The Grimme D2 scheme provides an empirical dispersion correction to the DFT energy , and the D3 scheme improves this method by adding higher order corrections to the energy , and by taking the chemical environment of a particular ion (i.e., its coordination number) into account. The vdW-DFx methods, like vdW-DF2 explored here, explicitly account for a density dependent non-local correlation term. The mathematical form of these methods, and a deeper discussion of them, can be found in Section IV C.