1,3-Benzenediamidoethanethiolatemercury [BDT-Hg or BD(S)-Hg] and its derivatives are investigated utilizing the Dirac exact relativistic normalized elimination of the small component method in connection with B3LYP, CCSD(T), and polarizable continuum calculations. It is shown that the chelating energy of BDT-Hg can be significantly increased by replacing sulfur with selenium or tellurium, thus leading to BD(Se)-Hg or BD(Te)-Hg. In this particular case, the chalcogenophilicity of mercury increases from S to Te because increasing the E-Hg bond lengths leads to a reduction of ring strain. Various possibilities of increasing the metal (M) chelating strength in BDT-M complexes are investigated, and suggestions for new chelating agents based on the BDT-M template are made.