Free induction decays in nuclear spin- 12 lattices with a small number of interacting neighbors: The cases of silicon and fluorapatite

Nuclear spin-1/2 lattices where each spin has a small effective number of interacting neighbors represent a particular challenge for first-principles calculations of free induction decays (FIDs) observed by nuclear magnetic resonance. The challenge originates from the fact that these lattices are far from the limit where classical spin simulations perform well. Here we use the recently developed method of hybrid quantum-classical simulations to compute nuclear FIDs for $²⁹\mathrm{Si}$-enriched silicon and fluorapatite. In these solids, the small effective number of interacting neighbors is either due to the partition of the lattice into pairs of strongly coupled spins (silicon), or due to the partition into strongly coupled chains (fluorapatite). We find a very good overall agreement between the hybrid simulation results and the experiments. In addition, we introduce an extension of the hybrid method, which we call the method of coupled quantum clusters. It is tested on $²⁹\mathrm{Si}$-enriched silicon and found to exhibit excellent performance.