Incorporating spin-orbit effects into surface hopping dynamics using the diagonal representation: a linear-response time-dependent density functional theory implementation with applications to 2-thiouracil.

In this study, we present a trajectory surface hopping (TSH) method that incorporates spin-orbit (SO) effects using the "diagonal representation" within the Linear-Response Time-Dependent Density Functional Theory (LR-TDDFT) framework. In this approach, the evaluation of spin-orbit coupling (SOC) matrix elements between singlet and triplet states employs the Casida's wave functions and the Breit-Pauli (BP) spin-orbit Hamiltonian with effective charge approximation. The new TSH approach is then used to investigate the excited-state relaxation of 2-thiouracil (2TU) in vacuum and water. On the basis of the simulation results, relaxation of the initially populated bright state is found to be dominated by the route S2 → S1 → T. The intersystem crossing (ISC) can occur at either the C2-puckered structure or the C2-pyramidalized S1 minimum, and is promoted by a three-state near-degeneracy (S1/T2/T1 in vacuum or S1/T3/T2 in water) as well as sizable SOCs. Our simulations achieve a good agreement with the available experimental measurements in terms of the internal conversion (IC) and ISC time scales, and complement the picture of the relaxation mechanisms of 2TU after photo-excitation to the first bright state.