I am trying to compute the free energy of insertion of relatively large molecules in polymer matrices using thermodynamic integration & the Jarzynski equality. LAMMPS has some handy soft potentials which can be employed in this respect: one can vary the lambda parameter in these potentials and record the potential energy using the group/group command between the penetrant and the polymer matrix. Nevertheless, when using this thermodynamic integration formula, one is interested in the first derivative of the potential energy with respect to lambda rather than the energy itself. As an approximation, I use a finite difference scheme to compute numerically the derivative of the potential energy which adds some noise. Is there a way of extracting the “exact” values of the first derivative without resorting to this approximation?