Ab initio molecular orbital methods in combination with DFT calculations were used to study the structural and thermodynamic properties of 17 complexes containing zinc cation and four first-shell ligands as models of active site of metalloenzymes (e.g. angiotensin converting enzyme, thermolysin). The geometry of the complexes was relaxed by complete optimization by ab initio molecular orbital methods at Hertree-Fock level with 3-21G* basis set. Following single point calculation with tight SCF criteria at the B3LYP level with 6-311+G(2d,p) basis set was used to calculate accurate interaction enthalpies. The structure and thermodynamics of optimized complexes are discussed from the point of view of their biological importance.