Ab initio theory of the Drude plasma frequency

We derive a theoretical expression to calculate the Drude plasma frequency $\omega_p$ based on quantum mechanical time dependent perturbation theory. We show that in general $\omega_p^2$ should be replaced by a second rank tensor, the Drude tensor $\mathcal{D}$, which we express in terms of products of the velocity expectation values integrated over the Fermi surface, and which is amiable to analytical and numerical evaluation. For the Sommerfeld's model of metals our expression yields the ubiquitous plasma frequency $\omega^2_p=4\pi n_e e^2/m_e$. The Drude tensor takes into account the geometry of the unit cell and may be calculated from first principles for isotropic as well as anisotropic metallic systems. We present results for the noble metals, Cu, Ag, and Au without stress and subject to isotropic and uniaxial strains, and we compare the results to those available from experiment.