Zero-point effects — quantum mechanical phenomena arising from the fact that nuclei never truly stand still, even at absolute zero — are essential for accurately describing many chemical and biological processes, especially those involving hydrogen. Yet, capturing these effects in large-scale molecular simulations remains a major challenge. To address this, we developed the Constrained Nuclear-Electronic Orbital (CNEO) framework, which incorporates zero-point effects along with certain other components of nuclear quantum effects directly into quantum chemistry calculations and molecular dynamics simulations, while maintaining computational efficiency.
Our methods — CNEO density functional theory (CNEO-DFT) and CNEO molecular dynamics (CNEO-MD) — significantly outperform conventional DFT and ab initio MD in predicting vibrational spectra, particularly for hydrogen-dominated modes. With CNEO transition state theory (CNEO-TST), we achieve more accurate hydrogen/proton/hydride transfer rate predictions at little additional cost. CNEO simulations with periodic boundary conditions also reveal shifts in hydrogen adsorption preferences on metal surfaces driven by zero-point effects. We have also extended the framework to excited-state calculations, nonadiabatic dynamics, and hybrid QM/MM calculations. Together, these developments establish CNEO as a versatile and efficient tool for bridging classical simulations with a quantum mechanical description of nuclear motion.