Equilibrium Populations over Multiple Minima

It is not uncommon for a single molecule to have multiple populations. At non-zero temperatures, the population of different conformations will be dictated by Boltzmann statistics. If we make the approximation that we may neglect the continuous character of conformational space and simply work with discrete potential energy minima, we can replace a statistical mechanical probability integral with a discrete sum, and the equilibrium fraction F of any given conformer A at temperature T may be computed as 

In fortunate instances, one conformer in a population has a free energy that is much lower than that of any of tire other possibilities. Inspection of Eq. (10.50) makes clear that in that instance, only die low-energy term contributes significantly to the sum, in which case that free energy may be taken as the population free energy. 

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