This work is concerned with an ab initio calculation of the spin lattice relaxation time T1 of the negatively charged nitrogen vacancy center (NV center) in diamond. Spin lattice relaxation is the mechanism by which the energy between a spin system and its surrounding is transferred. In the case of a solid, the most important mechanism for spin coupling is given by the interaction of a spin system with the moving ions which constitute the lattice of the material. The NV center in diamond as the spin system of choice and its applications in measurement technology and quantum theory are introduced and the implications of this thesis are pointed out in Chapter 1. The theoretical foundations for the treatment of a quantum mechanical many body problem in a solid are laid in Chapter 2: Starting from the Hohenberg-Kohn theorem, the machinery of density functional theory for the Kohn-Sham system with its different levels of approximations for a treatment of the many body effects is presented. For the calculation of the relaxation time T1 , the dynamics of the ions have to be modeled: Chapter 3 is dedicated to the quantum mechanical calculation of the lattice dynamics in the harmonic approximation, where a proper description of phonons, the quantized vibrations in solids, is derived. In Chapter 4, electron spins and phonons are coupled. At the beginning of this Chapter, we will introduce the history of the treatment of spin-lattice relaxation. Subsequently, the expressions of relaxation rates via first and second order time dependent perturbation theory are deduced and two different mechanisms of spin-phonon coupling are considered: Coupling via the magnetic spin-spin interaction and coupling via the spin-orbit interaction. Expressions for the relaxation time T1 are given for both coupling cases. The relaxation rates are calculated ab initio in Chapter 5, where the electronic and ionic properties of the NV center are simulated and effects of the local vibrations are taken into account. The simulations show that the measured relaxation times may be explained by the changes of the spin-spin interaction, when the ions start to move. The excellent spin properties of the NV center are explained by the strong covalent bonds in diamond, which result in high frequency phonons, way above the spin transition frequency. Further simulations show that induced crystal damage alters the phononic properties of the system and reduces T1. Chapter 6 concludes and gives a small outlook for possible future investigations.