Structured force reformulation of many-body dispersion: towards effective atom--atom decomposition and surrogate modeling

We present a structured force reformulation of the many-body dispersion (MBD) model that enables a physically consistent decomposition of forces into pairwise components. By introducing a many-body correlation matrix that scales dipole–dipole interactions, we derive unified expressions for the MBD energy, force, and Hessian. This reformulation reveals a natural structure for effective atom–atom force decomposition and provides a promising foundation for interpretable analysis and machine learning surrogate modeling of MBD interactions.