The Distribution of Energy in Molecules

Abstract

The author has recently attempted to account for the rates of unimolecular reactions by a theory [1] which assumes activation by collision and treats the reacting molecules as mechanical systems with many internal degrees of freedom. A somewhat similar theory had been advanced earlier by Rice and Ramsperger [2]. For the complete development of the author's theory it is necessary to solve the problem: Given a number of oscillators, classical or quantum, harmonic or otherwise, and a value for the total energy of these oscillators, calculate the chance that a specified one of the oscillators shall have energy in excess of some given value. The solution of this problem for the case of classical harmonic oscillators was given in the author's first paper. The methods used there, however, were somewhat elementary and not suitable for more complex cases. The problem may be solved, in general, by a consideration of the total phase-space volumes associated with various conditions of the molecule. Some of the special cases have been worked out, and will be considered here.