The quality of Mueller type functionals in reduced density matrix functional theory

Reduced density matrix functional theory, which uses the one-body density matrix as its fundamental variable, provides a powerful tool for the description of many-electron systems. While the kinetic energy is known exactly as a functional of the one-body density matrix the correlation energy needs to be approximated. Most approximations that are currently employed are modifications of the Mueller functional. The adiabatic extension of these functionals into the time-dependent domain proofs problematic because it leads to time-independent occupation numbers. We assess the general quality of these approximations for an exactly solvable two-electron system as well as for calculations of the fundamental gap. In addition, we address the impact of those functionals for excited state properties in optics