Theory and applications of the stress density

Drawing on the theory of quantum mechanical stress, we introduce the stress density in density functional theory. In analogy with the Chetty-Martin energy density, the stress density provides a spatial resolution of the contributions to the integrated macroscopic stress tensor. We give specific prescriptions for a practical and efficient implementation in the plane wave ultrasoft pseudopotential method within the local-density approximation. We demonstrate the abilities of the stress density studying 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.