Multinuclear Magnetic Resonance Crystallographic Structure Refinement and Cross-Validation Using Experimental and Computed Electric Field Gradients: Application to Na2Al2B2O7

An NMR crystallographic method is presented for the refinement of structures using electric field gradient (EFG) tensors measured using solid-state NMR spectroscopy and those calculated using the projector-augmented wave DFT method. As the calculated EFG data often overestimate the experimental data, the former are scaled to yield optimal agreement for a test set of compounds having highly accurate NMR data. A least-squares optimization procedure is then performed to minimize the difference between the experimental and the scaled calculated EFG tensors. This procedure yields high-quality crystal structures comparable to those obtained from pure DFT energy minimizations, as judged by their rmsd from single-crystal X-ray structures, and is based on experimental observables. Further improvement is obtained by simultaneously refining the structures against the experimental EFG tensor parameters and optimizing the lattice energy with DFT. We use this hybrid experimental-theoretical approach to refine the crystal structure of Na2Al2B2O7, a member of an important family of nonlinear optical materials, which has been the focus of study due to its tendency to form stacking faults. The resulting structures are subjected to a systematic cross-validation process using experimental Na-23, B-11, O-17, and Al-27 EFG and chemical shift data, thereby demonstrating the validity of our strategy. This approach may be useful for the refinement of crystal structures of intrinsically polycrystalline materials for which typically only low quality structures are obtainable through traditional diffraction-based methods.