A Coupled-Trajectory Strategy for Decoherence, Frustrated Hops and Internal Consistency in Surface Hopping

In this work, we discuss decoherence, frustrated hops and internal consistency in surface-hopping-based methodologies. We demonstrate that moving away from an independent-trajectory picture is the strategy which allows us to propose a robust and reliable surface-hopping scheme. Based on the exact factorization and on the idea of coupled trajectories, we consider the swarm of trajectories, that mimics the nuclear dynamics in nonadiabatic processes, as a unique entity. In this way, imposing energy conservation of the swarm and allowing the trajectories to share energy when hops occur clearly indicates the route toward a new surface hopping scheme. Encouraging results are reported, in terms of electronic and vibrational time-dependent properties on the photodynamics of fulvene and 4-(dimethyloamino)benzonitrile, modeled with full-dimensional linear vibronic coupling Hamiltonians.