Analytic Nonadiabatic Derivative Couplings Using Noncollinear Spin-Flip TDDFT

Nonadiabatic molecular dynamics is an important tool for investigating chemical reaction mechanisms, particularly in photochemical processes. Its central challenge is to efficiently and accurately obtain, at the electronic-structure level, the energies, nuclear forces (gradients), and nonadiabatic derivative couplings (NADCs) associated with multiple potential-energy surfaces. We have previously developed a noncollinear spin-flip time-dependent density functional theory (SF-TDDFT) based on the multicollinear approach. This method enables the computation of potential-energy surfaces and analytic nuclear gradients for multiple excited states and leads to improved energy degeneracy, spin symmetry, and formal consistency relative to collinear SF-TDDFT. In the present work, analytic NADCs are formulated within this framework. Their accuracy is assessed through comparison with finite-difference results and by evaluating the Berry phase in the vicinity of conical intersections. As an initial application, nonadiabatic molecular dynamics simulations were performed for azomethane and ethylene, showing that the analytic derivative couplings behave reasonably and stably for these systems. Since the additional computational cost of the NADCs is comparable to that of energies and gradients in SF-TDDFT, the method may be suitable for nonadiabatic dynamics simulations of moderately large molecular systems.