Dissecting energy level renormalization and polarizability enhancement of molecules at surfaces with subsystem TDDFT

Molecules in the vicinity of extended systems, such as metal surfaces, behave in peculiar ways. Their energy levels are broadened, and their molecular properties are so profoundly enhanced that they hardly resemble the ones of the isolated molecule. This is due to dynamical interactions (i.e., interactions that couple excited electronic states) between the molecular, finite system and the extended, infinite system. Since the early days of quantum mechanics, Fermi golden rule has been employed to explain some of the dynamical interactions (such as the broadening of the energy levels). However, a fully quantum-mechanical and ab initio model of these systems remains elusive, in most part due to the computational complexity entailed in the simulations. In this work, we present subsystem time-dependent DFT (TDDFT) simulations of water and benzene molecules as they interact with surfaces of MoS2 monolayer and Au(111). A manybody expansion of the supersystem response function in terms of molecule and surface responses allows us to dissect and describe the dynamical interactions. Not only do we compute and clearly identify terms related to dissipation, broadening, and peak shift, but we also provide a connection between subsystem TDDFT and Fermi golden rule. This work sets the stage for subsystem TDDFT simulations of interfaces relevant to energy materials and nonadiabatic dynamics at such interfaces.