Geometry optimization for pure transition metals structures Ni6 , Co5 , Au12 , Y5 and alkali-transition metals structures Ni6Li , Co5Li , Au12Li , Y5Na at B3LYP level, 3-21G and LaNL2DZ basis sets has been investigated by using Density Functional Theory (DFT) throughout Gaussian09 package. Electrostatic potential,contours, infrared spectra, symmetry, energy gap has been studied for all structures. Total energy for pure transition metals structures is greater than the total energy for alkali-transition metals structures, One can say that the orbitals that generate between Lithium and atoms of pure Nickel structure will be from anti-bonding type. Dipole moment for some pure Nickel structure has zero value because it is homostructure, the other pure transition structures has nonzero values although they are homostructures this is result because of the geometry structures, but the dipole moment for all alkali-transition structures has nonzero numerical values because it is hetrostructures. Energy gap for Y5Na is the smallest value of energy gaps of the structures under study, it approaches to the energy gap of GaAs, this property is very useful in electronic applications such as manufacturing of processors of laptops, Eg of Y5Na = 0.95 eV, Eg of GaAs = 0.8 eV.