Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals

Abstract

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile tools in elucidating molecular structures. To eliminate ambiguities of experimental assignments, accurate calculations of NMR spectra are of great importance. Here, a method for theoretical evaluation of the NMR shielding constants by analytic derivatives using gauge including atomic orbitals (GIAO) has been implemented for the XYG3 type of doubly hybrid density functionals (xDH), namely, the GIAO-xDH method. Benchmark calculations on shielding constants and chemical shifts demonstrate the remarkable accuracy of the GIAO-xDH method, compared to the accurate CCSD(T) references. It is shown here that the XYGJ-OS functional is able to give a mean absolute deviation (MAD) of ∼3.0 ppm in the calculated shielding constants for 13 C, 15 N, 17 O, 19 F, while both XYGJ-OS and xDH-PBE0 functionals are able to provide a satisfactory estimation of chemical shifts with MADs of ∼0.03 and 1.0 ppm for 1 H and 13 C, respectively. The basis set influence upon the method has been examined and a computational scheme considering both accuracy and efficiency has been proposed and tested to predict the experimental 13 C chemical shifts of five medium-sized natural product molecules, yielding a MAD of ∼1.0 ppm, which demonstrates the practical feasibility of the GIAO-xDH method.

Do Models beyond Hybrid Density Functionals Increase the Agreement with Experiment for Predicted NMR Chemical Shifts or Electric Field Gradient Tensors in Organic Solids?

“…However, it is notable that none of these rms errors versus experiment is smaller than what is obtained from a PBE0 or B3LYP monomer correction (3.5–3.6 ppm), and two of the double-hybrid functionals give errors versus experiment that are slightly larger than results of the uncorrected GIPAW itself. The failure to obtain more accurate chemical shifts with the double-hybrid functionals is surprising, given previous studies that have demonstrated that double-hybrid functionals are more faithful to high-level benchmark absolute shielding constants (e.g., refs − ).…”

“…These results are perhaps surprising, given that previous studies have found double-hybrid DFT, and MP2 absolute chemical shieldings reproduce high-accuracy benchmarks more faithfully than lower-level DFT functionals. − It seems likely that considerable error cancellation is involved in the strong performance of basic hybrid functionals such as PBE0. Further evidence of error cancellation being involved comes from the work of Dračı́nský et al, who found that including spin–orbit and nuclear quantum effect corrections in their GIPAW + PBE0 results improved the accuracy of their 1 H chemical shifts relative to experiment, while decreasing the accuracy of their 13 C shifts.…”

“…39 shieldings, 15 Yan and Xu found similarly good performance for XYG3-type double-hybrid functionals for shielding constants and theoretical chemical shifts in small molecules and organics. 16 In contrast, a large benchmark study of 148 experimental solution-phase 1 H chemical shifts found double-hybrid density functionals to produce errors that were similar to or larger than those from GGA or hybrid density functionals. 40 Dracǐ ́nskýet al applied the local double-hybrid DFT, MP2, and CCSD gasphase molecular corrections to GIPAW for a set of six small amino acid crystals.…”

“…This raises the question of what further accuracy improvements might be obtained by using even higher-level electronic structure models, such as double-hybrid density functionals or correlated wave function methods like second-order Møller–Plesset perturbation theory (MP2) and coupled cluster singles and doubles (CCSD). Double-hybrid density functionals exhibit superior performance over GGA and hybrid functionals for thermochemistry, noncovalent interactions, barrier heights, and conformational energies, for example. − Various studies on small systems have also demonstrated improvements in the absolute NMR shielding constants predicted with double-hybrid functionals, MP2, and CCSD instead of GGA or hybrid functionals. − …”

“…) found clear improvement in the predicted chemical shifts upon switching to MP2 or double-hybrid DFT. Shattenberg and Kaupp similarly found excellent performance for MP2 and double-hybrid functionals relative to coupled cluster benchmarks for a set of 372 light, main-group nuclear shieldings, Yan and Xu found similarly good performance for XYG3-type double-hybrid functionals for shielding constants and theoretical chemical shifts in small molecules and organics …”