Function for Energized Molecules

At equilibrium the distribution of molecules among the various energy states E is given by the Maxwell-Boltzmann expression. Thus for a molecule with n classical internal, harmonic oscillators, the fraction of molecules with energy J i, E2,. , En present in these oscillators is 

The fraction of molecules P E) with total internal energy in the range E to E + dE, with E = /i l + /i 2 + + En, is obtained by integrating this expression over all values of Et subject to their sum being E  

On performing the term-by-term integration between limits E — Et — 1. A. Marcus, J. Chem. Phys., 20, 364 (1952). 

When a chemical reaction is occurring, these distribution functions are perturbed by the reaction, and in general we may expect to find the stationary-state concentration of energized molecules lower than that at equilibrium. Lindemann was the first to propose a scheme for computing the influence of the reaction on these distributions. His scheme involved the competition between destruction of energized molecules by collisional deactivation and by chemical reaction. If B represents a molecule which ultimately reacts spontaneously to produce products, then 

When /cd(B) kr, that is, collisional deactivation is much more probable than spontaneous decomposition, we have what is referred to as the high-pressure limit  

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