Simulation of NMR chemical shifts in heterocycles: a method evaluation

Abstract

An alternative approach to evaluating the performance of computational methods for predicting chemical shifts is presented. The influence of the theoretical level and basis set on the accuracy in calculating both proton and carbon NMR spectra of a large number of heterocyclic molecules is assessed using a linear regression method, thus omitting the need for a reference (as a potential source of error). The best theoretical levels employed herein (GIAO-PBE0/6-31G(d)//ωB97xD/6-31G(d) or GIAO-ωB97xD/6-31G(d)//ωB97xD/6-31G(d)) approach the accuracy of the most elaborate benchmark-quality calculations. One interesting observation is an unexplained distortion of the derived chemical shifts when an internal reference is used: It leads to larger relative shifts and deviations when the "quality" (size) of the basis set employed is increased. This effect can be corrected by using simple linear regression, but a lack of a systematic correlation between the quality of the basis set and the accuracy of the calculated shifts can still be observed; in fact, very good results can be achieved with modest basis sets. Although the general reliability of this approach needs to be evaluated for other theoretical levels and other substance classes, the abovementioned levels of theory appear robust enough for wider applicability. Graphical Abstract Correlation between computed chemical shieldings and experimental chemical shifts for various heterocyclic compounds.

DELTA50: A Highly Accurate Database of Experimental 1H and 13C NMR Chemical Shifts Applied to DFT Benchmarking

“…Table 3 shows the errors and computation times for 40 basis sets from double to quadruple zeta, including polarization and diffuse functions on both heavy atoms and hydrogens. While counterintuitive (yet similar to other benchmark studies), smaller basis sets were found to provide more accurate carbon chemical shift predictions [ 48 , 51 , 71 ], with def2-SVP identified as the best performing basis set when paired with the ωB97X-D functional. Conversely, proton chemical shift predictions typically require larger basis sets, and diffuse functions appear to be productive for reducing errors.…”

“…For instance, Konstantinov and Broadbelt found BMK to be the best performing functional for chemical shift predictions [ 48 ], while Toomsalu and Burk found it to be the worst performing [ 49 ]. Granted, these two studies used different solvent conditions (viz., toluene- d 8 and CDCl 3 ), but even for the same solvent system there have been significantly different findings, such as Benassi recommending WP04 for δ C predictions in CDCl 3 based on a benchmark test set of 104 diverse, small organic molecules [ 50 ], while Buß and Koch found the performance of WP04, for a test set of 24 heterocycles in CDCl 3 , to be the second worst performing density functional for δ C [ 51 ]. Paradoxically, the worst performing functional, WC04, from Buß and Koch’s study [ 51 ] was specifically parameterized for accurate δ C predictions by Wiitala and coworkers [ 52 ].…”

“…Granted, these two studies used different solvent conditions (viz., toluene- d 8 and CDCl 3 ), but even for the same solvent system there have been significantly different findings, such as Benassi recommending WP04 for δ C predictions in CDCl 3 based on a benchmark test set of 104 diverse, small organic molecules [ 50 ], while Buß and Koch found the performance of WP04, for a test set of 24 heterocycles in CDCl 3 , to be the second worst performing density functional for δ C [ 51 ]. Paradoxically, the worst performing functional, WC04, from Buß and Koch’s study [ 51 ] was specifically parameterized for accurate δ C predictions by Wiitala and coworkers [ 52 ]. More to this point, Stoychev, Auer, and Neese found double-hybrid density functionals, such as DSD-PBEP86, to provide superior performance for δ H predictions that were most comparable to extremely costly coupled cluster calculations [ 53 ], while de Oliveria et al recently reported no benefit for the use of double hybrids over conventional density functionals (i.e., GGAs, meta-GGAs, and hybrids) [ 54 ].…”

Simple, accurate, adjustable-parameter-free prediction of NMR shifts for molecules in solution

“…As observed in previous work, 10,31,44 the largest outliers arise due to non-scalar relativistic effects that do not vary systematically as a function of local atomic environment, so are not Table 2 Mean absolute deviations (MAD) and maximum absolute error (MAX) between predicted gas-phase 1 H and 13 C NMR shieldings (ppm) and experimentally-measured shifts in chloroform (ppm). Post hoc correction models are defined according to choice of reference molecule (2 point correction scheme) or using parameters obtained by linear regression analysis.…”

“…39 Although smaller, less flexible basis sets yield less accurate predictions of absolute chemical shieldings, 43 literature evidence suggests that basis set incompleteness errors largely cancel – or can be adequately accounted for – when predicting chemical shifts. 44 However, what has not been explored is the interplay between basis set incompleteness errors and continuum solvation model effects. Our results imply that the apparent decrease in random error previously observed may be due to fortuitous cancellation of errors between these two effects.…”