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(c) 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(c), 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 2 dimensions. Both models being glass formers, we comment briefly on the temperature (T) dependence of the (corrected) shear modulus G( T) around the glass transition temperature T-g.