Optimal initial condition sampling for multi-configurational Ehrenfest dynamics

Abstract

The multi-configurational Ehrenfest (MCE) method offers a promising trajectory-based alternative to exact quantum dynamics for simulating non-adiabatic transitions, combining quantum and semiclassical elements through a basis of independent mean-field trajectories. A critical challenge in MCE lies in the optimal selection of initial trajectory conditions. In this work, we systematically evaluate different strategies for generating such initial conditions, including physical approaches based on Wigner and compressed Wigner distributions, as well as regular geometric constructions such as single- and multi-layered spherical and cubic grids. Among them, the cubic grid with a unit spacing in dimensionless coordinates emerges as a nearly universal and system-independent choice. We further demonstrate that, in systems with multiple conical intersections, trajectory cloning improves performance, but only after achieving convergence with respect to trajectory number using a well-constructed basis. Overall, MCE proves particularly advantageous for problems involving many coupled electronic states and offers flexibility for parallel implementation, making it especially relevant for the simulation of broadband excitation processes in attosecond science.