Elastic and dielectric characteristics of the graphene-like A$_N$–B$_{8-N}$ compounds

Harrison’s bond orbital method is applied to the con- sideration of graphene, silicone, hexagonal NB and 14 hypothetical graphene-like IV–IV, III–V and II–VI compounds. Simple analytical formulas for the central $(k_0)$ and noncentral $(k_1)$ force constants, linear dielectric susceptibilities for the electronic ($\chi^{\mathrm{el}}_1)$ and ionic $(\chi^{\mathrm{ion}}_1)$ subsystems are obtained. Calculations show, that within the scope of the applied theory the 2D hexagonal structure for ZnS and ZnSe is unstable $(k_1<0)$. Comparison of the calculated values of the high-frequency $(\varepsilon_\infty)$ and static $(\varepsilon_0)$ dielectric constants with the available experimental data for the corresponding 3D compounds demonstrates quite reasonable agreement.