Revealing atomic–scale distributions of energy and stress in defective or complex systems, based on the behavior of electrons, should contribute
much to materials science and engineering, while only few practical ab initio methods were developed for this purpose. Thus, we developed computational
techniques of local–energy and local–stress calculations within the plane–wave PAW (projector augmented wave)– GGA (generalized gradient
approximation) framework. This is natural extension of ab initio energy–density and stress–density schemes, while the inherent gauge dependency is
removed by integrating these densities in each local region where the contained gauge–dependent terms are integrated to be zero. In this overview, we
explain our scheme with some details and discuss the concepts or physical meanings of local energy and local stress via the comparison with related
schemes using similar densities, LCAO (linear combination of atomic orbitals) methods, Green’s function formulation implemented by multiple scattering or
TB (tight–binding) methods, or EAM (embedded–atom method) potentials. We present recent applications to metallic surfaces, grain boundaries (GBs) with
and without solute segregation, tensile tests of metallic GBs, local elastic constants of microstructures in alloys, and machine–learning based GB–energy
prediction, where the local–energy and local–stress analyses provide novel aspects of phenomena, deep insights into the mechanism, and effective data
for novel machine–learning based modelling.