Quantum and dynamical effects of proton donor-acceptor vibrational motion in nonadiabatic proton-coupled electron transfer reactions

Abstract

This paper presents a general theoretical formulation for proton-coupled electron transfer (PCET) reactions. The solute is represented by a multistate valence bond model, and the active electrons and transferring proton(s) are treated quantum mechanically. This formulation enables the classical or quantum mechanical treatment of the proton donor-acceptor vibrational mode, as well as the dynamical treatment of the proton donor-acceptor mode and the solvent. Nonadiabatic rate expressions are presented for PCET reactions in a number of well-defined limits for both dielectric continuum and molecular representations of the environment. The dynamical rate expressions account for correlations between the fluctuations of the proton donor-acceptor distance and the nonadiabatic PCET coupling. The quantities in the rate expressions can be calculated with a dielectric continuum model or a molecular dynamics simulation of the full system. The significance of the quantum and dynamical effects of the proton donor-acceptor mode is illustrated with applications to model PCET systems.

Theoretical studies of proton-coupled electron transfer: Models and concepts relevant to bioenergetics

“…[27] A PCET reaction is vibronically nonadiabatic when the vibronic coupling is significantly less than the thermal energy k B T. In this formulation, the active electrons and transferring proton are treated quantum mechanically, and the PCET reaction is described in terms of nonadiabatic transitions between pairs of reactant and product mixed electron-proton vibronic states. In the derivation of the rate expression, the nonadiabatic rate constant is expressed as the time integral of the probability flux correlation function, which in turn is expressed in terms of time correlation functions of the energy gap (i.e., the difference between the energies of the reactant and product states) and the R coordinate, where R is the distance between the proton donor and acceptor.…”

“…[34,35,47,48,[61][62][63][64][65][66][67][68][69][70] Our calculations of this reaction were based on the vibronically nonadiabatic formulation for PCET reactions that includes the quantum mechanical effects of the active electrons and the transferring proton, as well as the motions of all atoms in the complete solvated enzyme system. [27,39] As described above, the rate is represented by the time integral of a probability flux correlation function that depends on the vibronic coupling, the average of the energy gap and R coordinate, and the time correlation functions of the energy gap and R coordinate. The vibronic couplings were estimated to within a constant factor by calculating the overlaps between reactant and product hydrogen vibrational wavefunctions for model systems, and the other quantities were calculated from classical molecular dynamics simulations of the entire system.…”

“…Rate expressions based on linear response theory and the Golden Rule have been derived in various well-defined limits. [25,27] Methods for calculating the vibronic couplings in PCET systems have also been developed and implemented. [28,31] These theoretical approaches enable the calculation of rates and deuterium kinetic isotope effects (i.e., the ratio of the rate for hydrogen to the rate for deuterium), as well as their temperature and pH dependences.…”

“…[19,20] A variety of theoretical approaches have been developed to study PCET reactions. [21][22][23][24][25][26][27][28][29][30] In the vibronically nonadiabatic formulation for PCET, [25][26][27] the active electrons and transferring proton are treated quantum mechanically, and the PCET reaction is described in terms of nonadiabatic transitions between pairs of reactant and product mixed electron-proton vibronic states. The dynamics of the proton donor-acceptor mode and the solvent/protein environment can be included in this formulation.…”

A qualitative quantum rate model for hydrogen transfer in soybean lipoxygenase

“…An alternative transfer mechanism is also possible: the transferring particle may tunnel 5 through the barrier instead of hopping over it. This has been discussed in a number of enzymatic systems that catalyse hydrogen transfer and have high kinetic isotope effects (KIEs), such as soybean lipoxygenase (SLO) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] .…”