abstrac The main motivation of this study is to find out what is the smallest particle size for data storages . It is understood that low cost computing method to study clusters and larger systems is density functional theory . Although many studies have been performed for variety of elements by the usage of density functional theory , the accuracy of these calculations is not discussed as well . The starting point of this study is diatomic molecules . The studies show that Density functional theory the ground state electronic instead Predicted to form excited state. and it is the greatest defect of density functional theory in the case of this group of elements . The results for cobalt's dimer is associated with greater uncertainty . Therefore, we study Co2 and the nearest neighbors Fe2 and Ni2 . Calculations has been performed by using computational packages such as Gaussian on the best multiplicity . In order to study the correlation effects by considering a fixed share exchange , and various correlations we calculate the ground state properties, then we study the energy gap , distribute charge and NBO calculations . The various functional exchange-correlation anticipate different results . Since the orbital’s filling is different , we get different results that show Correlation effects in transition metals has a large effect on the energy of the ground state properties . thus , using a more accurate method is needed to perform such studies . Up to data diffusion Monte Carlo method is the most accurate tools available . In these calculations , we use the wave function to obtain the ground state energy . Parameters are dependent on the energy of the wave function . At each step exerting variation of parameters will changed energy that is negative compared to the previous state . Calculations are performed with statistical methods, ergo it has some flaws . We tried to minimize sources of error . The main sources of error is Slater Determinant , time step and jastrow factor . Then we find the appropriate wave function for diffiusion Monte Carlo calculations using the computational package CASINO in two different time step and repeat it by extrapolation method , the ground state energy at zero gain . . Results are repeated for the other spin states . Unfortunately , the results for the two nickel atoms does not comply with expectations and has a slight discrepancies’ with experimental data , therefore , the best methods of computational chemistry calculations in terms of accuracy is Quantum Monte Carlo . The results confirmed Monte Carlo results . In the last step , the Heisenberg exchange interaction Hamiltonian Frmghnatys mode A mode Ntyfrvmghnatys has been used . The results of this interaction decreases exponentially by increasing distance . Keywords: Density functional theory, Diffusion of Monte Carlo, diatomic of transitional metal, Hyzenberg model , wave function , Variation method