Mechanical properties and elastic constants of atomistic systems through the stress-fluctuation formalism

A rigorous approach to computing the mechanical properties of solids is based on the stress-fluctuation formalism. The main advantages of this route are its applicability to both homogeneous and inhomogeneous systems and its fast convergence compared to strain-fluctuation based methods. However, its implementation has been hindered by the complexity of evaluating strain derivatives of many-body interactions such as the angle-bending and the torsional ones. In this study, its implementation in open-source software is presented. It utilizes recently-proposed analytical expressions by Van Workum et al. [K. Van Workum, G. Gao, J.D. Schall, J.A. Harrison, J. Chem. Phys. 125 (2006) 144506] to compute strain derivatives of many-body interactions. Thus, their numerical evaluation, which induces numerical fluctuations in the computed quantities, is avoided. The mechanical properties and the elastic constants of long-chain atactic polystyrene are estimated. The convergence behavior of the Born and the stress correlation terms is investigated. The estimated elastic moduli are in good agreement with experimental data.