Analysis of isotope effects by the perturbation theory technique. D/H Isotope effects in alkyl ethers

Abstract

The reduced isotopic partition function ratio, (S₂/S₁)f, for D/H isotope effects in a series of monodeuterated alkyl ethers with transferable molecular force field, have been analysed by a statistical-mechanical perturbation theory approach. In this approach it is possible to express (S₂/S₁)f in terms of well characterised multiplicative factors: the C_i factors, representing the ith coordinate oscillator and the P_j–k factors, corresponding to the interaction between the jth and kth coordinate oscillators. The important C_i and P_j–k factors valid for D-substitution at any site on any ether have been identified and listed. It is found that (S₂/S₁)f evaluated from these few C_i and P_j–k factors is within ca. 1–2% of the exact value obtained from the usual normal-mode vibrational frequency calculations. The perturbation theory technique, besides helping to compute (S₂/S₁)f in a very simple manner, also gives a clearer understanding of the origin of isotope effects.