Mapping the Energy Flow of Cooperativity: Real-Space Energy Decomposition Analysis of the Three-Body Effect

Many-body effects play a governing role in molecular assembly and recognition, yet their physical origins are not fully elucidated. In this work, we extend the recently developed real-space energy decomposition analysis method, called DM-EDA(RS), to enable the direct visualization and atomic-level quantification of three-body interaction energies. By projection of energy components onto three-dimensional grids, this method uniquely bridges the gap between integrated energy numbers and spatially resolved chemical insight. The results show that three-body cooperativity is driven by highly localized, counterdirectional flows of polarization energy localized on specific atoms. DM-EDA(RS) identifies the real-space energy distribution, directly mapping how interaction terms are transferred across molecular networks. Remarkably, even in systems with nearly zero net cooperativity, intense local energy redistributions are revealed that cancel out globally. This work establishes DM-EDA(RS) as a transformative approach that bridges integrated energy numbers with chemical intuition, providing a spatially resolved tool for probing many-body interactions in complex chemical and biological environments.