Nuclear–Electronic Orbital Theory: Exploring Nuclear Quantum Effects in Chemistry, Biology, and Materials

Abstract Nuclear quantum effects play a critical role throughout chemistry, biology, and materials science. This Perspective presents the nuclear–electronic orbital (NEO) framework as a viable approach for incorporating nuclear quantum effects into calculations of relatively large, complex systems. The NEO approach treats specified nuclei, often protons or deuterons, quantum mechanically on the same level as the electrons using wave function theories or density functional theory. This approach incorporates nuclear quantum effects such as zero-point energy, nuclear delocalization, and nuclear tunneling into quantum chemistry calculations and molecular dynamics simulations. Nonadiabatic effects beyond the standard Born–Oppenheimer approximation between electrons and nuclei are also incorporated. NEO methods are computationally practical, straightforward to use, and accessible to nonexperts. This Perspective highlights the broad applicability of the NEO framework and emphasizes the fundamental insights provided by NEO calculations. The applications discussed include water clusters, double proton transfer dynamics, proton-coupled electron transfer, hydrogen tunneling dynamics, enzymatic reactions, pKa calculations, kinetic isotope effects, hydrogen and deuterium adsorption and water monolayers at metal electrode surfaces, geometric isotope effects, phase transitions in hydrogen-rich materials such as superconducting hydrides and ice, photoinduced proton transfer, plasmon-induced H2 dissociation, vibrational spectroscopy, and polaritonic chemistry. These examples showcase the ubiquitous importance of nuclear quantum effects as well as the accessibility of the NEO approach.