Benchmark Study on the Calculation of ²⁰⁷Pb NMR Chemical Shifts

Abstract

A benchmark set for the computation of 207Pb nuclear magnetic resonance (NMR) chemical shifts is presented. The PbS50 set includes conformer ensembles of 50 lead-containing molecular compounds and their experimentally measured 207Pb NMR chemical shifts. Various bonding motifs at the Pb center with up to seven bonding partners are included. Six different solvents were used in the measurements. The respective shifts lie in the range between +10745 and −5030 ppm. Several calculation settings are assessed by evaluating computed 207Pb NMR shifts for the use with different density functional approximations (DFAs), relativistic approaches, treatment of the conformational space, and levels for geometry optimization. Relativistic effects were included explicitly with the zeroth order regular approximation (ZORA), for which only the spin–orbit variant was able to yield reliable results. In total, seven GGAs and three hybrid DFAs were tested. Hybrid DFAs significantly outperform GGAs. The most accurate DFAs are mPW1PW with a mean absolute deviation (MAD) of 429 ppm and PBE0 with an MAD of 446 ppm. Conformational influences are small as most compounds are rigid, but more flexible structures still benefit from Boltzmann averaging. Including explicit relativistic treatments such as SO-ZORA in the geometry optimization does not show any significant improvement over the use of effective core potentials (ECPs).

[Ba4@Sn56]36– as a Main-Group Second-Order Superatom. Interpenetrated Dodecahedrons as a Three-Dimensional Cluster-of-Clusters Structure

“…119 Sn nuclear magnetic resonance (NMR) calculations were carried out by using the exchange proposed by Handy and Cohen, and correlation by Perdew, Burke, and Ernzerhof (OPBE) at the TZ2P/ZORA-SO/OPBE level of theory, , incorporating spin–orbit coupling through the two-component ZORA Hamiltonian , and solvent effects (COSMO with DMFA as solvent). A similar method has been pointed out as a reliable choice for 119 Sn and 207 Pb calculations, from recent benchmarks. , Absolute nuclear-shielding tensors (σ) were referenced to tetramethyltin (σ SnMe4 = 2876.9 ppm), leading to relative chemical shifts (δ = σ SnMe4 – σ probe ). Graphical representation of σ for representative Sn sites was obtained following the approach by Autschbach and co-workers, considering an f ( r ) = ∑ ij r i r j σ ij expression centered at the respective nucleus, plotted in polar coordinates in a regular cube file.…”