Computer simulations of elastic constants without calculating derivatives of the interaction potential

Two Monte Carlo methods of elastic constants determination which do not require using any derivatives of the interaction potential between the particles are described. The first method corresponds to the free energy differentiation with respect to deformation in the fixed box ensemble (NVT). The second method is based on the analysis of the box fluctuations in the constant pressure ensemble with variable box shape (NpT). Its additional advantage is that it does not require any knowledge of the reference state of the system prior to simulations.