ABSTRACT
A quantum mechanical treatment of molecular systems usually starts with the Born-Oppenheimer approximation, i.e., the separation of the electronic and nuclear degrees of freedom. This is a very good approximation for well separated electronic states. The expectation value of the total energy in this case is a function of the nuclear coordinates and the parameters in the electronic wavefunction, e.g., orbital coefficients. The wavefunction parameters are most often determined by the variation theorem: the electronic energy is made stationary (in the most important ground-state case it is minimized) with respect to them. The optimized energy, calculated as a function of the nuclear coordinates, is known as the potential energy surface (PES). Finding its (local) minimum gives the calculated equilibrium structure. The latter, although experimentally not directly accessible, is perhaps the most satisfactory definition of molecular geometry, and serves as the best starting point for a treatment of molecular vibrations. A large part of the total effort expended in quantum chemical calculations is spent in optimizing either electronic parameters or molecular geometries; the latter task is dominant in empirical force field calculations. The optimization of electronic wavefunctions is usually treated separately from the optimization of molecular geometries; however, there are enough similarities between the two problems to discuss them together.
