The electronic states of composite systems

Abstract In order to relate the electronic eigenstates of a composite system to those of its constituent parts one requires the matrix elements of the interaction Hamiltonian between the unperturbed states of the system . It is shown that in the absence of electron exchange these matrix elements, which are usually approximated as multipole series, may be accurately expressed as electrostatic repulsion energies between three-dimensional electric distributions localized on the subsystems. These distributions are them selves the matrix elements of the electric density operator between the eigenstates of the individual subsystems, and their multipole moments are identified as the permanent moments of the subsystems in their various states and the transition moments between these states. The name ‘transition density' is proposed for the off-diagonal elements of the electric density operator, and an examination of its properties suggests that the transition density may be a useful concept for summarizing and systematizing spectroscopic data on atomic and molecular assemblies.