Isotope chemistry and molecular structure. Total deuterium isotope effects

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Abstract
A qualitative discussion is given on the relationship between the magnitude of isotope effects in polyatomic systems and bending and stretching force constants. This is followed by a general method for the calculation of the isotope effect which can be ascribed to each force constant in the general quadratic potential energy for the vibration of a polyatomic molecule. The method is applied to deuterium isotope effects in the molecules H2O, CH2O, CH4, C2H4, C2H6, and C6H6 at and above 300°K. It is found that deuterium isotope effects associated with individual internal valence force constants are nearly additive at room temperature. Strict additivity holds in the high temperature limit. Bond stretching force constants account for at least 65% of the total deuterium−to−protium reduced partition function ratio at 300°K and become even more dominant at higher temperatures. The origin of the relative importance of stretching and bending forces as a function of temperature is found in the first two terms of the finite orthogonal polynomial method of Bigeleisen and Ishida. Correlations are established between the magnitude of deuterium isotope effects in different molecules as a function of temperature with stretching and bending force constants.