Analysis of isotope effects by the perturbation theory technique: 13C/12C isotope effects in alkyl ethers

Abstract

The ¹³C/¹²C isotope effect, conventionally represented by the reduced isotopic partition function ratio, (S₂/S₁)f, for a pair of ¹³C and ¹²C isotopic molecular species, in a series of alkyl ethers having a transferable molecular force field, has been analysed by a statistical-mechanical perturbation theory approach by expressing it as multiplicative factors: C factors, representing individual uncoupled coordinate oscillators [e.g. bond stretches, angle bends and torsions] and P factors, corresponding to the interaction between the coordinate oscillators. A few of the important C and P factors, which suffice to compute, with utmost ease, the (S₂/S₁)f for any ¹³C substitution site in an ether, have been listed. The (S₂/S₁)f calculated from these factors is found to be within ca. 0.2–0.3% of the exact value, computed on the basis of the usual normal-mode vibrational frequency calculation approach. The slight loss in accuracy of (S₂/S₁)f computed by the perturbation theory approach is outweighed by (a) the ease with which the values of isotope effects are obtained and (b) because its origin is better understood.