The main aim of this thesis is studying of iron dimer by the Quantum Monte Carlo (QMC) Method. The QMC method is a stochastic method which is used to solve the Schr?dinger equation. The character of being stochastic is due to using random numbers. As a matter of fact, QMC is a Monte Carlo method sor solving the Srodinger equation. The main advantage of this method is its accuracy is independent of the integral dimension. Also, this method, due to its independence of the integral dimension, is the best accessible method to deal with complicated systems such as strongly correlated systems, as well as large systems in which modern quantum chemistry methods such as configuration interactio fail to apply. Variational Monte Carlo method (VMC) and diffusion Monte Carlo method (DMC) are the most popular QMC method in electronic structure calculations which are used in the present project. The CASINO code was used for the QMC calculations. This code is capable of dealing with limited systems such as various kinds of atoms, molecules, crystals, systems with periodic boundary conditions, 2-dimensional and 3-dimensional homogenous and inhomogeneous gases in crystalline or fluid phases. Beginning the QMC calculations requires an input trial wave function. There are several ways to produce the trial wave function. One of the ways is to use the output file of the density functional theory (DFT) method. To perform the DFT calculations, the GAUSSINA03 code was used. The more similar is the input trial wave function to the ground wave function of the system, the more accurate is the variational QMC method. For the same reason, a great deal of attention was assigned to choosing the basis set used in the DFT calculations, in order to find the optimum basis set for DFT calculations. Before finding the optimum basis set, the proper multiplicity of the system was obtained and found to be 7. Ultimately, the output file of the DFT calculations by GAUSSIAN03 code was used to produce the trial wave function for the QMC method. At the beginning of the calculations, the variance of the VMC calculations was high. Studying the texts clarified that the intense fluctuations of the core electrons causes the enhancement in the variance of the calculations. Therefore, an effective core potential with 12 core electrons was utilized in performing the calculations and the variance of the calculations fell off to an acceptable value. The wave function produced by the VMC calculations was used as the guide function in order to impose the importance sampling in the DMC method. The DMC calculations were performed with the same effective core potential used in the VMC method. To enhance the accuracy of the calculations, some different ways such as changing the number of steps and walkers and optimizing the backflow factor, were examined. Applying the backflow factor enhanced the calculation time to 6 times while did not change the variance so much. Therefore, finally the backflow factor was omitted. For different via-atoms length chosen around the bond length obtained by the DFT method, the DMC calculations were performed and the diagram of energy versus via-atoms length was fitted to the 4 th order polynomial. Ultimately the iron bond length was found to be 2.054 ? and its binding energy turned out to be -1.143 eV which is in a good agreement with the experimental reports. In addition to the main goal of the project, other results were obtained. For example it was observed that for walker numbers larger than a plausible value, the variance of the calculations does not change significantly. Also the prominence of using effective core potential in the large and strongly correlated system was clarified. Key words: Quantum Monte Carlo (QMC), VMC, DMC, Density Functional Theory (DFT), CAINO code, GAUSSINA03 code