Vibronic approach to the calculation of the decay rate of the photoexcited charge-transfer state of Guanine-Cytosine stacked dimer in water solution

We compute the rate of the charge recombination (CR) process from the minimum of the charge transfer (CT) Guanine-Cytosine stacked dimer in water solution to the ground electronic state (GS). We adopt the quantum non-adiabatic theory of electron transfer reactions, where key ingredients to determine the CR rate are the electronic coupling and the so-called Franck-Condon density of states (FCWD). In order to compute the FCWD, we exploited recent developments in the field of the time-independent and time-dependent simulations of vibronic spectra of large systems, based on model harmonic potential energy surfaces (PESs). Both mean-field solvent effects on the PESs and the solvent reorganization effects on the CR rate were described by implicit polarizable continuum model. We show that an improper treatment of the contributions of the inter-base modes to the FCWD results in artefacts which can change the estimate of the CR rates by orders of magnitude and we devise a computational protocol in internal coordinates able to determine "effective normal modes" that separate the stiff (intra-base) modes and the inter-base ones. The results for the CR rate are qualitatively consistent with available experimental data. By computing the CR rate for four different stacking geometries, we show that all the parameters ruling the CR rate, namely the CT character of the excited state (ES), the equilibrium position of stiff modes (and therefore the FCWD), the electronic coupling and the energy gap between the GS and ES are all strongly dependent on the fluctuation of the dimer structure along the inter-base modes. On this ground, we discuss some possible future theoretical developments to achieve a non-phenomenological fully first-principle estimate of the CR rate that can be directly compared with experiment.