Universal Vibrational and Entropic Scaling Relationships for Dehydrogenations

Linear scaling relationships (LSRs) and Brønsted – Evans – Polanyi (BEP) relationships aid with prediction of electronic energies using data from adsorbed local minima; however, other Arrhenius parameters involved in the calculation of kinetic properties, such as temperature effects and pre-exponentials, are often taken as constants across metal surfaces or a homologous series in microkinetic modeling. Recently, vibrational frequencies related to adsorbate-surface interactions have been shown to scale with electronic energies [1]. Our group correlated the slopes of LSRs to vibrational scaling relationships (VSRs) for AH_X (A = C, N, O) adsorbates [1], and we expanded the theory to predict transition state vibrational scaling relations (TSVSRs) from the corresponding BEP relationships for AH_X diffusions [2]. Using density functional theory (DFT), we further extend TSVSRs to CH_X, NH_X, and OH_X dehydrogenation reactions on transition metal surfaces, relating vibrational modes of local minima to transition states. We validate previous theory developed for BEP-like energy relations and fundamentally link the slopes of BEPs to TSVSRs for AH_X dehydrogenations. In contrast to the theory developed for diffusion reactions, we incorporate hybridization variation into our derivation for AH­_x dehydrogenations; we examine how molecular geometries and bonding properties change between local minima and transition states. We predict the slopes of the TSVSRs from corresponding BEPs and pertinent geometric data. Additionally, we uncover universal thermochemical property scaling, demonstrating the potential for estimation of entropies and temperature corrections to enthalpies across dehydrogenation reactions.

[1] Lansford, J. L., et al. Nat. Commun. 8, 1842 (2017).

[2] Lansford, J. L., et al. J. Phys. Chem. C 125 (13), 7119-7129 (2021).