Relativistic and non-relativistic calculations have been performed on hydrogen peroxide, dihydrogen disulfide, dihydrogen diselenide and dihydrogen ditelluride, H₂X₂ (X = O, S, Se, Te), in order to investigate the consequences of relativistic effects on their structures as well as their nuclear magnetic resonance (NMR) spin-spin coupling constants and spin-spin coupling constant polarizabilites. The study has been performed using both one-component non-relativistic and four-component relativistic calculations at the density functional theory (DFT) level with the B3LYP exchange-correlation functional. The calculation of nuclear spin-spin coupling constant polarizabilities has been performed by evaluating the components of the third order tensor, nuclear spin-spin coupling polarizability, using quadratic response theory. From this the pseudoscalar associated with this tensor has also been calculated. The results show that relativistic corrections become very important for H₂Se₂ and H₂Te₂ and hint that a new chiral discrimination technique via NMR spectroscopy might be possible for molecules containing elements like Se or Te.