Year: 2026
Type: preprint
Abstract: In Marcus theory, reorganization energy links thermodynamics and kinetics for outer-sphere electron transfer, in which the redox centre exchanges an electron without changing its bonding to the electrode. Most electrocatalytic elementary steps are instead inner-sphere processes: the reacting intermediate is part of the interface, and surface bonding changes with charge transfer. A general thermodynamic definition of the full nonequilibrium preparation cost of such a bonded interface is lacking, leaving equilibrium descriptors and measured rates without a common theoretical basis. Here we define this quantity thermodynamically and provide a first-principles procedure for its calculation. A Legendre transform of fixed-potential thermodynamics yields an internal free-energy surface in which interfacial polarization and surface bond state are coupled variables, while electrode potential remains an external control. For a specified elementary event, inner-sphere reorganization energy is the finite free-energy cost of preparing a product-like interface before relaxation. Writing this cost as a Bregman difference separates it from the reaction driving force and relates it to a weighted integral of local interfacial stiffness. The classical Marcus expression is recovered as the one-dimensional harmonic charge-only limit of this framework. Applied to Volmer hydrogen oxidation on
Source: ChemRxiv
Authors: Kaicong Yang, Bing Huang, Lin Zhuang
Institution: Wuhan University
Language: English
Field: Energy
Domain: Physical Sciences
Open Access status: green
Award: G3876699350
OpenAlex ID: W7213865816