In this thesis, Quantum Monte Carlo (QMC) techniques applied to calculate electronic and structural properties of a single graphene sheet. Our aim is to gain better accuracy than other current electronic structure methods such as Density Functional Theory (DFT). The computational time in QMC scales reasonably with size of system. Also QMC can take into account electronic correlation very accurately. Therefore QMC is a good candidate when a large system (such as big molecules or crystal systems) needs to be treated very accurately. We used both DFT and QMC methods for graphene. PWscf code was used for DFT calculations. Then we feeded CASINO code with wavefunctions of PWscf. Finally by using Variational Monte Carlo (VMC), the PWscf wavefunctions were improved to better trial wavefunctions. To do this we added Jastrow factor to PWscf wavwfunctions. We needed to improve trial wavwfunctions because of Diffusion Monte Carlo (DMC). DMC method is the most accurate method in QMC and with better wavefunctions we can reduce errors in this method. Also in VMC calculations we could guess the effective length of electron-electron correlation. We compared DFT, VMC and DMC results. At the end we calculated cohesive energy of graphene within LDA, GGA and DMC and compared them with experimental data. Key Words: Graphene, Variational Monte Carlo, Diffusion Monte Carlo, DFT, QMC, VMC, DMC, PWscf, CASINO
