Coherent modified Redfield approach to describe photoinduced proton-coupled electron transfer

Abstract

Coherent modified Redfield theory is employed to describe photoinduced proton-coupled electron transfer for a model Hamiltonian. This formalism is an extension of Redfield theory to capture weak to moderate system–bath coupling strengths, and the dynamics is secular and non-Markovian. In the model Hamiltonian, the electron is coupled to the proton and a phonon bath and is initially photoinduced from the ground electronic site to a donor site. At small bath reorganization energies, the system parameters, such as the energy bias between the donor and acceptor sites and overlaps of the vibronic states, play a crucial role in influencing the population decay and isotope effect. The energy bias decides the spacing between adjacent pairs of donor–acceptor levels as well as the energetically favorable acceptor states for the non-adiabatic transition. For the models we considered, the overlaps of the donor–acceptor wavefunctions of the proton are larger than those of deuterium. When the population is initially distributed over several donor vibrational states, the H/D population decays faster for the case that has the smaller adjacent donor–acceptor spacing. The donor population decay shows an inverse isotope effect when this spacing is smaller for deuterium than for protons. These models demonstrate a subtle balance between the spacing and overlaps in deciding the rate of population decay. Weak electron–phonon coupling leads to coherent oscillations in the electronic population decay and proton wavepacket dynamics. Larger coupling strengths lead to wavepacket localization and the transition to incoherent population decay.