Quantum Tunneling Contribution for the Activation Energy in Microwave-Induced Reactions

Abstract

In this study, a quantum approach is presented to explain microwave-enhanced reaction rates by considering the tunneling effects in chemical reactions. In the Arrhenius equation, the part of the Hamiltonian relative to the interaction energy during tunneling, between the particle that tunnels and the electrical field defined in the medium, whose spatial component is specified by its rms value, is taken into account. An approximate evaluation of the interaction energy leads to a linear dependence of the effective activation energy on the applied field. The evaluation of the rms value of the field for pure liquids and reaction mixtures, through their known dielectric properties, leads to an appreciable reduction in the activation energies for the proton transfer process in these liquids. The results indicate the need to move toward the use of more refined methods of modern quantum chemistry to calculate more accurately field-induced reaction rates and effective activation energies.

On the Theory of Electrolytic Dissociation, the Greenhouse Effect, and Activation Energy in (Electro)Catalysis: A Tribute to Svante Augustus Arrhenius

“…The occurrence of negative energies (Anti‐Arrhenius) and curved Arrhenius plots, particularly for reactions presumed to be of elementary nature have also been ascribed by some studies to be due to the prevalence of more complex mechanisms and the contribution of non‐thermal effects, including quantum mechanical tunneling, where the reactant species surmount energy barriers that they are not otherwise predicted to be able to overcome . Examples of reactions that exhibit negative activation energies can be found in the reports by McMahon, and Suez et al., among others.…”

“…In such reactions, the microcanonical rate coefficient is a decreasing function of energy. Modification of the Arrhenius equation to account for quantum tunneling events is therefore necessary, particularly, for reactions that clearly exhibit negative activation energies (Anti‐Arrhenius) and curved Arrhenius plots …”