A dimensionless reaction coordinate for quantifying the lateness of transition states

The Hammond-Leffler postulate asserts that transition states of exothermic reactions are reactant-like (early), whereas transition states of endothermic reactions are product-like (late). Related postulates have been proposed to describe the sensitivity of activation barriers for reactions occurring on catalytic surfaces to the catalyst structure. To evaluate the validity of these postulates for different chemical reactions, a general method for classifying transition states as either early or late is needed. One can envision a dimensionless reaction coordinate that changes continuously and monotonically from 0 to 1 along a minimum energy reaction pathway. The value of the dimensionless reaction coordinate for the transition state (W(TS)) classifies transition states as (a) early when W(TS) < 0.5, (b) late when W(TS) > 0.5, and (c) equidistant between reactants and products when W(TS) = 0.5. In this article, we derive such a dimensionless reaction coordinate and illustrate its usefulness for several different chemical reactions.