Multidimensional Hydrogen Tunneling in Supported Molecular Switches: The Role of Surface Interactions

The nuclear tunneling crossover temperature ($T_c$) of hydrogen transfer reactions in supported molecular-switch architectures can lie close to room temperature. This calls for the inclusion of nuclear quantum effects (NQEs) in the calculation of reaction rates even at high temperatures. However, computations of NQEs relying on standard parametrized dimensionality-reduced models quickly become inadequate in these environments. In this Letter, we study the paradigmatic molecular switch based on porphycene molecules adsorbed on metallic surfaces with full-dimensional calculations that combine density-functional theory for the electrons with the semiclassical ring-polymer instanton approximation for the nuclei. We show that the double intramolecular hydrogen transfer (DHT) rate can be enhanced by orders of magnitude due to surface fluctuations in the deep-tunneling regime. We also explain the origin of an Arrhenius temperature dependence of the rate below $T_c$ and why this dependence differs at different surfaces. We propose a simple model to rationalize the temperature dependence of DHT rates spanning diverse fcc [110] surfaces.

Figure 1

(a) Top view of the local minima of porphycene on Cu(110). Concerted and stepwise DHT mechanisms are represented by blue and orange arrows, respectively. Lateral view of the cis (b) and trans (c) conformers, of porphycene on Cu(110) and Ag(110).

Figure 2

(a) Calculated DHT rates $k_{\mathrm{inst}}$ for the $cis\to cis$ reaction of porphycene on Cu(110) between 75 and 150 K. At these temperatures, $k_{\mathrm{inst}}$ includes only contributions from the stepwise mechanism. The inset shows experimental results from Ref. [23]. (b) Calculated DHT $k_{\mathrm{inst}}$ for the $cis\to cis$ reaction of porphycene on Ag(110) between 7.5 and 110 K. Orange circles represent $k_{\mathrm{inst}}$ of the stepwise mechanism and blue squares of the concerted mechanism. The inset shows experimental results from Ref. [4]. (c) Schematic 1D potential energy surfaces of the stepwise (left) and concerted (right) reactions. The zero-point energy (ZPE) for reactant and products are shown, while the ZPE at the barrier top is not (but it was included in the multidimensional calculations). (d) Schematic representation of the different temperature dependence regimes of the stepwise (orange) and concerted (blue) DHT rate of adsorbed porphycene. Full (dashed) lines represent the dominant (minor) mechanism. The numbers 1, 2, and 3 illustrate the three different regimes; see the text.