?Statistical-mechanical? understanding of chemical reaction mechanism in solution: Energy fluctuations and heat capacities for isomerization of formamidine in aqueous solution

Abstract

To explore the energy flow-mechanism of a solution-chemical reaction on the basis of an energy-fluctuation analysis and the time evolution of various kinds of energies [J. Phys. Chem. 48, 12506 (1994)], a chemical reaction molecular dynamics simulation was carried out in the microcanonical ensemble for the proton-transfer reaction of formamidine in an aqueous solution. The energy ΔE required to surmount the reaction barrier was found to be supplied mainly from the potential energy of the solvent water rather than from the solvent kinetic energy. The ratio of the reactive energy flow from the solvent potential vs. the kinetic energy, ΔV/ΔK, was 2.34 and was found to be in good agreement with the value of 1.96 predicted from the classical constant-volume heat capacity of water, C, via the Lebowitz–Percus–Verlet relation [Phys. Rev. 153, 250 (1967)]. This finding confirmed the results of Wilson et al. [J. Am. Chem. Soc. 113, 74 (1991)]; namely, that the ratio should be determined only by the heat capacity of the solvent with no relation to the kinds of solute molecules, and in aqueous solution, the coordinate fluctuation plays a more important role in the reaction occurrence than in the momentum fluctuation. Furthermore, on the assumption that the solute internal distribution is assumed to accomplish instantaneously thermal equilibrium with the surrounding solvent and to be characterized as an instantaneous canonical ensemble, the instantaneous partial molar constant-volume heat capacity of solutes, C(t), is defined at first by a simple extension of the relationship between the equilibrium heat capacity C and the ratio of the kinetic- and potential-energy fluctuations of the solutes. On the average, C(t) has a larger value than that evaluated within the harmonic approximation in the gas phase, i.e., 199.5 J K−1mol−1. The incompatibility was brought about by the intervention of the solute–solvent interaction. In addition, an exceptionally large value of C(t) was observed just 0.06 ps after (or before) the barrier crossing time and can be explained by the smaller fluctuation in the instantaneous kinetic energy. It was also observed that, during the relaxing (or surmounting) process of the reaction, C(t) becomes relatively larger than those in the transition and equilibrium periods, originating from the simple fact that the relatively larger potential fluctuation makes it easier to dissipate (or supply) the reactive energy from (or to) the reactants, as translated by a larger C(t). © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 133–145, 1998