Molecular Partition Functions in Terms of Local Properties

The classical partition function for a polyatomic molecule is obtained in a form which has, for each atom, a factor that corresponds to free translational motion of the atom in an effective volume defined by the average vibrational amplitudes of the atom and the geometrical configuration of the neighboring atoms. A method is given for calculating the appropriate volume elements for any choice of internal coordinates. The treatment includes harmonic vibrations, internal rotations, and ``reaction coordinates.'' Quantum mechanical corrections introduce additional factors which shrink the volume elements for high-frequency vibrations. Since the principal factors in this form of the partition function are determined by local properties largely characteristic of the bonds in the vicinity of each atom, many of these factors remain practically constant and can be omitted in calculations which compare the reactants in a chemical reaction with the products or with the ``activated complex.''