Extended Benchmark Set of Main-Group Nuclear Shielding Constants and NMR Chemical Shifts and Its Use to Evaluate Modern DFT Methods

Abstract

An extended theoretical benchmark set, NS372, for light main-group nuclear shieldings and NMR shifts has been constructed based on high-level GIAO-CCSD­(T)/pcSseg-3//CCSD­(T)/cc-pVQZ reference data. After removal of the large static-correlation cases O3, F3 –, and BH from the statistical evaluations for the 17O, 19F, and 11B subsets, the benchmark comprises overall 372 shielding values in 117 molecules with a wide range of electronic-structure situations, containing 124 1H, 14 11B, 93 13C, 43 15N, 31 17O, 47 19F, 14 31P, and 6 33S shielding constants. The CCSD­(T)/pcSseg-3 data are shown to be close to the basis-set and method limit and thus provide an excellent benchmark to evaluate more approximate methods, such as density functional approaches. This dataset has been used to evaluate Hartree–Fock (HF) and MP2, and a wide range of exchange–correlation functionals from local density approximation (LDA) to generalized gradient approximations (GGAs) and meta-GGAs (focusing on their current-density functional implementations), as well as global hybrid, range-separated hybrid, local hybrid, and double-hybrid functionals. Starting with absolute shielding constants, the DSD-PBEP86 double hybrid is confirmed to provide the highest accuracy, with an aggregate relative mean absolute error (rel. MAE) of only 0.9%, followed by MP2 (1.1%). MP2 and double hybrids only show larger errors for a few systems with the largest static-correlation effects. The double-hybrid B2GP-PLYP, the two local hybrids cLH12ct-SsirPW92 and cLH12ct-SsifPW92, and the current-density functional meta-GGA cB97M-V follow closely behind (all 1.5%), as do some further functionals, cLH20t and cMN15-L (both 1.6%), as well as B2PLYP and KT3 (both 2.0%). Functionals on the lower rungs of the usual ladder offer the advantage of lower computational cost and access to larger molecules. Closer examination also reveals the best-performing methods for individual nuclei in the test set. Different ways of treating τ-dependent functionals are evaluated. When moving from absolute shielding constants to chemical shifts, some of the methods can benefit from systematic error compensation, and the overall error range somewhat narrows. Further methods now achieve the 2% threshold of relative MAEs, including functionals based on TPSS (TPSSh, cmPSTS).

Electron correlation and vibrational effects in predictions of paramagnetic NMR shifts

“…147 It is also known to provide excellent predictions of NMR shifts in closed-shell systems of main group elements. 101,[148][149][150][151][152] However, as shown in Table 2, for the case of cyanomethyl radicals the DSD-PBEP86 functional suffered from instabilities that resulted in erratic spin density on the nitrogen atom. Special care has to be taken when applying double hybrid functionals to open-shell systems.…”

High Level Electronic Structure Calculation of Molecular Solid-State NMR Shielding Constants

“…Recent work has demonstrated that a more rigorous treatment is provided by the Dobson ansatz for τ, 42 − 44 although the differences for some functionals, such as TPSS, are small. 21 We have included data calculated with TPSS and the Dobson ansatz in the Supporting Information ( Table S9 ), and indeed, the results are very similar.…”

“…However, in the presence of heavier nuclei, this might lead to deviations—in the case of sulfur, up to 0.5 ppm for 1 H SCs. 21 , 46 , 47 …”

“…Kaupp and co-workers, for example, have shown that, for NMR shielding calculations, local hybrid functionals fall between conventional functionals and DHs in terms of both accuracy and computational cost. 21 , 22 …”

Local Hybrid Functional Applicable to Weakly and Strongly Correlated Systems

“…The functional has been supplemented by D4 dispersion corrections . LH20t-D4 has been demonstrated to be one of the best-performing rung 4 functionals for general main-group energetics (GMTKN55 test set), for transition-metal thermochemistry and barriers, and for many spectroscopic parameters. − However, it has not been constructed to give low FSEs or to generally account for sc effects.…”