Scaling of Transition State Vibrational Frequencies and Application of d -Band Theory to the Brønsted–Evans–Polanyi Relationship on Surfaces
Semiempirical energy relations provide a means of estimating thermodynamic properties. Specifically, linear scaling relationships (LSRs) and Brønsted–Evans–Polanyi (BEP) relationships correlate adsorption energies between adsorbates across surfaces and reaction energies with activation barriers, respectively. Although vibrational scaling relations (VSRs) exist between adsorbates at identical sites, scaling between vibrational frequencies of adsorbed local minima and transition states is lacking. Here, we present density functional theory calculations for AH X (A = C, N, O) diffusions on transition metal surfaces and reveal linear scaling between frequencies of local minima and the transition state between those minima. Using d-band theory and linear muffin tin orbital theory (LMTO), we derive the slopes of these transition state vibrational scaling relations (TSVSRs) and, in so doing, provide a rigorous theory extending the original BEP relations developed for solution chemistry to surface chemistry. Furthermore, with a single reference DFT calculation, we predict the slopes and quantify uncertainty in the predictions.