In this thesis, we perform ab initio molecular dynamics (MD) simulations at the Hartree-Fock level, where the forces are computed on-the-fly using the Born-Oppenheimer approximation. The theory behind the Hartree-Fock method is discussed in detail and an implementation of this method based on Gaussian basis functions is explained. We also demonstrate how to calculate the analytic energy derivatives needed for obtaining the forces acting on the nuclei. Hartree-Fock calculations on the ground state energy, dipole moment, ionization potential and population analysis are done for H₂, N₂, FH, CO, NH₃, H₂O, and CH₄. These results are in perfect agreement with the literature. Ab initio MD calculations with different Gaussian basis sets, are performed on the diatomic systems H₂, N₂, F₂, FH, and CO, for equilibrium bond length and vibration frequency analysis. Finally, a study on the reaction dynamics of the nucleophilic substitution reaction H⁻ + CH₄ → CH₄ + H⁻ is done, illustrating the importance of the initial vibrational energy of the methane molecule for the reaction to occur.