Quantum-mechanical stress and a generalized virial theorem for clusters and solids

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Abstract
Clusters and crystals are considered within the Born-Oppenheimer approximation. By means of the one-particle density matrix and the pair distribution a local stress tensor is defined with the divergence equal to the forces exerted upon the nuclei. From the local momentum balance follow (i) the stress theorem as a generalized virial theorem and (ii) an expression for the stress of a crystal involving integrals over the unit-cell surface. Within the Kohn-Sham formalism slightly modified expressions are obtained rigorously, and the form appropriate within the local-density approximation is given.

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