Theory and applications of the stress density

Drawing on the theory of quantum-mechanical stress, we introduce the stress density in density-functional theory, and give specific prescriptions for its practical and efficient implementation in the plane-wave ultrasoft pseudopotential method within the local-density approximation. In analogy with the Chetty-Martin energy density, the stress density provides a spatial resolution of the contributions to the integrated macroscopic stress tensor. While this resolution is inherently nonunique (gauge dependent), there exist gauge-independent ways of using it in practice. Here we adopt the following ones: (a) calculating integrated macroscopic stresses over appropriately defined parts of a system; (b) analyzing macroscopic averages of the stress density; (c) analyzing changes in the stress density in response to external perturbation. The abilities of the stress density are demonstrated for a set of representative test cases from surface and interface physics: in perspective, the stress density emerges as vastly more powerful and predictive than the integrated macroscopic stress.