On the calculation of force constants from mean amplitudes of vibration and isotope effect on mean amplitudes

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Abstract
The extremal properties of both bonded and nonbonded mean amplitudes of vibration are discussed, with a view to see beforehand if real solutions for the force constants could be obtained using such data. A detailed study of the effect of small mass changes in isotopically substituted molecules on mean amplitudes of vibration is made using the first order perturbation theory. Several interesting facts are explained with the help of this approach. The utility of other simple, approximate formulas in this regard is tested using specific examples.