Theoretical Limitations on the Temperature Dependence of Vibrational Properties of Harmonic Solids and Molecules

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Abstract
Upper and lower bounds have been found for the mean-square displacement and mean-square velocity of constituent atoms, and for the heat capacity associated with the atomic motions of a harmonic system. These limits are a direct consequence of the harmonic approximation and thermal equilibrium. These limits give the maximum and minimum allowable values of mean-square displacement, mean-square velocity, or heat capacity at any one temperature in terms of the value of the dynamic quantity at any other temperature. In many cases these limits are very restrictive, determining the value of a dynamic quantity at a second temperature to within a few percent.