With this Erratum, we provide corrections to certain mistakes appearing in the original publication.1 Namely, in Eq. (12), the -dependent Hamiltonian for the Hartree-Fock adiabatic connection lacks the external potential term. The correct equation is [Formula Presented]. The typos listed in the following all appear in the appendix. The parameter c in Eq. (A6) is wrong by a factor of two; the correct expression reads as follows: [Formula Presented]. In Eq. (A13), we have incorrectly used the parameter “c”; “c” has to be replaced by as defined in Eq. (A12). Also, the expression lacks the exchange energy. Thus, the proper expression reads as follows: [Formula Presented]. Finally, in Eqs. (A14) and (A15), the fractional powers appearing in the first terms are powers of the density and not of the position vector. Hence, [Formula Presented]. These corrections do not alter any of the results or conclusions shown in the paper.