Dynamics of large nuclear-spin systems from low-order correlations in Liouville space

Simulation of the coherent dynamics of a large lattice of strongly coupled nuclear spins is demonstrated. The evolution of N spins is simulated in a reduced Liouville space X which excludes coherences involving more than k spins, where k ≪ N is chosen to minimize the dimension of X without introducing unacceptable error. For polarization transfer within a spinning lattice of protons, comparison with exact simulations shows that k = 4 allows accurate simulation of the experimentally relevant powder-averaged curves. A simulation of polarization transfer among 144 protons is presented.