SHG in a centrosymmetric crystal - can it be possible?

The present report lists selected publications on centrosymmetric compounds that manifest second harmonic generation responses in a laser, along with a few publications that dispute the laser outcomes. Two studies provide a plausible explanation for this apparent contradiction between second-order nonlinear susceptibility and inversion symmetry: the crystals are noncentrosymmetric and are twinned by inversion. If crystal structures of SHG-active compounds are presented in centrosymmetric settings, the authors of the publications may consider stipulating that the true space group is likely to be one of the noncentrosymmetric sub-space groups.