Cross Section Analysis of the Gas-Phase Potential Surface for the Addition of Water to Formaldehyde. A Theoretical Study of the Energetics of Proton Transfer as a Function of ΔpK_a

The cyclic structure for the gas-phase addition of water to formaldehyde combines C-O bond formation and proton transfer. This structure and two different kinds of Jencks-More-O'Ferrall surfaces comprised of C-O bond formation and proton transfer, have been computed at both the semiempirical AMI and ab initio 3-21G levels. As the C-O distance is shortened, the thermodynamic driving force for the proton-transfer reaction increases, and linear Brónsted plots (ΔE^⋆ versus ΔE) result, with slopes 0.53-0.79 over a range of 55-80 kcal/mol in ΔE. Slopes calculated at the two different levels of theory are in good agreement. Despite the extended ranges of the linear Brónsted plots, the transition-state structures for the proton-transfer reactions vary significantly, and the BEMA HAPOTHLE principle is obeyed. Consequently, the slopes of the Brönsted plots cannot be used to estimate the degree of proton transfer at the transition state. Although, in general, the Marcus equation successfully predicts the activation energies and the variation in the transition-state structure, statistical analysis reveals that the accommodation of the data to the linear Brónsted equation is an order of magnitude better than the quadratic Marcus equation. Because the barriers for the proton-transfer reactions are significant, at the cyclic transition state ΔE(≡ΔpK_a) between the proton donor and acceptor moieties is not zero, and a thermodynamic driving force of 30-40 kcal/mol is needed to achieve the proton jump.