The bonding nature of some simple sigmatropic transition states from the topological analysis of the electron localization function

It is shown that the topological analysis of the electron localization function (ELF), a measure of the local Pauli repulsion, is a useful tool to describe the bonding nature of transition structures of simple pericyclic processes. In this work, we have revisited the [1_s,3_a]hydrogen, [1_a,3_s]methyl, and [1_a,3_s]fluorine simple sigmatropic rearrangements in the allyl system. Results based on the integrated densities over the ELF basins and their related properties at the B3LYP/6-311++G(d,p) level of theory showed explicitly a delocalized structure for the antarafacial (C_s hydrogen rearrangement, a two radical interaction for the methyl suprafacial (C₂) migration, and a pair-ion interaction for the fluorine suprafacial (C_s) transfer. Results on these well-studied systems confirm the topological analysis of the ELF as a useful descriptor for the study of bonding structure of pericyclic transition states. In this context, the ELF analysis is shown to be a complementary value to the Woodward-Hoffmann rules, which provide an orbital symmetry basis of understanding.