The siting of B, Al, Ga or Zn and bridging OH groups in the framework of mordenite was studied by ab initio Hartree-Fock MO methods. The basis set effect on the calculation results was investigated in details. It was shown that heteroatoms including B, Al, Ga and Zn prefer the same T sites, T-3 and T-4, when replacing Si in mordenite framework. The presence of the charge-balancing protons does not influence the siting sites of heteroatoms, but stabilizes the structure of the substituted clusters. For the two preferred substitution sites T3 and T4, the charge-compensating protons prefer to attach to O-9 and O-10, respectively, in case of B, Al or Ga substitution. For Zn substitution at T3 or T4 site, the two charge-compensating protons favor bonding with O-9 and O-1 or O-10 and O-2, respectively.