Evaluating the Anharmonicity Contributions to the Molecular Excited State Internal Conversion Rates with Finite Temperature TD-DMRG

In this work, we propose a new method to calculate the molecular nonradiative electronic relaxation rates based on the numerically exact time-dependent density matrix renormalization group theory (TD-DMRG). This method could go beyond the existing frameworks under the harmonic approximation (HA) of the potential energy surface (PES) so that the important anharmonic effect could be considered when large electronic energy is transferred into the vibrations to excite them to the high energy levels. The effectiveness and scalability of the method are verified in calculating the internal conversion (IC) rate of azulene by comparing it with the analytically exact results under HA. Furthermore, we investigate the validity of HA in a two-mode model with Morse potential. We find that HA is unsatisfactory unless only the lowest several vibrational states of the lower electronic state are involved in the transition process when the adiabatic excitation energy is relatively low. As the excitation energy increases, HA first underestimates and then overestimates the IC rates when the excited state PES shifts towards the dissociative side of the ground state PES. On the contrary, HA slightly overestimates the IC rates when the excited state PES shifts towards the repulsive side. In both cases, higher temperature enlarges the error of HA.