Bond dissociation energies (BDEs) of neutral HgX and cationic HgX(+) molecules range from less than a kcal mol(-1) to as much as 60 kcal mol(-1). Using NESC/CCSD(T) [normalized elimination of the small component and coupled-cluster theory with all single and double excitations and a perturbative treatment of the triple excitations] in combination with triple-zeta basis sets, bonding in 28 mercury molecules HgX (X = H, Li, Na, K, Rb, CH(3), SiH(3), GeH(3), SnH(3), NH(2), PH(2), AsH(2), SbH(2), OH, SH, SeH, TeH, O, S, Se, Te, F, Cl, Br, I, CN, CF(3), OCF(3)) and their corresponding 28 cations is investigated. Mercury undergoes weak covalent bonding with its partner X in most cases (exceptions: X = alkali atoms, which lead to van der Waals bonding) although the BDEs are mostly smaller than 12 kcal mol(-1). Bonding is weakened by 1) a singly occupied destabilized sigma*-HOMO and 2) lone pair repulsion. The magnitude of sigma*-destabilization can be determined from the energy difference BDE(HgX)-BDE(HgX(+)), which is largest for bonding partners from groups IVb and Vb of the periodic table (up to 80 kcal mol(-1)). BDEs can be enlarged by charge transfer from Hg and increased HgX ionic bonding, provided the bonding partner of Hg is sufficiently electronegative. The fine-tuning of covalent and ionic bonding, sigma-destabilization, and lone-pair repulsion occurs via relativistic effects where 6s AO contraction and 5d AO expansion are decisive. Lone pair repulsion involving the mercury 5d AOs plays an important role in the case of some mercury chalcogenides HgE (E = O, Te) where it leads to (3)Pi rather than (1)Sigma(+) ground states. However, both HgE((3)Pi) and HgE((1)Sigma(+)) should not be experimentally detectable under normal conditions, which is in contrast to experimental predictions suggesting BDE values for HgE between 30 and 53 kcal mol(-1). The results of this work are discussed with regard to their relevance for mercury bonding in general, the chemistry of mercury, and reactions of elemental Hg in the atmosphere.