Reformulating the Woodward-Hoffmann Rules in a Conceptual Density Functional Theory Context: the Case of Sigmatropic Reactions

In this contribution, we have investigated the performance of the initial hardness response, a reactivity index from conceptual DFT, in the prediction of the allowed or forbidden character of a series of sigmatropic hydrogen shifts, which are traditionally explained using the famous Woodward-Hoffmann rules for pericyclic reactions. Previously, it was observed that this quantity can be linked to the activation hardness of a chemical reaction and, in this case, thus to the aromaticity of the transition state in these kinds of reactions. It is shown, both by considering approximate reaction coordinates and intrinsic reaction coordinates that the allowed mode of the sigmatropic rearrangement corresponds to the largest value of the initial hardness response, in agreement with earlier work on cycloadditions and electrocyclizations.