Regression formulas for density functional theory calculated ¹H and ¹³C NMR chemical shifts in toluene- d ₈

This study aimed at investigating the performance of a series of basis sets, density functional theory (DFT) functionals, and the IEF-PCM solvation model in the accurate calculation of ¹H and ¹³C NMR chemical shifts in toluene-d₈. We demonstrated that, on a test set of 37 organic species with various functional moieties, linear scaling significantly improved the calculated shifts and was necessary to obtain more accurate results. Inclusion of a solvation model produced larger deviations from the experimental data as compared to the gas-phase calculations. Moreover, we did not find any evidence that very large basis sets were necessary to reproduce the experimental NMR data. Ultimately, we recommend the use of the BMK functional. For the ¹H shifts the use of the 6-311G(d) basis set gave linearly scaled mean unsigned (MU) and root-mean-square (rms) errors of 0.15 ppm and 0.21 ppm, respectively. For the calculation of the ¹³C chemical shifts the 6-31G(d) basis set produced MUE of 1.82 ppm and RMSE of 3.29 ppm.