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

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.