How reliable are GIAO calculations of ¹H and ¹³C NMR chemical shifts? A statistical analysis and empirical corrections at DFT (PBE/3z) level

Abstract

Reliability of calculated (1)H and (13)C NMR chemical shifts for various classes of organic compounds obtained with gauge-invariant atomic orbital (GIAO) approach has been studied at the PBE/3ζ level (as implemented in PRIRODA code) using linear regression analysis with experimental data. Empirical corrections for the calculated chemical shifts δ(H,calc) = δ(PBE/3ζ) - 0.08 ppm (RMS 0.18 ppm, MAD 0.66 ppm) and δ(C,calc) = δ(PBE/) (3) (ζ) - 6.35 ppm (RMS 3.09 ppm, MAD 9.42 ppm) have been developed using the sets of 263 and 308 experimental values for (1)H and (13)C chemical shifts, respectively. The confidence intervals of NMR chemical shifts at 95% confidence probability are δ(H,calc) ± 0.35 ppm for (1)H and δC,calc) ± 6.05 ppm for (13)C.

1H NMR spectra of alcohols and diols in chloroform: DFT/GIAO calculation of chemical shifts

“…In recent work, several approaches have been proposed for reducing systematic errors in DFT/GIAO calculations and for improving their ability to distinguish between diastereoisomers: empirical scaling, multi-standard approaches, neural networks and so on. [3,5,[12][13][14][15][16][17][18] In the present work, very good overall RMSD values are obtained for saturated alcohols and diols without any form of correction, particularly for the former, although not all individual compounds reach the 0.1 ppm level of performance. [3] For these alcohols, the only obvious empirical correction is to add 0.035 ppm to all computed values, which reduces the RMSD from 0.078 to 0.069 ppm.…”

“…In our hands, DFT/GIAO works better than the semi‐empirical CHARGE model based on classical physical chemistry but is much more time consuming. There are various ways of reducing the computer time for DFT/GIAO calculations: the use of modest basis sets, single‐point calculations on molecular mechanics (MM) geometries, selection of preferred conformers and so on . The CHARGE model uses MM geometries and very often only one or two conformers; 107 unique conformers are neglected in the case of pentane‐1,5‐diol .…”

“…There are various ways of reducing the computer time for DFT/GIAO calculations: the use of modest basis sets, single-point calculations on molecular mechanics (MM) geometries, selection of preferred conformers and so on. [5,[11][12][13][14][15][16][17][18] The CHARGE model uses MM geometries and very often only one or two conformers; 107 unique conformers are neglected in the case of pentane-1,5-diol. [43,44] Moreover, MM force fields are not well parameterised for interacting functional groups.…”

“…The computation of nuclear magnetic resonance (NMR) chemical shifts and coupling constants by quantum mechanical methods, essentially by the density functional theory/gauge‐including atomic orbital (DFT/GIAO) approach, has now reached a stage where it is no longer necessary to point out its importance in the structural and stereochemical elucidation of organic compounds . The state of the art is such that the focus is now on the development of methods for reducing the computer time, by using modest basis sets, and the elimination of systematic errors by empirical scaling, multi‐standard and other approaches …”

“…[1][2][3][4][5][6][7][8][9][10] The state of the art is such that the focus is now on the development of methods for reducing the computer time, by using modest basis sets, [11] and the elimination of systematic errors by empirical scaling, multi-standard and other approaches. [3,5,[12][13][14][15][16][17][18] There has been no systematic study of saturated alcohols, and the two studies reported correspond to rather different approaches. The 1 H and 13 C shifts of methylcyclohexanols in chloroform were computed by taking into account all conformers and using optimised functionals with large basis sets, and the results were further refined by linear correction.…”