Simplified Procedure for the Theoretical Calculation of Isotope Effects Involving Large Molecules

It is demonstrated that one can simplify statistical-mechanical calculations of isotope effects on rates and on equilibria, without introducing significant error, by omitting large portions of the molecules involved. One can usually ``cut off'' parts of the molecules more than two bonds removed from the position(s) of isotopic substitution at which force-constant changes occur between reactant and transition state in a rate process or between reactant and product in an equilibrium process. Sometimes more extreme cutoff is possible. The force-constant and geometry changes at the isotopic position(s) must be the same in the cutoff and complete calculations. The success of the cutoff procedure focuses attention on the fact that experiments which determine isotope effects in the room-temperature region and above can directly yield information regarding only changes occurring in the neighborhood of the isotopic position(s).