Diabatic Potential Energy Matrices at the Interface of Nonadiabatic Dynamics, Machine Learning, and Quantum Computing

The accurate description of nonadiabatic quantum molecular dynamics represents one of the most significant challenges in modern computational chemistry, serving as a gateway to understanding complex phenomena ranging from photochemistry and electron transfer to surface scattering and biological exciton transport. A key difficulty lies in bridging high-level electronic structure theory for ground and excited states with accurate quantum dynamics theory. Although on-the-fly semiclassical approaches are increasingly viable, most quantum dynamics simulations still rely on pre-constructed potential energy surfaces, or in the nonadiabatic context, diabatic potential energy matrices (DPEMs). This perspective paper addresses the theoretical foundations, construction methodologies, and emerging frontiers of DPEMs. We examine the mathematical framework of the adiabatic-to-diabatic transformation, addressing the inherent topological challenges imposed by the geometric phase and the curl condition. We further analyze the transformative impact of machine learning, detailing how machine learning algorithms, such as permutation invariant polynomial neural networks and deep learning architectures, are reshaping the construction of global, high-dimensional DPEMs. Finally, we explore the disruptive potential of quantum computing, discussing how quantum algorithms are automating the direct simulation of nonadiabatic dynamics. In emerging quantum-centric workflows, DPEMs will continue to provide the critical bridge which enables the mapping of realistic, time-dependent molecular Hamiltonians onto quantum hardware.