Reverse Engineering Atomic Densities for Charge Model 5 (CM5) to Compute Atomic Properties Beyond Charges

Charge Model 5 (CM5) refines Hirshfeld charges to better reproduce charge-dependent properties, such as molecular dipole moments. Although it was parametrized using a limited set of molecules in the gas phase, CM5 charges demonstrate broad applicability, computational robustness, and conformational stability. Being merely a charge model, CM5 does not produce atomic densities, limiting its ability to compute other atomic properties and related quantities. We present a novel algorithm to reverse-engineer atomic densities corresponding to a given set of charges and apply it to CM5, by leveraging the recently developed constrained variational Hirshfeld framework. Using these reconstructed atomic densities, we evaluate a range of CM5-consistent atomic properties and compare them with results from similar methods. This computationally efficient approach broadens the utility of the CM5 model, enabling the evaluation of additional atomic properties and molecular interaction terms.