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 Ci factors, representing the ith coordinate oscillator and the Pj–k factors, corresponding to the interaction between the jth and kth coordinate oscillators. The important Ci and Pj–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 Ci and Pj–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.