Theoretical calculations were carried out on some neutral nest-shaped heterothiometallic cluster compounds [MOS(3)Py(5)Cu(3)X] (M=Mo, W; X=F, Cl, Br, I) with the high first static hyperpolarizabilities beta values. The geometries of these cluster compounds were optimized by the restricted DFT method at B3LYP level with LanL2DZ base set without any constrains. In order to understand the relationship between the first static hyperpolarizabilities and the compositions of these clusters, the frontier orbital compositions and energy gaps between the HOMO and LUMO orbitals were calculated and analysed. In these clusters the HOMO orbitals are mainly composed of halogen atoms and the first static hyperpolarizability increases from F to I atom. The LUMO orbitals of clusters [MoOS(3)Py(5)Cu(3)X] are comprised of Mo, O and S atoms while the LUMO orbitals of clusters [WOS(3)Py(5)Cu(3)X] composed of W atom and pyridine ring. The energy gaps between the HOMO and LUMO orbitals of the clusters [MoOS(3)Py(5)Cu(3)X] are smaller than those of the clusters [WOS(3)Py(5)Cu(3)X]. As a result the first static hyperpolarizability values of the clusters [MoOS(3)Py(5)Cu(3)X] are higher than those of the clusters [WOS(3)Py(5)Cu(3)X].