Empirical functionals for reduced-density-matrix-functional theory

We present fully empirical exchange-correlation functionals to be used within reduced-density-matrix-functional theory (RDMFT). These are of the popular J-K form [involving only Coulomb- (J) and exchange- (K) type integrals over the natural orbitals], where the function of the occupation numbers that multiplies the Fock orbital term is written as a Padé approximant. The coefficients of the Padé approximant are optimized for a test set of eight molecules, and then refined for a larger set of 35molecules . Two different approaches were tried, either keeping the self-interaction terms, or by removing them explicitly from the functional. The functionals thus obtained involve very few parameters, but are able to outperform other RDMFT functionals, yielding correlation energies that are, on average, even slightly better than second-order Møller-Plesset theory.