A method for calculating the Kohn-Sham exchange-correlation potential $v_{\mathrm{XC}}(\mathbf{r})$ from a given electronic wave function is devised and implemented. It requires on input one- and two-electron reduced density matrices and involves construction of the generalized Fock matrix. The method is free from numerical limitations and basis-set artifacts of conventional schemes for constructing $v_{\mathrm{XC}}(\mathbf{r})$ in which the potential is recovered from a given electron density, and is simpler than various many-body techniques. The chief significance of this development is that it allows one to directly probe the functional derivative of the true exchange-correlation energy functional and to rigorously test and improve various density-functional approximations.

• Received 9 April 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.083001