Effective Directionality in Electron-Transfer-Driven Reactions on Bifurcating Multidimensional Potential Energy Surfaces
- 1John A. Paulson School of Engineering and Applied Sciences
- 2Harvard University
Abstract
Electron transfer (ET) is microscopically reversible under a closed, finite, Hermitian Hamiltonian, yet ET-driven reactions are strongly directional: of several possible products, one is formed and kept. Standard theories explain this through thermodynamic driving forces, free-energy surfaces, or coupling to a continuum of environmental modes. We ask whether the geometry of a multidimensional Born-Oppenheimer surface, combined with relaxation into the molecule's own vibrational modes, can supply this directionality without an external bath. On model surfaces with a reaction coordinate and an orthogonal branching coordinate, the shape of the surface after the transition state decides which product forms within about one vibrational period, independently of barrier heights. Relaxation into a closed, energy-conserving set of internal harmonic modes, an idealized model of intramolecular energy redistribution, keeps that decision for hundreds of vibrational periods, even where the microcanonical equilibrium of the full system (reacting coordinates and modes together, at the same energy) favors the other product almost completely. When the branching follows an electron-transfer crossing between coupled diabatic surfaces, the decision can be quantum, and the same internal modes keep it. The decision is kept when the internal modes drain the exchange coordinate, the motion that carries one product into the other, faster than the products exchange. Across random surfaces, spectral densities and coupling patterns, an a priori estimate of this competition predicts most outcomes, and its failures trace to which coordinate holds the energy. Thermal and quantum modes remove the kept decision before they remove commitment. The irreversibility supplied by the internal modes is statistical, as for any finite bath; the geometry fixes the direction, both which product forms and which motion must be drained for it to be kept.
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BibTeX
@misc{le2026effective,
title = {{Effective Directionality in Electron-Transfer-Driven Reactions on Bifurcating Multidimensional Potential Energy Surfaces}},
author = {Linh M. Le},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15007426/v3},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007426/v3},
note = {CC BY},
}
RIS
TY - UNPB
TI - Effective Directionality in Electron-Transfer-Driven Reactions on Bifurcating Multidimensional Potential Energy Surfaces
AU - Linh M. Le
PY - 2026
DA - 2026/10/21
PB - ChemRxiv
DO - 10.26434/chemrxiv.15007426/v3
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007426/v3
AB - Electron transfer (ET) is microscopically reversible under a closed, finite, Hermitian Hamiltonian, yet ET-driven reactions are strongly directional: of several possible products, one is formed and kept. Standard theories explain this through thermodynamic driving forces, free-energy surfaces, or coupling to a continuum of environmental modes. We ask whether the geometry of a multidimensional Born-Oppenheimer surface, combined with relaxation into the molecule's own vibrational modes, can supply this directionality without an external bath. On model surfaces with a reaction coordinate and an orthogonal branching coordinate, the shape of the surface after the transition state decides which product forms within about one vibrational period, independently of barrier heights. Relaxation into a closed, energy-conserving set of internal harmonic modes, an idealized model of intramolecular energy redistribution, keeps that decision for hundreds of vibrational periods, even where the microcanonical equilibrium of the full system (reacting coordinates and modes together, at the same energy) favors the other product almost completely. When the branching follows an electron-transfer crossing between coupled diabatic surfaces, the decision can be quantum, and the same internal modes keep it. The decision is kept when the internal modes drain the exchange coordinate, the motion that carries one product into the other, faster than the products exchange. Across random surfaces, spectral densities and coupling patterns, an a priori estimate of this competition predicts most outcomes, and its failures trace to which coordinate holds the energy. Thermal and quantum modes remove the kept decision before they remove commitment. The irreversibility supplied by the internal modes is statistical, as for any finite bath; the geometry fixes the direction, both which product forms and which motion must be drained for it to be kept.
ER -