Polarizable embeddings and quantum chemistry: Concepts, progress, and open challenges

Polarizable embedding (PE) methods—both in their continuum and atomistic formulations—have become important tools for accurately modeling molecules in complex environments. Recent advances have enabled their integration with a wide range of quantum-chemical approaches, allowing the calculation of energies, structures, optical properties, and even molecular dynamics for systems of significant chemical and biological relevance. Despite this progress, several obstacles still limit the routine application of PE QM/MM approaches. Among them, the most important ones are the lack of efficient geometry-optimization strategies in the presence of mutual polarization, the absence of fully implemented second derivatives, and conceptual challenges associated with the consistent treatment of multiple electronic states in non-adiabatic dynamics. At the same time, novel computational developments—including linear-scaling algorithms, self-consistent field (SCF) extrapolation techniques, and machine-learning models trained to reproduce environment-dependent quantum-mechanical effects—are opening new possibilities for extending the scope and efficiency of PE simulations. This Perspective reviews the formal foundations of PE models, critically examines their current limitations, and highlights promising directions for future development. The combined progress in theory, algorithms, and data-driven approaches suggests that PE methodologies are poised to become central components of next-generation multiscale quantum simulations.