A Nonlinear Dynamical Model for Ultrafast Catalytic Transfer of Electrons at Zero Temperature

TL;DR

This paper develops a nonlinear dynamical model for ultrafast electron transfer at zero temperature, revealing how nonlinearities and a catalytic site can induce rapid, targeted electron transfer in complex biological and chemical systems.

Contribution

It introduces a nonlinear Schrödinger equation framework with dissipative and stochastic terms to model electron transfer, highlighting the role of nonlinearities and catalytic sites at low temperatures.

Findings

Ultrafast electron transfer can be triggered by a weakly coupled catalytic site.

Nonlinearities enable ultrafast transfer near the inversion point at zero Kelvin.

The model explains ultrafast electron transfer observed in photosynthetic reaction centers.

Abstract

The complex amplitudes of the electronic wavefunctions on different sites are used as Kramers variables for describing Electron Transfer. The strong coupling of the electronic charge to the many nuclei, ions, dipoles, etc, of the environment, is modeled as a thermal bath better considered classically. After elimination of the bath variables, the electron dynamics is described by a discrete nonlinear Schrodinger equation with norm preserving dissipative terms and Langevin random noises (at finite temperature). The standard Marcus results are recovered far from the inversion point, where atomic thermal fluctuations adiabatically induce the electron transfer. Close to the inversion point, in the non-adiabatic regime, electron transfer may become ultrafast (and selective) at low temperature essentially because of the nonlinearities, when these are appropriately tuned. We demonstrate and illustrate numerically that a weak coupling of the donor site with an extra appropriately tuned (catalytic) site, can trigger an ultrafast electron transfer to the acceptor site at zero degree Kelvin, while in the absence of this catalytic site no transfer would occur at all (the new concept of Targeted Transfer initially developed for discrete breathers is applied to polarons in our theory). Among other applications, this theory should be relevant for describing the ultrafast electron transfer observed in the photosynthetic reaction centers of living cells.