First-principles studies of the Optical anisotropy of R3 space group chalcogenides crystal AX2MQ6

In order to explain the reason that all the sythesised \ce{AX2MQ6} chalcogenides compounds are phase-matching while isomorphic chalcogenides compounds \ce{AX4M5Q12} are not phase-matched materials. The linear optical property birefringence and non-linear optical property of $R3$ space group crystals \ce{AX2MQ6} have been calculated to compare with \ce{AX4M5Q12}. Their Electron Localization Function(ELF) was calculated to show that the acentricity of the bonds on $sp^3$ hybridization \ce{Q^2-} ions is the main origin of optical anisotropy. To quantificat the acentricity, a geometric parameter dihedral angle between tetrahedral undersides and xy-planes was defined. We find theoretically the birefringence depend on the defined geometric parameter and ion radius. This relation between birefringence and structure resonalbly explain the abnormal difference of birefringence of isostructural \ce{AX2MQ6} and \ce{AX4M5Q12} and useful for exploring new phase-matching IR-NLO crystals.