Errors in DFT integration grids and their potential impact on chemical shift calculations

Abstract

Quantum chemical methods are often employed to estimate the shielding tensors and magnetic susceptibilities of nuclei in a system, chief among these techniques being density functional theory (DFT). In the estimation of chemical shift and coupling constants, molecular conformers are weighted in order to scale their contributions to the magnetic properties being computed. This is commonly carried out by employing a Boltzmann analysis based on the relative free energies of these molecular conformers. Bootsma and Wheeler have recently identified significant concerns regarding the estimation of computed free energies for regioselective and stereoselective reactions using variable DFT integration grids, energies being highly sensitive to the orientation of the system due to the deficiencies in rotational invariance present for common techniques. Grid points in DFT calculations refer to the method employed to carry out the numerical integration step in the estimation of the exchange‐correlation energy of a system. The integration grid in DFT is the product of radial and angular grids, angular effectively integrating spherical harmonics up to a specified order, and radial featuring a number of shells on which the angular points are mapped. These uncertainties in computed free energies can have a significant impact on the outcome of calculations to determine reactivity property relationships; a 1 kcal mol ΔG in free energy barriers for regioselective and stereoselective reactions can be expected to mediate selectivity. Whilst only sampling a relatively small number of systems, Bootsma and Wheeler determined errors in relative free energies of more than 5 kcal mol; magnitudes that exceed those often described as discriminatory for theoretical property determination, as well as barriers in catalytic cycles. Their approach involved the sampling of a selection of grid points in DFT calculations of free energies for torsions (cf. electronic energies of 2‐butyne relative to 1,3‐ butadiene), diastereomers (human immunodeficiency virus integrase inhibitor), and transition structures (torsion of 4,4 ‐dimethyl‐1,1 ‐biphenyl), and selective reactions requiring the estimation of relative free energies.