Factorized electron-nuclear dynamics with effective complex potential: on-the-fly implementation for H$_2^+$ in a laser field

Abstract

Conventional theoretical and computational approaches to fully coupled quantum molecular dynamics, i.e. when both the electrons and nuclei are treated as quantum-mechanical particles, are impractical for all but the smallest chemical systems. In this paper we describe the formalism and implementation of the Factorized Electron Nuclear Dynamics (FENDy) with effective complex potential [J. Chem. Theory Comput. 19 (2023), pp 1393-1408], which goes beyond the established framework of the Born-Oppenheimer approximation or Born-Huang expansion of the molecular wavefunction. This method is based on the exact factorization of the molecular wavefunction, with the nuclei evolving under a complex time-dependent potential which captures the key features of dynamics in the nuclear subspace. The complementary electronic component of the molecular wavefunction is normalized to one for all nuclear configurations. We implement and employ FENDy to model the dynamics of H$_2^+$ molecular ion under a femtosecond laser pulse. The electronic wavefunction is represented within the standard electronic structure bases without referencing the electronic eigenstates. The nuclear wavefunction is represented as a quantum-trajectory ensemble, which in principle circumvents the exponential scaling of the numerical cost with the system size. The challenging evaluation of the gradients on unstructured grids is performed by projection on auxiliary bases.