Relativistic all-electron full-potential first-principles calculations have been performed in order to study the symmetry of the energy levels around the valence band maximum in the zinc blende II-VI semiconductors beta-HgS, HgSe, and HgTe. It is demonstrated that in general, an inverted band-structure does not necessarily lead to a zero fundamental energy gap for systems with zinc blende symmetry. Specifically, beta-HgS is found to have at the same time an inverted band structure, and a small, slightly indirect, fundamental energy gap. Possibly, the energy levels around the valence band maximum order differently in each of these systems.
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