Ehrenfest dynamics accelerated with SPEED

Multi-trajectory techniques, such as surface hopping and Ehrenfest dynamics, have proven successful in efficiently managing complex multistate systems. However, these methods still require substantial computational resources to propagate many independent trajectories. We propose a variation of Ehrenfest dynamics, termed single-potential evaluation Ehrenfest dynamics (SPEED), in which all trajectories are guided by a common local quadratic effective potential in the diabatic representation. This approach replaces the cost of propagating multiple trajectories with the evaluation of a single Hessian at each time step. We demonstrate the equivalence of standard Ehrenfest dynamics and our new approach in two realistic systems with (at most) quadratic diabatic surfaces and couplings: a quadratic vibronic coupling Hamiltonian model describing internal conversion in pyrazine and a system representing atomic adsorption on a solid surface. The efficiency gain is particularly valuable for on-the-fly ab initio applications. For this reason, we applied our approach in combination with the ALMO(MSDFT2) electronic structure method, which conveniently provides the diabatic potential describing charge transfer between two molecules. We show that SPEED provides a good qualitative estimate of the hole transfer rate between two furan moieties at different temperatures and accurately predicts the final charge distribution after the collision. In contrast, but as expected, our approach is insufficient to describe the photoisomerization of retinal because of the high anharmonicity of the diabatic surfaces.