Mechanistic Pathways in Cyanide-Mediated Benzoin Condensation: A Comprehensive Electron Localisation Function (ELF) and Catastrophe Theory Analysis of the Umpolung Reaction

Abstract

This research investigates the mechanism of the cyanide-type umpolung reaction in benzoin condensation using topological analysis of ELF and catastrophe theory. The study achieves a comprehensive understanding of the evolution of chemical bonds and non-bonding electron density in the reaction of benzaldehyde and cyanide ions. The results reveal that the reaction proceeds through five transition state structures, with the formation of Lapworth's cyanohydrin being the rate-determining step. The study characterises topological catastrophes in the evolution of the ELF field and provides a detailed description of the evolution of electron density in the mechanism of the reaction. An in-depth analysis of ELF catastrophes confirms the well-established Lapworth mechanism.

Keywords: BET; ELF; benzoin condensation; umpolung reaction.

Figure 1

The Lapworth mechanism of the cyanide-catalysed benzoin condensation.

Figure 2

The Gibbs free energy of activation barriers and relative Gibbs free energies for umpolung transition states (TSs), with blue values representing relative energies and red values indicating activation energies from the reagent side, $\Delta G_{\mathrm{a}}\left(\mathrm{I}\right)$.

Figure 3

Optimised transition state (TS) structures for all steps of the umpolung reaction at the DFT(B3LYP)/6-311++G(d,p) computational level.

Figure 4

The evolution of the total energy (red lines), ${\mathrm{E}}_{\mathrm{TOT}}$, and both Hausdorff distances (green lines), dH(A,B) and dH(B,A), for the umpolung reaction as a function of the IRC coordinate. The peaks above the dashed line (dH = 0.2) indicate significant topological changes in the ELF map.

Figure 5

The evolution of APT charge of C1 and H1 atoms during the proton transfer in Lapworth’s cyanohydrin formation. The “DP” refers to the dressed proton state.