  Classical simulations of high-temperature nuclear spin dynamics in solids are
known to accurately predict relaxation for spin 1/2 lattices with a large
number of interacting neighbors. Once the number of interacting neighbors
becomes four or smaller, classical simulations lead to noticeable
discrepancies. Here we attempt to improve the performance of the classical
simulations by adding a term representing two-spin quantum correlations. The
method is tested for a spin-1/2 chain. It exhibits good performance at shorter
times, but, at longer times, it is hampered by a singular behavior of the
resulting equations of motion.
