thermodynamic isotope effect

https://doi.org/10.1351/goldbook.T06319
The effect of isotopic substitution on an @[email protected] is referred to as a thermodynamic (or equilibrium) @[email protected] For example, the effect of isotopic substitution in reactant A that participates in the equilibrium: $\text{A}+\text{B}\rightleftharpoons \text{C}$ is the ratio $$\frac{K^{\text{l}}}{K^{\text{h}}}$$ of the @[email protected] for the reaction in which A contains the light isotope to that in which it contains the heavy isotope. The ratio can be expressed as the @[email protected] for the isotopic exchange reaction: $\text{A}^{\text{l}}+\text{C}^{\text{h}}\rightleftharpoons \text{A}^{\text{h}}+\text{C}^{\text{l}}$ in which reactants such as B that are not @[email protected] do not appear. The potential energy surfaces of isotopic molecules are identical to a high degree of approximation, so thermodynamic isotope effects can only arise from the effect of isotopic mass on the nuclear motions of the reactants and products, and can be expressed quantitatively in terms of @[email protected] ratios for nuclear motion: $\frac{K^{\text{l}}}{K^{\text{h}}} = \frac{(Q_{\text{nuc}}^{\text{l}}/Q_{\text{nuc}}^{\text{h}})_{\text{C}}} {(Q_{\text{nuc}}^{\text{l}}/Q_{\text{nuc}}^{\text{h}})_{\text{A}}}$ Although the nuclear @[email protected] is a product of the translational, rotational and vibrational @[email protected] functions, the @[email protected] is determined almost entirely by the last named, specifically by vibrational modes involving motion of isotopically different atoms. In the case of light atoms (i.e. @[email protected] vs. @[email protected] or @[email protected]) at moderate temperatures, the @[email protected] is dominated by zero-point energy differences.