Performance of Becke’s half-and-half functional for non-covalent interactions: energetics, geometries and electron densities

Abstract

The performance of Becke’s half-and-half functional, BHandH, for description of non-covalent interactions is reported, using high-level ab initio results as benchmarks. Binding energies are found to be well reproduced for complexes that are bound predominantly by dispersion, whereas significant and consistent overestimation is observed for hydrogen bonded complexes. Overall, the mean average error is around 2 kcal mol⁻¹, for all basis sets considered. The effect of changing the proportion of exact and Slater exchange in the functional is shown to alter the balance of description of hydrogen bonded and dispersion bound complexes, but does not improve the overall performance. However, a simple multiplicative scaling of binding energies is possible, and reduces the mean average error to less than 1 kcal mol⁻¹. The performance of the BHandH functional for geometry optimization was also studied, and in almost all cases the difference from ab initio geometries is small, with root mean square deviations of between 0.05 and 0.20 Å. Harmonic frequency calculation allow us to check whether optimized geometries are true minima at this level, and to estimate the zero point vibrational energy change on binding.