All the following are essential approaches to extracting information on the excited states of a system consisting of M nuclei and N electrons. The coordinates R α of the individual nuclei with charges Z α and r i of the individual electrons are combined into the variables R = (R 1 , R 2 , ... , R M ) and r = (r 1 , r 2 , ... , r N ), respectively. For a simpler presentation, we consider a system with a spin-singlet, closed-shell ground state. Hartree atomic units are used throughout. Using the Born-Oppenheimer separation with the adiabatic approximation, the stationary Schrödinger equation for the electrons reads