Constructing a map from the electron density to the exchange–correlation potential
Near-exact exchange–correlation potentials calculated with the procedure of Zhao, Morrison and Parr (ZMP) for 35 systems are combined in a histogram average to construct an exchange–correlation potential. The histogramming scheme makes use of a self-adjusting Cartesian grid (SACG), whereby the bin size is adjusted based on the number of data points in a region. The two-dimensional SACG approach is first tested against an analytic exchange–correlation potential of two-variables and shown to reproduce it to the required accuracy. The SACG approach is then applied to the ZMP data, and Kohn–Sham eigenvalues and densities are compared. Further extensions are discussed.