Calculating curly arrows from ab initio wavefunctions

Abstract

Despite being at the heart of chemical thought, the curly arrow notation of reaction mechanisms has been treated with suspicion—the connection with rigorous molecular quantum mechanics being unclear. The connection requires a view of the wavefunction that goes beyond molecular orbitals and rests on the most fundamental property of electrons. The antisymmetry of electronic wavefunctions requires that an N-electron wavefunction repeat itself in 3N dimensions, thus exhibiting tiles. Inspection of wavefunction tiles permits insight into structure and mechanism. Here, we demonstrate that analysis of the wavefunction tile along a reaction coordinate reveals the electron movements depicted by the curly arrow notation for several reactions. The Diels–Alder reaction is revealed to involve the separation and counter propagation of electron spins. This unprecedented method of extracting the movements of electrons during a chemical reaction is a breakthrough in connecting traditional depictions of chemical mechanism with state-of-the-art quantum chemical calculations.

Extended curly arrow rules to rationalise and predict structural effects on quantum interference in molecular junctions

“…While curly arrows may appear somewhat abstract to non-chemists, ab initio simulations of the movement of electrons during chemical reactions were recently shown to agree well with curly arrow notation. 51 CARs provide chemists with an intuitive means of interpreting many observed QI effects. While this use of curly arrows is widely accepted in the literature, surprisingly few works set out how curly arrows work in this context.…”

Electronic Wavefunction Tiles

“…The smooth variation of the Voronoi diagram along the reaction path corresponds closely to the 'curly arrow' notation of organic chemists. [26] We found that S N 2 and nucleophilic carbonyl addition proceeded as per chemistry textbooks. In the attack of hydroxide on formaldehyde, one of the double-bonding sites 'peels off' to smoothly morph into a non-bonding site on the carbonyl oxygen (Fig.…”

“…One of the double bonds peels off to become a lone pair, as per the classical mechanism based on Lewis structures. Figure adapted from ref [26]…”

Electronic transitions of molecules: vibrating Lewis structures

“…We and others demonstrated that if the boundaries between like-signed tiles are defined by a Voronoi diagram, with sites given by the centre-of-mass of the tile, the tiles reproduce Lewis structures of molecules and the double-quartet structures of Linnett 5–10. Further, by following the tiles as a function of a reaction coordinate, one obtains electron movements akin to the “curly arrows” beloved of organic chemists 11. Our procedure to obtain these structures is designated dynamic Voronoi Metropolis sampling (DVMS).…”