  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
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
quantum-mechanical models. The formulas are examined via comparisons with full
ab initio molecular simulations.
