Adiabatic integration formula for the correlation energy functional of theHartree-Fock density

An adiabatic integration formula for the quantum chemistry correlation ener gy functional of the Hartree-Fock density, E-c(QC)[n], is presented. The fu nctional E-c(QC)[n] is meant to be added to the completed Hartree-Fock ener gy to produce the exact ground-state energy of the system under considerati on. The initial slope of the integrand in this connection formula is identi fied as a second-order energy and an explicit expression for the initial sl ope of the integrand is presented. Our expression should be useful for arri ving at new improved approximations to E-c(QC)[n]. Previous numerical resul ts by Huang and Umrigar (1997) Phys Rev A 56:290, for two-electron densitie s are proved. and a generalization to more than two electrons is presented. Results obtained by means of the present density functional theory correla tion energy functionals, when used to approximate the initial slope in our adiabatic integration formula for E-c(QC)[n], are compared against exact nu mbers.