Strong electron correlation in molecules

Dense-lying frontier orbitals in molecules have always posed a severe challenge to quantum chemical methods that aim at accurately predicting or explaining molecular properties. In this talk, I will present and discuss recent approaches that set out to solve the electronic Schroedinger equation for such strongly correlated systems which have been elusive to traditional methods. These recent approaches, of which the density matrix renormalization group is one, are conceptually very different from well-established methods such as configuration interaction and coupled cluster. I shall discuss their basic ideas and potential drawbacks and present results from now routine calculations.