Quantum simulation of nuclear rearrangement in electron transfer reactions

Heat transport induced by electron transfer: A general temperature quantum calculation

Electron transfer dominates chemical processes in biological, inorganic, and material chemistry. Energetic aspects of such phenomena, in particular, the energy transfer associated with the electron transfer process, have received little attention in the past but are important in designing energy conversion devices. This paper generalizes our earlier work in this direction, which was based on the semiclassical Marcus theory of electron transfer. It provides, within a simple model, a unified framework that includes the deep (nuclear) tunneling limit of electron transfer and the associated heat transfer when the donor and acceptor sites are seated in environments characterized by different local temperatures. The electron transfer induced heat conduction is shown to go through a maximum at some intermediate average temperature where quantum effects are already appreciable, and it approaches zero when the average temperature is very high (the classical limit) or very low (deep tunneling).

An improved path-integral method for golden-rule rates

We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunneling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang, and Richardson [J. Chem. Phys. 150, 104107 (2019)]. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and co-workers. We then study a multidimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretization of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime without the need for the analytic continuation required by Wolynes theory.

Revisiting nuclear tunnelling in the aqueous ferrous–ferric electron transfer

We find that golden-rule quantum transition-state theory predicts nearly an order of magnitude less tunnelling than some of the previous estimates. This may indicate that the spin-boson model of electron transfer is not valid in the quantum regime.

Effects of tunnelling and asymmetry for system-bath models of electron transfer

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of the Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.

Direct simulation of electron transfer in the cobalt hexammine(ii/iii) self-exchange reaction

We present an atomistic simulation of electron transfer in a transition metal complex system using path integral methods.

Quantum-Classical Path Integral Simulation of Ferrocene-Ferrocenium Charge Transfer in Liquid Hexane

We employ the quantum-classical path integral methodology to simulate the outer sphere charge-transfer process of the ferrocene-ferrocenium pair in liquid hexane with unprecedented accuracy. Comparison of the simulation results to those obtained by mapping the solvent on an effective harmonic bath demonstrates the accuracy of linear response theory in this system.

Molecular dynamics simulations of porphyrin-dendrimer systems: toward modeling electron transfer in solution

We have performed computational simulations of porphyrin-dendrimer systems--a cationic porphyrin electrostatically associated to a negatively charged dendrimer--using the method of classical molecular dynamics (MD) with an atomistic force field. Previous experimental studies have shown a strong quenching effect of the porphyrin fluorescence that was assigned to electron transfer (ET) from the dendrimer's tertiary amines (Paulo, P. M. R.; Costa, S. M. B. J. Phys. Chem. B 2005, 109, 13928). In the present contribution, we evaluate computationally the role of the porphyrin-dendrimer conformation in the development of a statistical distribution of ET rates through its dependence on the donor-acceptor distance. We started from simulations without explicit solvent to obtain trajectories of the donor-acceptor distance and the respective time-averaged distributions for two dendrimer sizes and different initial configurations of the porphyrin-dendrimer pair. By introducing explicit solvent (water) in our simulations, we were able to estimate the reorganization energy of the medium for the systems with the dendrimer of smaller size. The values obtained are in the range 0.6-1.5 eV and show a linear dependence with the inverse of the donor-acceptor distance, which can be explained by a two-phase dielectric continuum model taking into account the medium heterogeneity provided by the dendrimer organic core. Dielectric relaxation accompanying ET was evaluated from the simulations with explicit solvent showing fast decay times of some tens of femtoseconds and slow decay times in the range of hundreds of femtoseconds to a few picoseconds. The variations of the slow relaxation times reflect the heterogeneity of the dendrimer donor sites which add to the complexity of ET kinetics as inferred from the experimental fluorescence decays.

Gaussian fluctuations and linear response in an electron transfer protein

In response to charge separation or transfer, polar liquids respond in a simple linear fashion. A similar linear response for proteins might be expected from the central limit theorem and is postulated in widely used theories of protein electrostatics, including the Marcus electron transfer theory and dielectric continuum theories. Although these theories are supported by a variety of experimental data, the exact validity of a linear protein dielectric response has been difficult to determine. Molecular dynamics simulations are presented that establish a linear dielectric response of both protein and surrounding solvent over the course of a biologically relevant electron transfer reaction: oxido-reduction of yeast cytochrome c in solution. Using an umbrella-sampling free energy approach with long simulations, an accurate treatment of long-range electrostatics and both classical and quantum models of the heme, good agreement is obtained with experiment for the redox potential relative to a heme-octapeptide complex. We obtain a reorganization free energy that is only half that for heme-octapeptide and is reproduced with a dielectric continuum model where the heme vicinity has a dielectric constant of only 1.1. This value implies that the contribution of protein reorganization to the electron transfer free energy barrier is reduced almost to the theoretical limit (a dielectric of one), and that the fluctuations of the electrostatic potential on the heme have a simple harmonic form, in accord with Marcus theory, even though the fluctuations of many individual protein groups (especially at the protein surface) are anharmonic.