Exact and Approximate Ensemble Density Functionals for a Simple model

Ensemble density functional theory (eDFT) has been of recent interest since it provides an alternative to the traditional time-dependent density functional theory (TD-DFT). Although TD-DFT has many benefits, and is thus considered the standard method for solving for excited states, it still has many difficulties that are vital for understanding chemical processes. Such difficulties include: not being able to solve for multiple excitations, long range charge transfers, and conical intersections, thus making eDFT a useful alternative method to investigate. We have chosen the Hubbard dimer as the simple system to study where eDFT. This model is truncated to be a two site, dimer making all of the solutions analytic, and therefore a “toy-like” model where we can control the correlation and the potential between the two sites. After derivation of simple functionals, the symmetry eigenstate hartree exchange approximation (SEHX) was tested for this model system. Using the SEHX approximation the first excited singlet state has been extracted for the dimer, as well as for the doubly occupied second excited state, which is a double excitation. Charge transfer excitations are also investigated.