Basis Set Superposition Error along the Free-Energy Surface of the Water Dimer

In this article we review the behavior of static plane wave basis set calculations in comparison to Gaussian basis set calculations. This was done in the framework of density functional theory for description of hydrogen bonds with the water dimer as an example. Furthermore we carried out molecular dynamics simulations enforcing the self-dissociation reaction of the water dimer to study the influence of the basis set onto the reaction. Not surprisingly, we find strongly varying results of the calculated forces for a chosen cutoff along the reaction coordinates. The basis set superposition errors of the dimer interaction energy are analyzed along the free-energy surface, i.e., along the trajectories. Based on the analysis along the trajectories a qualitative and quantitative estimate depending on the particular point of the free-energy surface can be provided. Namely, at the intermolecular O···H distance close to the equilibrium geometry the errors are smaller than at shorter O···H distances. However, the distribution at the equilibrium distance is more unsymmetrical than the distribution at short distances. It is wider, and the standard deviation is larger than at shorter distances where the basis set superposition error is larger.