Impulsive correction to the elastic moduli obtained using the stress-fluctuation formalism in systems with truncated pair potential

The truncation of a pair potential at a distance r_cut is well-known to imply in general an impulsive correction to the pressure and other moments of the first derivatives of the potential. That depending on r_cut the truncation may also be of relevance to higher derivatives is shown theoretically for the Born contributions to the elastic moduli obtained using the stress-fluctuation formalism in d dimensions. Focusing on isotropic liquids for which the shear modulus G must vanish by construction, the predicted corrections are tested numerically for binary mixtures and polydisperse Lennard-Jones beads in, respectively, d=3 and d=2 dimensions.