Isothermal and adiabatic elastic constants from virial fluctuations

We derive expressions for classical isothermal and adiabatic elastic constants for periodic systems with the boundary contributions included explicitly. The potential-dependent part of these expressions is written in terms of potential energies of atomic groups that make up the total potential energy. It is shown that in the thermodynamic limit, the Born term, which depends on the second derivatives of potential energy, can be expressed exactly in terms of equilibrium averages that involve two types of atomic-group virials. As a result, the new form of the Born term involves only first derivatives of either atomic-group or total potential energies. The derived elastic constant expressions involving the two forms of the Born terms are tested and compared using molecular-dynamics simulations of crystalline argon and silicon. For both materials, the elastic constants obtained using the two forms of the Born term are in good agreement. In particular, the new form of the Born term converges to the same value as the original Born term but at a slower rate. The results for silicon also agree well with the results from the previous molecular-dynamics studies.