Liquid-state paramagnetic relaxation from first principles

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 Ni²⁺ ion. Taking advantage of Kubo's theory, the spin-lattice (T₁) and spin-spin (T₂) 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.