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.