<i>Ab initio</i> calculations of third-order elastic coefficients

Third-order elasticity (TOE) theory predicts strain-induced changes in second-order elastic coefficients (SOECs) and can model wave propagation stressed media. Although third-order tensors have been determined based on first principles previous studies, their current definition is an expansion of thermodynamic energy terms the Lagrangian strain near natural, or zero pressure, reference state. This inconvenient for predictions SOECs under significant initial stresses. Therefore, when TOE necessary to study dependence elasticity, seismological community has resorted empirical version theory. reviews tensor proposes using ``effective'' tensor. An explicit expression effective given verified. We extend ab initio approach calculate finite pressure apply it two cubic systems, namely, NaCl MgO. As applications validations, we evaluate (a) (b) derivatives calculations. Good agreement between elasticity-based numerically calculated values confirms validity our