Ab initio analyses provide new insights into the nature of defective systems.

The distributions of local energy and local stress are important features when studying surfaces, grain boundaries, defects and various nanostructures. However, it is not possible to analyse these features in density-functional theory (DFT) calculations because in usual plane-wave DFT methods the total energy and stress tensors are given as averaged or integrated quantities within the supercell. In J. Phys.: Condens. Matter 25 305006 we completed a practical computational technique for ab initio local energy and local stress (diagonal sum) in general defective systems by utilizing the Bader partitioning to decide such local regions satisfying the above condition.

Schemes to calculate energy density and stress density in plane-wave methods have been proposed in the past. However due to the presence of gauge-dependent terms in the energy and stress densities, simple integration of such densities does not lead to unique physical quantities. Previously, we proposed that such gauge-dependent problems can be settled if the densities are integrated within proper local regions where the gauge-dependent terms are integrated to be zero (Shiihara et al 2010). Our work in J. Phys.: Condens. Matter 25 305006 develops this strategy.

We applied the present technique to tilt and twist grain boundaries and vacancies in Al and Cu as typical face-centred cubic metals with quite different bonding natures and contrasting mechanical properties. Obtained atomic energies and atomic stresses were compared with those by embedded atom method (EAM) potentials as conventional inter-atomic potentials, and those by local-region partitioning using different numerical schemes.

We observed that valence electrons in Al show a remarkable response to structural disorder in the form of significant valence-charge redistribution or bond reconstruction in the inter-atomic space of defect-core regions. This often leads to long-range variations of charges, energies and stresses, quite different from the d electrons in Cu mainly located near the nuclei. These features can be well represented by our local energy and local stress using the Bader integration. The EAM potential for Al does not reproduce correct local energy or local stress, while the EAM potential for Cu provides rather satisfactory results.

Recently, our scheme was also applied to Fe grain boundaries (Bhattacharya et al 2013). We believe that the local-energy and local-stress scheme should provide new insights into the stability and properties of various defective systems or nanostructures.