Vibrational strong coupling influences product selectivity in a model for post transition state bifurcation reactions

Abstract

Understanding the mechanism of chemical reaction rate modulation by vibrational strong coupling (VSC) has been the focus of several recent studies. However, a definitive explanation for the mode-specificity of VSC still eludes us. In this study, we highlight the dynamics under VSC by utilizing a model for post-transition state bifurcation (PTSB) reactions coupled to an optical cavity. The minimal two-dimensional PTSB model features a valley-ridge inflection (VRI) point leading to bifurcated energetically asymmetric product wells. Here, we are interested in exploring whether the product selectivity (branching ratios) in such PTSB systems, known to be sensitive to dynamical effects, can be significantly perturbed under VSC conditions. Detailed classical and quantum dynamical calculations, along with systematic variation of the model parameters, reveals that the branching ratio can be enhanced under VSC by nearly a factor of two. Interestingly, for certain parameter regimes we find excellent classical-quantum correspondence. Apart from emphasizing the role of both cavity-system and intramolecular energy transfer in the observed enhancements, our study brings out the complexity of VSC in terms of the choice of the cavity frequency vis--à--vis the various molecular mode frequencies. In addition, our work highlights the potential of cavity quantum electrodynamics as a tool for reshaping dynamical outcomes in reactions with complex potential energy landscapes.

Figures (7)

• Figure 1: Model potential energy surface Eq. \ref{['modelPES']} exhibiting a post transition state bifurcation. The reactant (R), transition states (TS$_{1}$, TS$_{2}$), products (P$_{1}$, P$_{2}$), and the valley ridge inflection (VRI) point are indicated.
• Figure 2: (a) Variation of the harmonic frequencies associated with the different stationary points (indicated) with the parameter $V^{\ddagger}_{n}$. Solid and dash-dot lines show the $x$-mode and the $y$-mode frequencies respectively. In addition, dotted lines show the $x$-mode fundamental frequencies ($0 \rightarrow 1$) associated with the two product wells. (b) Variation of the $2^{\mathrm {nd}}$ and $3^{\mathrm {rd}}$ eigenvalues of Eqn. \ref{['modvscham']} with cavity frequency $\omega_{c}$ for parameter value $V^{\ddagger}_{2}$ exhibiting avoided crossings. (c) show the corresponding absorption spectrali2021cavity in the presence (black) and absence (blue) of cavity-molecule coupling. The cavity-system coupling strength is fixed at $\lambda_{c} = 0.1$ a.u.
• Figure 3: (a) and (b) Two different representations of the classical normalized branching ratio Eq. \ref{['normbranchrat']} as a function of the cavity frequency $\omega_c$ and barrier parameter $V^{\ddagger}_n$. The landscape is computed on a $311 \times 100$ grid (see supplementary for details on the grid setup) for an initial state with energy $\langle E_{S}\rangle \approx 0.01$ a.u with the cavity-system coupling strength $\lambda_{c} = 0.1$ a.u and asymmetry parameter $\alpha = 0.1$. In (b) the varying harmonic (solid lines) and fundamental (dashed lines) frequencies of the reactant well $\omega_{\mathrm{R}}^{x}$ (cyan), the deeper product well $\omega_{\mathrm{P}_{1}}^{x}$ (magenta), and the product well $\omega_{\mathrm{P}_{2}}^{x}$ (black) are superimposed. (c) Classical (lines with symbols) and quantum (solid lines) branching ratios for specific $V^{\ddagger}_{n}$ values. The $x$-mode harmonic frequencies for the two product wells are indicated with arrows.
• Figure 4: Intrinsic reaction coordinate (IRC, red curve) projected onto the two-dimensional PES for varying barrier parameter $\overline{V}^\ddagger = V_{n}^{\ddagger}/x_{s}^{4} \equiv V^{\ddagger}/n x_{s}^{4}$ with $n=1,\ldots,5$.
• Figure 5: Classical normalized time averaged domain probabilities Eq. \ref{['pd_cm']} corresponding to the branching ratios shown in \ref{['fig:xcoupledBR']}(c). Apart from the $x$-mode frequencies of the product wells, the transverse mode frequency at TS$_{2}$ is also indicated (green arrow).