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.''

## REFERENCES

*Estimation of Thermodynamic Properties*(Academic Press, New York, 1958).

*Statistical Mechanics*(John Wiley & Sons, Inc., New York, 1940), pp. 213–217, have described this viewpoint, for example; it is of course closely analogous to the cell theory of crystals and liquids.

^{2}have given a detailed treatment of the triatomic molecule from a somewhat different point of view.

*Molecular Spectra and Molecular Structure*(D. Van Nostrand Company, Inc., Princeton, New Jersey, 1945), pp. 501–530.

*Molecular Vibrations*(McGraw‐Hill Book Company, Inc., New York, 1955). We shall follow the notation in this book as closely as is practicable.

*S*is used to emphasize that the form taken by the elements of the $Fs$ and $Gs$ matrices and the Jacobian $Js$ depends on the choice of internal coordinates. For our purposes it is important to note that as long as the coordinates used are geometrical ones (in contrast to dynamical coordinates such as normal modes), the

*F*matrix will not involve the masses and the

*G*matrix will not involve the force constants.

*The Mathematics of Physics and Chemistry*(D. Van Nostrand Company, Inc., Princeton, New Jersey, 1943), p. 308.

**s**vectors given in reference 6 for these coordinates are not needed in the present application, as they would appear in the nondiagonal blocks of the original $3N\xd73N$ Jacobian. Also we may ignore the signs of the

**s**vectors, and take them in any order in Eq. (20), as always $J\alpha <0.$

*Quantum Chemistry*(Prentice‐Hall, Inc., Englewood Cliffs, New Jersey, 1953), pp. 239–243; 482–487; 492–500;

*u*of $(Fq\u2212Fc)/RT.$,

^{16}of $(F\u2212Ff)/T$ at the proper value of $1/Qf,$ and multiplying by exp ($\u2212u/2$) to conform with our convention.

^{17}This method would usually be less convenient than Eq. (30), since it requires one to calculate

*Qf*, which involves a reduced moment of inertia.

*Advances in Chemical Physics*, I. Prigogine, editor (Interscience Publishers, Inc., New York, 1958), Vol. I, pp. 15–76, and references cited therein.

*Proceedings of the Amsterdam Symposium on Isotope Separation*(North‐Holland Publishing Company, 1958), pp. 122–23], if the comparison indicated in Eq. (11) is made for two isotopic molecules, one obtains a proof of the Teller‐Redlich product rule (see reference 6, pp. 182–186) relating the vibrational frequencies of isotopic molecules.

*Theory of Rate Processes*(McGraw‐Hill Book Company, Inc., New York, 1941).

^{21}