Topological aspects of chemical reactivity. Destiny of electron pairs in allowed and forbidden pericyclic reactions

Abstract

The paper represents an attempt to provide a sound theoretical subsidy for the so-called "curved arrow formalism," which proved unprecedented usefulness in shaping our ideas about the mechanisms of organic reactions. The basic idea is to characterize the extent to which the electron pairs are conserved or broken for a given nuclear configuration by the probability of finding the pair of electrons of opposite spin in a given point of space. This probability is quantitatively given by the αβ component of the pair density, with coinciding positions of both electrons. As a function of 3 variables, the quantity Π αβ (r, r) can be displayed in 3D and the monitoring of the snapshots of this quantity for different points along the reaction path thus can bring new interesting insights into the details of bond reorganization in the course of reactions. The paper reports the application of the above approach for the detailed scrutiny of the differences in the electron reorganization of allowed and forbidden pericyclic reactions at the level of simple topological description in terms of overlap determinant method. Despite its simplicity, the approach provided new interesting insights into the factors underlying the different role of electron pairs in allowed and forbidden pericyclic reactions, and we believe that this simple approach could inspire further straightforward extensions that would allow to apply its formalism at the level of contemporary sophisticated computations to real systems of chemical interest. KEYWORDS curved arrow formalism, electron reorganization, overlap determinant method, pericyclic reactions Dedicated to Professor Roald Hoffmann on occasion of his 80th anniversary

How effectively bonding evolution theory retrieves and visualizes curly arrows: The cycloaddition reaction of cyclic nitrones

“…Later, Lledós et al have shown that the motion of the centroids of localized orbitals along the intrinsic reaction coordinate (IRC) can be correlated with the curly arrows representing the electron motions as the reaction takes place . At the same time, Knizia et al have presented the so‐called intrinsic bonding orbitals, that can be associated with a nonempirical form of localized molecular orbitals to calculate the electron flow in many reaction mechanisms, while Ponec has demonstrated, based on the paper of Salem, the relationship between the electron reorganization during the reaction with the shifts of electron pairs, exemplifying the so‐called “curved arrow formalism.” Very recently Schmidt et al have demonstrated that the analysis of any electronic wave‐function in terms of the tiling along a reaction coordinate reveals the electron movements depicted by the curly arrow notation for several reaction.…”