Quantum chemistry 'without orbitals' - An old idea and recent developments

The role of one-electron functions known as orbitals in various theoretical methods used to describe molecules and complex materials at a quantum mechanical level is outlined in a historical perspective. A hierarchy consisting of three types of general formalism, ordered according to the importance of orbital-dependent expressions in the total energy, is presented. Two such formalisms, less known to the general chemistry community, are discussed in detail together with their recent applications in modelling complex systems: a) the orbital-free formulation of density functional theory, which does not use orbitals at all and which can be seen as the modern realization of the original ideas of Thomas and Fermi, and b) the density partitioning based formalism, in which the orbitals are used only for smaller parts of a larger system (subsystems). The emphasis is placed on the second type of formalism, a topic of strong interest of our Geneva group.