Towards Effective Full-Dimensional Quantum Dynamics: Predicting the Non-Adiabatic Transition Rates in Azulene

Non-radiative transitions among electronic states play a prominent role in a wide area of applied and fundamental science, such as electron transfer in biosystems,1a and in modern optoelectronic devices.1b Thus, reliable theoretical predictions of the rates of those processes from first principles could provide significant advances in all these fields. As shown in the past, the use of restricted vibrational spaces could often lead to wrong predictions in evaluating electronic spectra, lifetimes for charge migration, etc.,2 so that the theoretical procedure to be adopted has mostly to be faced with the challenge of taking properly into account the large number of vibrational degrees of freedom which can potentially be involved in the electronic transition. To tackle this challenge, we present a computational approach to solve the time-dependent Schrödinger equation in molecular systems where a large set of nuclear degrees of freedom plays a role. We employ a time-independent basis function set for each electronic state, a choice which allows to take into account the quasi-full-dimensional vibronic subspace, while reducing the computational burden by using effective procedures for: i) selecting the elements of the total Hilbert space of vibronic states which play a role in the dynamics; ii) controlling the convergence of the time-dependent wave function. By introducing additional cutoffs with respect to similar methodologies successfully used in the past,3 we further reduce the computational burden, still ensuring an accurate description of the population dynamics. Focusing in particular on non-adiabatic processes, the reliability of the approach is validated by studying the photophysics of azulene, a prototypical molecule exhibiting anti-Kasha behavior. The calculated rates for the decays of the first two excited singlet states are in almost quantitative agreement with experimental data and with data obtained using Fermi’s Golden rule approach, indicating that our methodology represents a valid tool for studying the time evolution of molecular systems with large vibrational spaces.4