GIAO versus GIPAW: Comparison of Methods To Calculate ¹¹B NMR Shifts of Icosahedral Closo-Heteroboranes toward Boron-Rich Borides

In this work, we perform first-principle density functional theory calculations with the Perdew–Burke–Ernzerhof (PBE) exchange correlation functional to compare the results of the gauge-including atomic orbital (GIAO) method with the gauge-including projector-augmented wave (GIPAW) approach for isotropic ¹¹B nuclear magnetic resonance shifts. GIPAW had been used successfully for the theoretical calculation of nuclear magnetic parameters of ¹¹B species in strong ionic solid-phase compounds such as borates but had been applied very rarely to structures where boron is mainly involved in complex covalent bonding situations, for example, in icosahedra of boron-rich borides. Thus, we investigate the accuracy of both well-known methods and reliability of the effective treatment of core electrons on a test set containing 16 experimentally known closo-(hetero)­dodecaboranes. In general, we find very good agreement between GIAO and GIPAW when compared to experimental observations. However, accidental degeneracies of the shift values are better predicted by GIPAW. The optimized molecular geometries on the PBE level agree well with gaseous electron diffraction data and lead to theoretical isotropic chemical ¹¹B shifts with root-mean-square errors of 2.1 and 1.0 ppm depending on the used model of converting absolute shieldings to chemical shifts. The comparison with results from hybrid functionals (B3LYP, B3LYP-D2, and PBE0) shows a minor improvement in accuracy, which is in agreement with ¹³C shifts of sp³-hybridized species. In order to prove the reliability of the conversion parameters obtained by PBE, we report the calculated ¹¹B shifts of 1,2-, 1,7-, and 1,12-PCB₁₀H₁₁ with GIAO and GIPAW to our knowledge for the first time. Additionally, Bader’s analysis is carried out on the converged electron density for all boron species within the molecular test set, yielding no simple direct relation between charge and isotropic shifts.