Excited-State Ehrenfest Dynamics within Ab Initio Many-Body Perturbation Theory

We present a novel excited-state Ehrenfest dynamics propagation method based on the Bethe-Salpeter equation (BSE) of many-body perturbation theory (MBPT). The method operates in the exciton basis, is nonperturbative in the atomic coordinates, and obtains the requisite nonadiabatic coupling matrix elements through an efficient finite-difference scheme that we previously developed [1]. By integrating out the time dependence associated with the evolution of excitonic states, our real-time approach allows us to take longer time steps and study dynamics in real materials approaching relevant time scales associated with atomic motion and phonons. These unique characteristics allow us to explicitly study arbitrarily coherent and incoherent exciton populations and large atomic displacements, as well as spin-orbit coupling driven transitions between singlet and triplet manifolds. To demonstrate this, we simulate the dynamics of photoexcited KCl, which hosts self-trapped excitons that exhibit intersystem crossings and result in the formation of F-center lattice defects [2]. This method bridges the gap between recent works on excited-state forces from MBPT and time-dependent GW approaches that treat atomic motion perturbatively.

[1] A.R. Altman, A. Ramdas, J.B. Haber, F.H. da Jornada, “Excited-state forces, relaxation, and higher-order derivatives from ab initio many-body perturbation theory.” To be submitted (2025).

[2] R.T. Williams, "Intersystem crossing, polarization, and defect formation induced by optical excitation of self-trapped excitons in alkali halides." Physical Review Letters 36.10 (1976): 529.