The computation of local stress in ab initio molecular simulations

Motivated by the increasingly more important role of ab initio molecular dynamics models in material simulations, this work focuses on the definition of local stress, when the forces are determined from quantum-mechanical (QM) descriptions. Two types of ab initio models, including the Born- Oppenheimer and Ehrenfest dynamics, are considered. In addition, formulas are derived for both tight-binding and real-space methods for the approximations of the QM models. The formulas are examined via comparisons with full ab initio molecular simulations.