Vacuum field in a cavity, light-mediated vibrational coupling, and chemical reactivity

Highlights

• Focus is on coupling between molecular vibrations and vacuum field in a microfluidic cavity.

• This effect is theoretically analyzed in the context of adiabatic reactions.

• The scale of the corresponding corrections of the Arrhenius parameters is demonstrated to be nearly negligible.

Abstract

Collective coupling between vibrations of molecules, participating in reaction, and the vacuum field of a microfluidic optical cavity is now sometimes considered to be one of the novel potential unconventional ways of influencing the reaction rate. Herein, this effect is theoretically analyzed focusing on adiabatic reactions occurring via the ground electronic state with a saddle point located between reactants and products. The key conclusion is that for cavities with a relatively large number of reactants ($~{10}^6-{10}^7$) the scales of the corresponding corrections of the pre-exponential factor and activation energy are nearly negligible.

Introduction

Chemical reactions occurring in condensed media form an important class of reactions with long and rich history of experimental and theoretical studies [1], [2], [3]. Customarily, such reactions are described in terms of nuclear motion along potential energy surfaces. The details and outcome of the corresponding models depend on a reaction subclass and, first of all, whether a reaction is adiabatic (i.e., occurs via the ground electronic state) or nonadiabatic (i.e., occurs with participation of excited electronic states). Adiabatic chemical reactions running under thermal conditions are usually associated with passing through an activation barrier located along the reaction coordinate linking the areas corresponding to reactants and products. In photochemical reactions, the transitions between potential energy surfaces are induced by photons. From these perspectives, one new interesting concept proposed and experimentally illustrated by Ebbesen’s group [4], [5], [6], [7], [8], [9], [10] is that in a reactor of small size (at least in one direction) or, more specifically, in a microfluidic Fabry-Perot cavity with the thickness determined by the light wavelength (Fig. 1), the reactivity can be influenced by coupling vibrations of molecules to light, and that this effect, referred to as vibrational strong coupling (VSC), is possible even without the presence of photons. Although similar experiments are now not numerous (see, e.g., Refs. [11], [12], [13]; reviewed in [14]), this concept has attracted attention of theorists [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. In particular, adiabatic reactions were treated in Refs. [17], [18], [19], [20].

Despite the high current theoretical activity in the area under consideration [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], the interpretation of the available experimental results is still open to debate [14]. The validity of and relation between various models can also debated. In particular, the outcome of two theoretical works [17], [18] focused on adiabatic reactions (Fig. 2) is contradictory. The first one predicts that the effect of VSC can be appreciable with an increase of a reaction rate constant by a factor up to ${10}^4$, while according to the second one the effect is predicted to be negligible. Although the latter conclusion is now considered to be more valid [14], an additional analysis is still desirable, because the available treatments are not fully comprehensive.

My analysis presented herein is also focused on adiabatic reactions. Compared to the earlier related studies [18], [19], [20], the approach I use is deliberately simpler and closer to the conventional transition state theory (TST) of rate processes (it makes the results more suitable for general readership). In addition, I pay more attention to the influence of VSC on the pre-exponential factor and activation energy of rate processes.