Critical Analysis of Cluster Models and Exchange-Correlation Functionals for Calculating Magnetic Shielding in Molecular Solids

Abstract

Calculations of the principal components of magnetic-shielding tensors in crystalline solids require the inclusion of the effects of lattice structure on the local electronic environment to obtain significant agreement with experimental NMR measurements. We assess periodic (GIPAW) and GIAO/symmetry-adapted cluster (SAC) models for computing magnetic-shielding tensors by calculations on a test set containing 72 insulating molecular solids, with a total of 393 principal components of chemical-shift tensors from 13C, 15N, 19F, and 31P sites. When clusters are carefully designed to represent the local solid-state environment and when periodic calculations include sufficient variability, both methods predict magnetic-shielding tensors that agree well with experimental chemical-shift values, demonstrating the correspondence of the two computational techniques. At the basis-set limit, we find that the small differences in the computed values have no statistical significance for three of the four nuclides considered. Subsequently, we explore the effects of additional DFT methods available only with the GIAO/cluster approach, particularly the use of hybrid-GGA functionals, meta-GGA functionals, and hybrid meta-GGA functionals that demonstrate improved agreement in calculations on symmetry-adapted clusters. We demonstrate that meta-GGA functionals improve computed NMR parameters over those obtained by GGA functionals in all cases, and that hybrid functionals improve computed results over the respective pure DFT functional for all nuclides except 15N.

Benchmark fragment-based1H,13C,15N and17O chemical shift predictions in molecular crystals

“…Holmes et al 14 also observed that PBE0 performed worse than the GGA and meta-GGA functionals they tested for nitrogen, while it and B3LYP perform the best here. The reasons for the discrepancy between that study and the current one are unclear, but the studies do differ in a few notable ways.…”

“…14 Here, no such behavior is observed for the isotropic 13 C and 17 O chemical shifts. For nitrogen, the meta-GGA TPSS does perform slightly better than PBE or OPBE, but the differences are ~0.1 ppm or less between TPSS and OPBE.…”

“…TPSS and TPSSh performed well in a recent molecular crystal study. 14 Using the fragment, cluster, and combined cluster/fragment models, rms errors for each of the 1 H, 13 C, 15 N, and 17 O chemical shifts on their respective molecular crystal test sets are given in Figure 4. Table 1 summarizes the rms errors along with linear regression parameters for each nucleus and density functional included in the present work.…”

“…29 The meta-GGA and hybrid meta-GGA functionals performed well for 15 N chemical shift tensors in a recent study using symmetry-adapted cluster calculations. 14 …”

Temperature Dependence of NMR Parameters Calculated from Path Integral Molecular Dynamics Simulations

“…1,[15][16] An alternative to the GIPAW approach are calculations of NMR parameters of molecular clusters, which allows application of a broader set of model chemistries, such as meta-GGA or DFT hybrid 3 functionals. [17][18][19] The quantum chemical calculations are typically performed using static structures, i.e. at 0 K and neglecting zero-point motion.…”