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Dielectric functions and collective excitations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">MgB</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
The frequency- and momentum-dependent dielectric function $\ensuremath{\epsilon}(\mathbf{q},\ensuremath{\omega})$ as well as the energy loss function $\mathrm{Im}[\ensuremath{-}{\ensuremath{\epsilon}}^{\ensuremath{-}1}(\mathbf{q},\ensuremath{\omega})]$ are calculated for intermetallic superconductor ${\mathrm{MgB}}_{2}$ by using two ab initio methods: the plane-wave pseudopotential method and the tight-binding version of the linear muffin-tin orbital method. We find two plasmon modes dispersing at energies $\ensuremath{\sim}2--8 …