Transition state looseness and alpha-secondary kinetic isotope effects

The correlation between hydrogen/deuterium alpha-secondary kinetic isotope effects and transition state looseness has been investigated by MP2/6-31++G(d,p) calculations on three identity X(-) + CH(3)X S(N)2 reactions. By varying the C-X distances in these systems it is shown that the secondary kinetic isotope effect increases with increasing transition structure looseness. Furthermore, it is shown that looseness is best defined as a Delta-elongation of the C-X bond lengths, where the reference state can be either the isolated reactants or the ion-dipole complex. The variation of kinetic isotope effects is shown by factor analysis to be determined by C-H bending vibrations. The contributions from C-H stretching vibrations are important for the absolute values of the kinetic isotope effects, and are partly due to C-H bond length changes. The variation of the secondary kinetic isotope effect from the stretching vibrations with looseness is in the opposite direction as the bending contribution, causing a level-off in the total kinetic isotope effect for tight transition structures.