Density functional theory study of the magnetic shielding mechanism for 11B in pentaborate minerals: ulexite and probertite

Abstract

Nuclear magnetic resonance (NMR) parameters of ¹¹B in borates and borosilicates, unlike those of many other nuclei such as ²⁹Si and ²⁷Al, vary only in limited ranges for a given polyhedral geometry, but mechanisms for such insensitivity to local structural environments remain poorly understood. In this contribution, ulexite and probertite, with the ([B₅O₆(OH)₆]³⁻) pentaborate polyanion as the fundamental building block, have been investigated in detail by ab initio theoretical calculations of the density of states (DOS) as implemented in WIEN2k, including optimization of the structures and determination of contributions to the magnetic shielding at each of the five distinct B sites. Calculated ¹¹B NMR parameters of these two pentaborates are compared with high-precision experimental data obtained at high (14 T) and ultrahigh (21 T) fields. Optimized structures using the linearized augmented plane-wave method with additional radial basis functions in the form of local orbitals (i.e., LAPW+lo) not only yield more accurate electric field gradients (EFG) at the distinct three- and fourfold-coordinated B sites (i.e., [BO₃] or ^[3]B and [BO₄] or ^[4]B) but also improve the calculated ¹¹B magnetic shielding. In particular, the magnetic shielding variation trends among the B sites in ulexite and probertite are determined mainly by the valence states and especially by the local p orbitals of B and its nearest-neighbor O atoms. Calculations with the water molecules removed or K⁺ substituting for Na⁺ in the structures show that the next-nearest-neighbor cations and water molecules have negligible effects. Theoretical calculations also reveal that the systematic differences in shielding between ^[3]B and ^[4]B are caused by multiple factors such as the occupancies and imbalance in the sp hybrid orbitals between B and its nearest-neighbor O atoms.