Vibrational Scaling Relationships for Transition States

Semiempirical energy relations provide means of estimating thermodynamic properties and simplifying underlying theoretical trends among classes of reactions. Specifically, Brønsted-Evans-Polanyi (BEP) relationships correlate reaction energies with activation barriers. Scaling relations are not limited to electronic energies; recently, vibrational frequencies of adsorbed surface species were shown to scale across transition metal surfaces.¹ However, scaling between vibrational modes of adsorbed local minima and transition states, which influence temperature corrections to free energies and reaction rate constants, is lacking. We present density functional theory calculations for AH_x (A = C, N, O) diffusions and dehydrogenations on transition metal surfaces, where normal modes are classified in relation to adsorbate-surface interactions. Vibrational scaling relationships (VSRs) correlating such normal modes between local minima and transition states are developed, and we fundamentally derive the slopes of the VSRs from corresponding BEP scaling. We extend BEP relationships across different surface sites to VSRs. Furthermore, we demonstrate how vibrational thermodynamic quantities scale across surfaces and resulting effects on thermodynamic/kinetic model projections.

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