Nuclear-Electronic Orbital at Scale: Capturing Nuclear Quantum Effects in Ultrafast Aqueous Dynamics

Abstract

Nuclear quantum effects play an important role in hydrogen-containing systems, influencing hydrogen bonding, vibrational spectroscopy, proton transfer, tunneling, isotope effects, and proton-coupled electron transfer. Conventional electronic-structure methods usually rely on the Born–Oppenheimer approximation, treating electrons quantum mechanically while describing nuclei through an electronic potential energy surface. Although efficient for many applications, this framework can miss important effects from proton delocalization, zero-point motion, and coupled electron–proton dynamics. The nuclear–electronic orbital (NEO) framework addresses this limitation by treating selected nuclei, typically protons, quantum mechanically on the same footing as the electrons. Its real-time extension, RT-NEO-TDDFT, further enables direct simulation of coupled electron–proton dynamics in the time domain. This dissertation develops scalable NEO algorithms for systems with many quantum protons and applies them to ultrafast aqueous electron chemistry. A real-time NEO formulation using gauge-including atomic orbitals is also developed to study coupled electron–proton dynamics in external magnetic fields.The first chapter reviews Hartree–Fock theory and Kohn–Sham density functional theory as the electronic-structure foundation for this work. The second chapter introduces the NEO framework and develops a simultaneous optimization scheme for electronic and nuclear orbitals to improve the robustness of NEO self-consistent-field calculations. The third chapter presents a multicomponent Cholesky decomposition that compresses electronic, protonic, and electron–proton two-particle integrals into compact three-index tensors. The fourth chapter extends this decomposition to distributed-memory architectures, enabling NEO calculations for larger systems with many quantum protons. The fifth chapter develops a gauge-including real-time NEO formulation to include external magnetic fields. The sixth chapter applies the scalable RT-NEO-TDDFT framework to ultrafast electron attachment in a 30-water cluster, showing that quantum protons open an early-time relaxation channel absent in classical frozen-nuclei propagation.