Revealing the field-counteracting term in the exact Kohn-Sham correlation potential

Abstract

We construct the (within numerical limits) exact correlation potential of Kohn-Sham density functional theory for a one-dimensional model chain of four hydrogen atoms from a highly accurate, correlated wave function. Specifically we investigate how the correlation potential changes when an external linear electrical field is applied. This model situation is of great interest to Kohn-Sham theory because it is well known that the exact Kohn-Sham exchange potential shows ultranonlocality in this situation, with the exchange potential responding opposite to the applied external potential. Here we show that the correlation potential shows a field-counteracting term as well. However, we also find that self-consistent exact exchange captures a major part of this term, contrary to the exact exchange potential that results from the exact orbitals. The results obtained here are relevant for providing guidance in the construction of improved approximate exchange correlation functionals.