The Transition Seam Ansatz of Kinetic Theory
- 1Department of Energy
- 2Aalborg University (AAU
- 3Pioneer Center for Accelerating P2X Materials Discovery (CAPeX, Technical University of Denmark, 2800 Kgs., Lyngby, Denmark
Abstract
The Eyring formulation of transition-state theory fixes a single activated-complex population by equilibrium with the reactant state, so that a population in equilibrium with one state has no net flux from that state. This paper keeps the three assumptions of that theory and takes the barrier as the seam at which the electronic-structure manifolds of reactant and product have equal energetic chemical potential. One transition state then has two populations, one on each manifold, with separate amounts and configurational chemical potentials and with a shared energetic chemical potential and configurational excess. The flux on each manifold is a shared attempt frequency times its seam population, and De Donder referencing of the two fluxes is the isothermal rate law. Each seam population is in equilibrium with its own state, so transitivity of equilibrium places no condition on the two states. Recrossing, tunnelling, and non-adiabatic passage are contained in the attempt frequency rather than distributed across the rate expression. The transition-state population is an explicit quantity of the law. An ideal catalyst binds its intermediates neither so weakly that there is nothing to form a transition state from, nor so strongly that there is nowhere to form it. Mass action, Langmuir, and Butler–Volmer are decisions on the two excesses, the classical two-rate-constant law collects the energetic pieces into forward and reverse rate constants that share the attempt frequency, and a directional law is the limit in which the running amount of one intermediate is negligible against its equilibrium amount. The reversibility of a step is the ratio of the two seam populations, which occupy the same nuclear configuration and differ in electronic structure.
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BibTeX
@misc{brandes2026transition,
title = {{The Transition Seam Ansatz of Kinetic Theory}},
author = {Benedikt Axel Brandes},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009414/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009414/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - The Transition Seam Ansatz of Kinetic Theory
AU - Benedikt Axel Brandes
PY - 2026
DA - 2026/09/24
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009414/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009414/v1
AB - The Eyring formulation of transition-state theory fixes a single activated-complex population by equilibrium with the reactant state, so that a population in equilibrium with one state has no net flux from that state. This paper keeps the three assumptions of that theory and takes the barrier as the seam at which the electronic-structure manifolds of reactant and product have equal energetic chemical potential. One transition state then has two populations, one on each manifold, with separate amounts and configurational chemical potentials and with a shared energetic chemical potential and configurational excess. The flux on each manifold is a shared attempt frequency times its seam population, and De Donder referencing of the two fluxes is the isothermal rate law. Each seam population is in equilibrium with its own state, so transitivity of equilibrium places no condition on the two states. Recrossing, tunnelling, and non-adiabatic passage are contained in the attempt frequency rather than distributed across the rate expression. The transition-state population is an explicit quantity of the law. An ideal catalyst binds its intermediates neither so weakly that there is nothing to form a transition state from, nor so strongly that there is nowhere to form it. Mass action, Langmuir, and Butler–Volmer are decisions on the two excesses, the classical two-rate-constant law collects the energetic pieces into forward and reverse rate constants that share the attempt frequency, and a directional law is the limit in which the running amount of one intermediate is negligible against its equilibrium amount. The reversibility of a step is the ratio of the two seam populations, which occupy the same nuclear configuration and differ in electronic structure.
ER -