We simulate nuclear and electron spin relaxation rates in a paramagnetic system from first principles. Sampling a molecular dynamics trajectory with quantum-chemical calculations produces a time series of the instantaneous parameters of the relevant spin Hamiltonian. The Hamiltonians are, in turn, used to numerically solve the Liouville-von Neumann equation for the time evolution of the spin density matrix. We demonstrate the approach by studying the aqueous solution of the Ni 2+ ion. Taking

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... antage of Kubo's theory, the spin-lattice (T 1 ) and spin-spin (T 2 ) relaxation rates are extracted from the simulations of the time dependence of the longitudinal and transverse magnetization, respectively. Good agreement with the available experimental data is obtained by the method.