ABSTRACT

NucleiThe speed of motion of a nuclei is quite different from that of electrons. Hence, frequencies of their motions are quite different. The ratio of the frequencies of the motion of electrons to those of molecular vibration and molecular rotation is 104:102:1. In such a case, we can consider their motions separately. For instance, suppose a lot of bees are flying around a lion, as shown in Fig. 12.1. The motions of the bees are so quick that the bees feel that the lion is not moving. The lion is indeed annoyed at the bees flying around it, but it is not interested in the detailed position of the bees’ flight path. Here it may be all right if we assume that the lion is not moving when we

deal with the motion of the bees, and if we consider only the average distribution density of the bees when we deal with the motion of the lion. In this way, we can separately deal with the motions of the bees and the lion. This does not mean that the motion of the bees has no effect on the motion of the lion. The average density distribution of the bees determined by their motions indeed influences the emotion and thus the motion of the lion. For example, the lion may be nervous enough to start moving. This effect of average distribution of light particles on heavier particles is seen in the electron-lattice (e-L) interaction in molecules and solid-state materials. It can be explained by solving Schröedinger equations with a Hamiltonian Hby H Wy y= (12.1) This equation describes the motions of the electrons bound in a molecule and of the nuclei, and we can separate the wave functions as ymolecule = yelectrons ynuclei (12.2) This equation can also be called the Born-Oppenheimer approximation or adiabatic approximation.