ABSTRACT
In this chapter we shall briefly consider the quantum mechanical treatment of molecules. Here the physical situation is much more complex than that of atoms. For one thing, the electrons move in a field which can no longer be considered spherically symmetric since there are two or more nuclei acting as sources of the field. However, one simplifying feature exists, and allows for separate calculation of the energy associated with nuclear motion and of the energy of electronic motion. This separation occurs as a consequence of the large ratio of nuclear mass to electron mass. Therefore, as we shall see below, the kinetic energy of the nuclei, En, is much smaller than the kinetic energy of the electrons, Ee. Since period of motion is of the order of h divided by energy, the nuclear periods are much larger than the electron periods. Hence it is expected that to a good approximation the nuclei can be considered fixed in calculating electron motion. The nuclear motion is calculated with the approximation that the motion can be classified into translations, vibrations, and rotations of the nuclei. This forms the basis of the Born-Opperiheimer approximation, which we now discuss.
