A theory of inner-sphere reorganization energy for electrocatalysis
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
Related
- Molecular Dynamics Simulations of the Outer-Sphere Reorganization Energies of Aqueous Oligothiophenes
- Nanostructure-Based Energy Electrocatalysis
- Spectroscopic–Catalytic Onset Decoupling in Energy Electrocatalysis: Evidence, Mechanistic Hypotheses and Research Priorities from 250 Studies
- Machine Learning-Guided Design of High Entropy Oxides for Photo-Electrocatalysis and Sustainable Energy Conversion
- Enhanced sampling enables binding site water reorganization in polarizable absolute binding free energy calculations
BibTeX
@misc{yang2026theory,
title = {{A theory of inner-sphere reorganization energy for electrocatalysis}},
author = {Kaicong Yang and Bing Huang and Lin Zhuang},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009169/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009169/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - A theory of inner-sphere reorganization energy for electrocatalysis
AU - Kaicong Yang
AU - Bing Huang
AU - Lin Zhuang
PY - 2026
DA - 2026/09/21
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009169/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009169/v1
AB - 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
ER -