Boltzmann distribution atom + diatomic

The initial state-specific reaction rate constant for both diatom-diatom and atom-triatom reactions is calculated by averaging the corresponding cross-section over a Boltzmann distribution of translational energy ... 

A problem which is even more difficult is to investigate the yield of vibrational energy accompanying three-body combination of atoms. The combination rate coefficients tend to be small compared to the fast (and second order) vibrational relaxation. Thus the stationary concentration of the diatomic product usually corresponds very closely to an ambient Boltzmann distribution. Callear58 observed S2 from S-atom combination, but concluded that the relaxation was too fast for any meaningful quantitative measurements to be made. 

The cross section and rate constant expressions for an A + reaction, where both reactants are polyatomics, are the same as those above for an atom + diatom reaction, except for polyatomics there are more vibrational and rotational quantum numbers to consider. If the polyatomics are symmetric tops with rotational quantum numbers J and K, the state specific cross section becomes a, (urel, vA, JA, KA, vB, JB, KB), where vA represents the vibrational quantum numbers for A. If the polyatomic reactants have Boltzmann distributions of vibrational-rotational energies, the reactive cross section becomes a function of viel and T = TA = TB [i.e., ffr(vTCl T)] and is determined by summing over the quantum numbers as is done in Eq. 

The states of polyatomic molecules are governed by the same Boltzmann probability distribution as those of atoms and diatomic molecules. The rotational levels of polyatomic molecules are generally large enough that many rotational states are occupied. The rotation of a linear polyatomic molecule such as acetylene or cyanogen is just... 

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