How fast does an electron move from donor to acceptor?
Electron transfer sits exactly at the interface between electronic structure, nuclear motion and kinetics. The electronic states tell us where the electron can be; the environment controls how costly it is to reorganize; the coupling determines how efficiently the two states communicate.
Define diabatic donor/acceptor states, electronic coupling, reorganization energy and driving force.
Locate a reaction in the normal, activationless or inverted Marcus regime.
Understand what energy-gap sampling can—and cannot—determine from molecular ensembles.
Diabatic states
Define donor and acceptor states before you talk about a rate
Electron transfer is controlled by both energetic alignment and wavefunction communication
What it is: The off-diagonal matrix element connecting donor- and acceptor-localized electronic states.
What it changes: It sets how strongly the two charge-localized states mix; in the nonadiabatic Marcus limit the rate scales as \(|V|^2\).
What you observe: Strong distance/orientation dependence of ET rates and avoided-crossing gaps between coupled states.
What it is: An electronic state defined to preserve a chemically meaningful identity such as 'electron on donor' or 'electron on acceptor' as nuclei move.
What it changes: It provides a stable basis in which coupling and energy-gap fluctuations can be defined.
What you observe: Not directly measured; it is a modelling construction whose parameters predict rates and spectra.
For an electron-transfer problem it is often useful to work with diabatic states: states whose charge localization retains a clear chemical meaning as the nuclei move. Schematically,
The two diabatic states are coupled by an electronic matrix element, often written \(V\) or \(H_{DA}\):
Weak coupling gives predominantly localized donor and acceptor states and leads naturally to a nonadiabatic golden-rule description. Strong coupling mixes the states substantially and can push the problem toward the adiabatic regime.
Reorganization
The nuclei have to rearrange too
Reorganization energy measures how much the environment must reshape for a new charge distribution
What it is: The free-energy cost of taking the nuclei/environment from the equilibrium configuration of one charge state to the geometry appropriate for the other without transferring the electron yet.
What it changes: It controls the curvature/barrier of Marcus free-energy surfaces and sets the activationless condition \(\Delta G^\circ=-\lambda\).
What you observe: It is inferred from kinetics, spectroscopy or energy-gap statistics rather than observed as a single direct spectral line.
What it is: The thermodynamic free-energy difference between product and reactant states.
What it changes: It shifts the relative vertical position of the Marcus parabolas and therefore changes the activation barrier.
What you observe: Changes in ET rate with redox potential, environment, mutation or molecular substitution.
When an electron moves, the preferred nuclear geometry and solvent polarization generally change. Marcus theory collects that energetic cost into the reorganization energy \(\lambda\).
Changes in bond lengths, angles and intramolecular vibrational coordinates of donor and acceptor.
Reorientation and polarization of the surrounding solvent, protein or dielectric environment.
The reaction driving force is the standard free-energy change \(\Delta G^\circ\). With the usual sign convention, a negative \(\Delta G^\circ\) means the electron-transfer reaction is thermodynamically downhill.
Marcus surfaces
Two parabolas are enough to understand the barrier
The activation barrier is the nuclear configuration the system must reach before electron transfer becomes energetically allowed
What it is: The free-energy cost of reaching the crossing region where reactant and product electronic states are energetically matched in the diabatic picture.
What it changes: It enters the rate exponentially, so small barrier changes can change electron-transfer kinetics by orders of magnitude.
What you observe: Strong temperature and environment dependence of ET rates.
What it is: The special case \(\Delta G^\circ=-\lambda\) in classical Marcus theory where the equilibrium reactant geometry can reach energetic degeneracy without a free-energy barrier.
What it changes: It maximizes the classical nonadiabatic Marcus rate for fixed coupling and temperature.
What you observe: A turnover from increasing to decreasing rate as the reaction is made progressively more exergonic.
What it is: The regime \(-\Delta G^\circ>\lambda\), where further thermodynamic driving moves the crossing away from the reactant minimum again.
