Reaction probabilities partition function

The ratio of translational partition functions (Qjr/Qtr) is 1 here, and for all unimolecular reactions, because the mass and number of molecules of the reactants is the same as for the transition state. The rotational ratio (Q, /Q, ) is given by the ratio of the moments of inertia (/ //t/2/3)1/2- The moments of inertia are probably slightly higher in the... 

There are two corrections to equation (12) that one might want to make. The first has to do with dynamical factors [19,20] i.e., trajectories leave Ra, crossing the surface 5/3, but then immediately return to Ra. Such a trajectory contributes to the transition probability Wfia, but is not really a reaction. We can correct for this as in variational transition-state theory (VTST) by shifting Sajj along the surface normals. [8,9] The second correction is for some quantum effects. Equation (14) indicates one way to include them. We can simply replace the classical partition functions by their quantum mechanical counterparts. This does not correct for tunneling and interference effects, however. 

From elementary statistical thermodynamics we know that the equilibrium constant can be written in terms of the partition functions of the individual molecules taking part in a reaction. These quantities represent the sum over all energy states in the system—translational, rotational, vibrational, and electronic. The probability that a molecule will be in a particular energy state, f ,-, is given by the Boltzmann law,... 

It is evident that if complicated changes in the modes of motion of molecules have to accompany a chemical transformation, the nonexponential term in the expression for the reaction rate will be small. That the probability factor will be low, that the partition function of the transition complex will be unfavourable, and that the entropy of activation wUl be small are all equivalent statements of the same fact. 

The molecular partition functions, Q, can be related to molecular properties of reactants and products. The partition function expresses the probability of encountering a molecule, so that the ratio of partition functions for the products versus the reactants of a chemical reaction expresses the relative probability of encountering products versus reactants and, therefore, the equilibrium constant. The partition function can be written as a product of independent factors at the level of various approximations, each of which is related to the molecular mass, the principal moments of inertia, the normal vibration frequency, and the electronic energy levels, respectively. When the ratio of isotopic partition function is calculated, the electronic part of the partition function cancels, at the level of the Born-Oppenheimer approximation, an approximation stating that the motion of nuclei in ordinary molecular vibrations is slow relative to the motions of electrons. 

Molecular weight of species A Avogadro s number Number of particles of species. A Hypothetical number of activated complexes Density of states for the ath degree(s) of freedom of an activated molecule with energy in the specified degree(s) of freedom Momentum flux in x direction Probability density for states of energy e Enthalpy release per mole of reaction Molar partition function for species A Reduced molar partition function for the activated complex... 

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