For the smallest covalent radius r cov = 0.1, it is evident from the graph that the modified interaction tensor closely resembles the form of the standard Coulombic interaction, T (n) , particularly when n = 0 and n = 1. Also, the singularities are removed as r ij → 0, and the full Coulomb potential is recovered systematically when decreasing the damping parameter r cov . Essentially, at the long-range, the modified interaction tensor is identical to the full Coulomb interaction, thus ensuring the exact physical behavior. When considering n = 2, the tensor displays more pronounced variations; however, it is noteworthy that the function continues to damp potential singularities effectively. This behavior ensures that even as r cov is reduced, the modified tensor retains a form that prevents the emergence of unphysical divergencies, thus providing a robust framework for modeling interactions at very short distances between interaction sites while fully retaining the long-range electrostatics.