Spectral Decomposition of Liquid Viscosity into Instantaneous Normal Modes

Viscosity, the resistance of a liquid to flow, is driven by atomic-scale friction but its microscopic origin remains poorly understood. We use a theoretical framework based on nonaffine linear response to decompose the viscosity of metallic and model liquids into contributions from individual instantaneous normal modes (INMs). Our approach reveals excellent agreement with simulations and exposes the specific excitations that govern viscous dynamics. Above the mode-coupling temperature ($T_{\text{MC}}$), viscosity is controlled by unstable localized INMs (ULINMs), which act as precursors for diffusive momentum transport. Below $T_{\text{MC}}$, we find a dynamical crossover where stable modes govern viscosity, a behavior consistent with a transition in the potential energy landscape from saddle-dominated to minima-dominated dynamics. We also propose a quantitative model connecting viscosity with ULINMs in both Arrhenius and non-Arrhenius regimes. This work provides a spectral decomposition of liquid viscosity, identifying the atomic modes responsible for it and opening a path to predict it from elementary excitations.