correlation energy from second-order perturbation theory. Another example is the finite-basis set formulation of the Optimized Effective Potential (OEP) theory which is known to lead to an ill-posed problem mathematically with undesirable features in the potential like strong oscillations near the nuclei. I shall argue that underlying the pathological behaviour of the potential lies a discontinuous limit of OEP, when the density-density response function Chi is truncated with a finite orbital basis set and then inverted. Restoring the continuity of OEP the problem becomes well posed. Time permitting, I shall comment on a fundamental problem that was first discussed by Andreas Savin and also by Mel Levy. The problem, which undermines all effective potential theories, is that the density-density response function Chi can have very small eigenvalues. The result is that large changes in the potential along the eigenfunctions of Chi with small eigenvalues, generate very small changes in the density.