The series of alkali metal perhalogenates, $MXO_4$ (M=Li, Na, K and X=F, Cl, Br, I) were theoretically studied with the help of MP2 methods. Bidentate as well as tridentate structures were found to be stable minima. The bidentate structures are becoming preferred as the size of halogen increases and as the size of metal decreases. Geometrically, the M-O and M-X distances of both bidentate and tridentate structures, increase with the size of metal. Generally, the M-$O_1$ distances of tridentate forms are longer than the corresponding distances of bidentate forms, while the M-X distances of tridentate forms show the opposite trend. Similarly, the X-O bonds increase with the size of halogens except $MXO_4$ pairs, where the X-O bonds are unusually long due to the enhanced oxygen-oxygen repulsions. In short, the relative energetics as well as the geometrical parameters are found to be strongly dependent on halogen and metal elements.