Despite its limitations (high cost, fragility, etc.), the HgCdTe ternary has qualities for infrared applications that are often superior to those of its competitors. One main purposes of the present work is to review the known data of this material, to list its advantages but also its disadvantages.  As exchange–correlation potential we used the generalized gradient approximation (GGA) of Perdew et al. in addition the modified Beck-Johnson potential (TB – mBJ) approach, and implemented in the WIEN2k calculation code. The band gap energy values of materials have been improved by the use of the recent approximation of (TB – mBJ) where the results are very close with the experimental data. The results obtained have been compared with experimental data from the literature and other results of theoretical work.