Closed-form expression relating the second-order component of the density functional theory correlation energy to its functional derivative - Ivanov, Stanislav; Lopez-Boada, R.; Görling, Andreas; Levy, Mel (Journal of Chemical Physics, 1998)
For helping to improve approximations to the density-functional exchange-correlation energy, E[n], and its functional derivative, the difference between the second-order component of the correlation energy, E[n], and the integral ∫dr v([n];r)n(r), involving its functional derivative, v([n];r), is given in terms of only the occupied Kohn-Sham orbitals and the exchange potential. The quantity 2E[n] is especially significant because it is the initial slope in the adiabatic connection formula for E[n]. The analytic expression for 2E[n]-∫dr v([n];r)n(r) is obtained for any spherically symmetric two-electron test density. Numerical examples are presented. © 1998 American Institute of Physics.