$Al27$ NMR chemical shift of $Al(OH)4−$ calculated from first principles: Assessment of error cancellation in chemically distinct reference and target systems

Predicting accurate nuclear magnetic resonance chemical shieldings relies upon cancellation of different types of errors between the theoretically calculated shielding constant of the analyte of interest and the reference. Often, the intrinsic error in computed shieldings due to basis sets, approximations in the Hamiltonian, description of the wave function, and dynamic effects is nearly identical between the analyte and reference, yet if the electronic structure or sensitivity to local environment differs dramatically, this cannot be taken for granted. Detailed prior work has examined the octahedral trivalent cation $Al(H2O)63+$⁠, accounting for ab initio intrinsic errors. However, the use of this species as a reference for the chemically distinct tetrahedral anion $Al(OH)4−$ requires an understanding of how these errors cancel in order to define the limits of accurately predicting $Al27$ chemical shielding in $Al(OH)4−$⁠. In this work, we estimate the absolute shielding of the $Al27$ nucleus in $Al(OH)4−$ at the coupled cluster level (515.1 $±$ 5.3 ppm). Shielding sensitivity to the choice of method approximation and atomic basis sets used has been evaluated. Solvent and thermal effects are assessed through ensemble averaging techniques using ab initio molecular dynamics. The contribution of each type of intrinsic error is assessed for the $Al(H2O)63+$ and $Al(OH)4−$ ions, revealing significant differences that fundamentally hamper the ability to accurately calculate the $Al27$ chemical shift of $Al(OH)4−$ from first principles.