ИСТИНА

In 2019, Andrea Bootsma and Steven Wheeler demonstrated that the absence of rotational invariance in popular density functional theory (DFT) integration grids leads to vast uncertainty in the calculated free energies for some reactions, which makes it difficult to evaluate their regio- and stereo- selectivity. In the absence of an external field, energy of a molecule should be independent of its orientation. However, since atomic-centered meshes of the Lebedev grids used in most quantum chemical packages are tied to the Cartesian axes and do not have spherical symmetry, the DFT energy is usually not invariant with respect to the molecular rotations. As Bootsma et al. noted, the grid dependence mainly comes from non-electronic energy (i.e., corrections to the electronic energies made to estimate Gibbs free energy). Here we describe our analysis of rotational invariance of various parts of the non-electronic energy, which has shown, that reasonable invariance (lower than in DFT electronic energies) can be obtained simply by scaling all vibrational frequencies below 300 cm-1 (including negative ones) to 300 cm-1. This happens because low frequencies have the largest sensitivity and, at the same time, have the greatest contribution into vibrational entropy and enthalpy. Interestingly, this scaling inherently accounts for quasi-harmonic effects, for which a similar scaling was previously proposed by Donald Truhlar. With the proposed scaling, accurate results−having rotational variance within 0.5 kcal/mol−can be obtained using grid 75,302 or larger, which corresponds to FineGrid in Gaussian package, which was default since Gaussian09. Thus, the proposed approach resolves the issue and allows using usual integral grids for quantum chemical calculations without compromising their accuracy.