Popular Integration Grids Can Result in Large Errors in DFT-Computed Free Energies

Density functional theory (DFT) has emerged as a powerful tool for analyzing (bio-)organic and organometallic systems and proved remarkably accurate in computing the small free energy differences that underpin many chemical phenomena (e.g. regio- and stereoselective reactions). We show that the lack of rotational invariance of popular DFT integration grids reveals large uncertainties in computed free energies for some isomerizations, torsional barriers, and regio- and stereoselective reactions. The result is that predictions based on DFT-computed free energies for systems with very low-frequency vibrational modes can change qualitatively depending on molecular orientation. For example, for a metal-free propargylation of benzaldehyde, predicted enantioselectivities based on B97-D/def2-TZVP free energies using a popular pruned (75,302) integration grid can vary from 62:38 to 99:1 by simply rotating the transition state structures. Relative free energies for the regiocontrolling transition state structures for an Ir-catalyzed C–H functionalization reaction computed using M06/6-31G(d,p)/LANL2DZ and the same grid can vary by more than 5 kcal/mol, resulting in predicted regioselectivities that range anywhere from 14:86 to >99:1. Errors of these magnitudes occur for different functionals and basis sets, are potentially widespread among modern applications of DFT, and can be reduced by using much denser integration grids than commonly employed.