Quantum-mechanical theory of stress and force

1985/09/15 by O. H. Nielsen, Richard M. Martin · 1 voice · 8 citations
Earth and Planetary Sciences · Materials Science · Chemistry · #High-pressure geophysics and materials #Thermal properties of materials #Advanced Physical and Chemical Molecular Interactions

paper · doi:10.1103/physrevb.32.3780

openalex publication_date 1985/09/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/25

Abstract

The stress theorem presented previously by the present authors is derived in detail and is related to the virial and force theorems. Stress fields are considered in two alternative forms, both of which give the same macroscopic stress and forces on nuclei when integrated over appropriate surfaces. A crucial concept is interactions that ``cross'' surfaces. Explicit forms of the stress field within the local-density approximation are given, together with a generalization of the approximate Liberman form for pressure. Reciprocal-space expressions and ab initio calculations are considered in detail in an accompanying paper.

Citations

• Dynamical Theory of Crystal Lattices
• One-Particle Properties of an Inhomogeneous Interacting Electron Gas
• Self-Consistent Equations Including Exchange and Correlation Effects

Cited by

• QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Fast method for force computations in electronic structure calculations
• Magnetic Stress as a Driving Force of Structural Distortions: The Case of CrN
• Pressure formulae for liquid metals and plasmas based on the density-functional theory
• Quantum stress in chaotic billiards
• First-principles study of lattice instabilities in ferromagneticNi2MnGa
• Ab initiocalculations of structural and electronic properties of gallium solid-state phases
• Continuum mechanics for quantum many-body systems: Linear response regime

Discussions

• Nielsen in his article Phys. Rev. B 35, 9308 (1987) derived the stress via a stretched particle coordinate $\mathbf{r}_{i\alpha}\rightarrow \mathbf{r}_{i\alpha}+\sum_\beta \epsilon_{\alpha\beta}\mathb [stackexchange, 0 points]