Density Matrix Functional Theory for Molecules and Solids

Density-matrix functional theory has enjoyed increasing popularity in recent years. For the onebody reduced density matrix, the theory rests on a Hohenberg-Kohn-type theorem which was formulated by Gilbert [1]. Employing some well-known reduced-density-matrix functionals [2] for the exchange-correlation energy, we minimize the total energy with the appropiate constraints ensuring N-representability of the density matrix and conservation of the total particle number. Atoms and molecules, periodic bulk insulators, and the electron gas are studied in this way. For molecules, we find that some of the more advanced functionals, such as the BBC3 functional [2], perform as well as MP2, with a much lower numerical cost. This is demonstrated by an extensive comparison using the so-called G2 set of molecules, see Fig 1 below.