Conservation of the pure adiabatic state in Ehrenfest dynamics of the photoisomerization of molecules.

We examined real-time-propagation time-dependent density functional theory (rtp-TDDFT) coupled with molecular dynamics (MD), which uses single-particle representation of time-evolving wavefunctions allowing exchange of orbital characteristics between occupied and empty states making the effective Kohn-Sham Hamiltonian dependent on the potential energy surfaces (PESs). This scheme is expected to lead to mean-field average of adiabatic potential energy surfaces (PESs), and is one of Ehrenfest (mean-field) approaches. However, we demonstrate that the mean-field average can be absent in simulating photoisomerization of azobenzene and ethylene molecules. A transition from the S2 to the S1 excited state without the mean- field average was observed after examining several rtp-TDDFT-MD trajectories of a photoexcited azobenzene molecule. The subsequent trans-cis isomerization was observed in our simulation, which is consistent with experimental observation and supported by previous calculations. The absence of the mean-field average of PESs was also observed for the transition between the S1 and S0 states, indicating that the MD simulation was on a single PES. Conversely, we found no transition to the ground state (S0 state) when we performed a MD simulation of an S1 excited ethylene molecule owing to the constraint on the occupation number of each molecular orbital. Thus, we conclude that, at least for azobenzene and ethylene molecules, the rtp-TDDFT-MD is an on-the-fly simulation that can automatically see the transition among the PESs of excited states without the mean-field average unless the simulation reaches the PES of the S0 state.