Vibrational Isotope Effects in Three-Particle Systems. Part I

Proceeding on the assumption of valence forces between the units of a general three-particle system, an analysis is made of the effects of isotopy on the three fundamental frequencies of oscillation. In conformity with Salant and Rosenthal, the effects are classified as end and central isotope effects. The quantities $\frac{\Delta {\omega }_1}{{\omega }_1}$, $\frac{\Delta {\omega }_2}{{\omega }_2}$ and $\frac{\Delta {\omega }_3}{{\omega }_3}$ are derived for both cases. It is demonstrated that the analysis provides a criterion for deciding between several hypothetical models of a single molecule.