Chem 521: Statistical Mechanics I Diatomic Ideal Gas

The internuclear potential V(r) of a diatomic molecule is spherically symmetric. It depends only on r, the internuclear separation. The internuclear potential v(r) can be determined using the Born-Oppenheimer approximation, where we assume that the motion of the nuclei is very slow compared to that of the electrons. We solve for the energy of ground electronic state as a function of the internuclear separation r to obtain v(r). r e r v(r) D e This is known as a central force problem, since the potential depends only on the separation between the nuclei. We can reduce such a two-particle problem to one involving the independent (translational) motion of an object whose mass is the total mas of the diatomic (m 1 + m 2) and the motion of a particle of reduced mass µ, 1 1 1 1 2 µ = + m m , which moves under the influence of the potential v(r). This transformation is presented