Correlated electron‐nuclear dynamics based on exact factorization: Theory and real‐world applications

Exact factorization (XF) offers an explicit form of electron–nuclear correlation (ENC) in its correlated electron–nuclear equations, equivalent to the molecular Schrödinger equation, beginning with an exact separation of a full molecular wavefunction into a nuclear and a conditional electronic component. Leveraging the mixed quantum‐classical (MQC) approach to the XF formalism, we develop practical nonadiabatic dynamics methods for real‐world applications. Treating nuclei as ensembles of classical trajectories, we formulate coupled‐trajectory MQC (CT‐MQC) schemes in which trajectories communicate via the XF‐derived ENC and independent‐trajectory algorithms, such as Surface Hopping based on XF (SHXF), for improved efficiency. We further propose CTv2 and SHXFv2, which include second‐order ENC terms and thereby provide a unified description of nuclear phase evolution and (de)coherence. Combining the accurate spin‐Restricted Ensemble‐reference Kohn–Sham (REKS) method with our XF methods, we investigate a broad range of photochemical reactions and present the rational design of molecular rotary motors together with the optical cavity effect. Beyond molecular systems, we combine XF with real‐time time‐dependent density functional theory (RT‐TDDFT) to yield Orbital‐based SHXF (OSHXF), leading to ab initio simulations of hole transport materials with more than 300 atoms.