Ehrenfest dynamics accelerated with SPEED

Mixed quantum-classical methods, such as surface hopping and Ehrenfest dynamics, have proven their ability to efficiently describe molecular processes involving multiple electronic states. However, propagating numerous independent trajectories remains computationally demanding. We propose a variation of multi-trajectory Ehrenfest dynamics, termed single potential evaluation Ehrenfest dynamics (SPEED), where all trajectories are propagated with a shared local quadratic effective potential in the diabatic representation. This approach replaces the computational cost of propagating multiple trajectories with the evaluation of a single Hessian at each time step. We demonstrate the equivalence of standard multi-trajectory Ehrenfest dynamics and SPEED 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 advantageous in 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 varying temperatures and accurately predicts the final charge distribution after the collision. In contrast, but as expected, our approach is insufficient to describe photoisomerization of retinal due to the high anharmonicity of the diabatic surfaces.