Non-linear optical (NLO) crystals are widely used in advanced photonic technologies for second harmonic and difference frequency generation (SHG and DFG, respectively), producing coherent light at frequencies where existing lasers are unavailable. Isotropic glasses do not exhibit SHG or DFG, except temporary induced anisotropy under external stimuli. However, recent reports on glasses with chiral structural motifs show promising permanent NLO properties. We propose an alternative solution: hybrid molecular/network glasses with non-centrosymmetric HgI2 monomers. Mercury (II) iodide consists of linear HgI2 triatomic molecules in the vapor phase and in the yellow orthorhombic polymorph stable above 400 K. At lower temperatures, the tetragonal red form is composed of corner-sharing HgI4/2 tetrahedra forming a layered extended framework. There is a gap in the molecular evolution; direct structural measurements of the liquid HgI2 phase are missing. Using high-energy X-ray scattering, pulsed neutron diffraction and Raman spectroscopy supported by structural and vibrational modeling, we show that the mercury (II) iodide melt and HgI2-containing sulfide glasses are built-up by bent HgI2 monomers (the bond angle ∠I-Hg-I = 156±2° in the melt). The non-centrosymmetric entities imply intrinsic optical non-linearity of the second order, confirmed by a strong SHG response.