Here, the new terms in the formula ∂E + ∂k and ∂E - ∂k may be recognized as the potential energy derivatives of the surface-perturbed trajectory frames. These potential derivatives are evaluated numerically using sufficiently small steps in k to avoid incurring machineprecision errors. All quantities in angle brackets representing ensemble averages are then evaluated as arithmetic averages over the trajectory frames. The computational cost of evaluating the full set of potential energy derivatives scales linearly with the number of parameters, and the added cost per parameter is significantly less than the simulation itself.