What it changes: The activation barrier grows even though the reaction becomes more exergonic.
What you observe: Electron-transfer rates that decrease as the driving force becomes more negative.
Classical Marcus theory approximates the reactant and product free-energy surfaces as harmonic functions of an effective solvent or nuclear reaction coordinate. The activation free energy is
This equation already contains the central result. As the reaction becomes more exergonic, the barrier first becomes smaller. It vanishes when \(\Delta G^\circ=-\lambda\). If the reaction is made even more exergonic, the barrier grows again: the Marcus inverted region.
Making the reaction more exergonic lowers the activation barrier.
The classical activation barrier reaches zero.
More negative driving force now increases the barrier again.
Rate theory
The standard nonadiabatic Marcus rate
In the weak-coupling, classical high-temperature limit, the electron-transfer rate is
The rate depends quadratically on the electronic coupling \(V\), exponentially on the activation free energy, and only more gently on temperature through the prefactor and Boltzmann factor.
Marcus-rate explorer
The current driving force is exergonic but not yet beyond the activationless point.
This is the classical nonadiabatic Marcus expression. It does not automatically cover strong electronic coupling, quantum vibrational effects, non-equilibrium solvent response or conformational gating.
Ensemble energetics
How do you obtain \(\lambda\) and \(\Delta G^\circ\) from simulations?
One useful route is vertical energy-gap sampling. Define the instantaneous energy gap
where the two electronic states are evaluated at the same nuclear geometry \(\mathbf R\). If both reactant and product ensembles are sampled and the linear-response Marcus assumptions hold,
A single ensemble of vertical gaps is therefore not, by itself, enough to determine both \(\lambda\) and \(\Delta G^\circ\) without extra assumptions. Two properly equilibrated state-specific ensembles give a much cleaner Marcus construction.
Beyond one number
Proteins can gate electron transfer through conformational subensembles
In a flexible protein, \(V\), \(\Delta G^\circ\) and even the effective reorganization energy can depend on conformation. Because the rate depends on \(V^2\) and exponentially on the activation barrier, averaging structures first and calculating one rate afterwards can be very misleading.
In general,
A small fraction of strongly coupled or nearly activationless conformations can dominate the ensemble-averaged kinetics. This is why electron-transfer calculations in proteins naturally connect to conformational sampling.
When Marcus is not enough
Know which assumption is breaking
The weak-coupling golden-rule treatment can fail and the dynamics becomes more adiabatic.
High-frequency intramolecular modes may require vibronic or Marcus–Levich–Jortner-type treatments.
The solvent or protein may not relax to the equilibrium distribution assumed by standard Marcus theory.
Slow structural motion can create kinetic bottlenecks or distinct subensembles with different transfer rates.
Selected reading
Examples from my work
Conformational Switching Controls Biradical Spin Dynamics in Flavin–Tryptophan Dyads
How conformational subensembles reshape radical-pair kinetics and spin evolution.
JACS (2026) →Magnetosensitivity of Model Flavin–Tryptophan Radical Pairs in a Dynamic Protein Environment
Connecting fluctuating molecular structure to radical-pair parameters and observables.
J. Phys. Chem. B (2025) →Multiscale modeling approaches in biomolecular physics
Broader strategies for connecting molecular sampling, quantum chemistry and kinetic observables.
Advances in Physics: X (2026) →Key external literature
Where to read next
These are deliberately selected from outside my own work: foundational papers or reviews that are especially useful for this topic.
On the Theory of Oxidation-Reduction Reactions Involving Electron Transfer. I
R. A. Marcus · The Journal of Chemical Physics (1956). The classic derivation of the electron-transfer free-energy framework that became Marcus theory.
Open DOI →Contemporary Issues in Electron Transfer Research
P. F. Barbara, T. J. Meyer and M. A. Ratner · The Journal of Physical Chemistry (1996). A highly useful overview of rates, free-energy surfaces, solvent response and the inverted region.
Open DOI →