Vacuum field in a cavity, light-mediated vibrational coupling, and chemical reactivity
Graphical abstract
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 , 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.
Section snippets
General equations
Below, I first reproduce the text-book TST expression for the rate constants of rate processes in general (Section 2.1) and the simplest reaction under consideration in the absence of VSC in particular (Section 2.2). Then, I outline the standard Dicke model allowing one to describe VSC (Section 2.3). The VSC-related corrections of the reaction rate constant are derived in Section 2.4.
Conclusion
In general, the rate constant of adiabatic reaction occurring in the presence of VSC can be represented as a product of the rate constant of reaction occurring without VSC and the correction factor, , taking VSC into account. For adiabatic reactions (Fig. 2) in the framework of TST [as e.g. in (26)], this correction factor can in turn be represented as a product of two correction factors,related to the partition functions and the shift of . The analysis presented shows that these two
Declaration of Competing Interest
The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The work was supported by Russian Academy of Sciences and Federal Agency for Scientific Organizations (project 0303-2016-0001). The author thanks Timur Shegai for the related discussions.
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