DFT ionization formulas and a DFT perturbation theory for exchange and correlation, through adiabatic connection

The link between a uniform scaling of the electron density and a scaling of the electron–electron interaction is reviewed. The effective potential along the coupling constant path which connects a noninteracting and a fully interacting system with the same electron density is considered. The effective potential for an arbitrary coupling constant is here expressed in terms of the exchange–correlation potential at a coupling constant of unity. The effective potential is then investigated for ionization processes. Use of the fact that the ionization energy is determined by the exponential decay of the electron density allows us to derive new formulas for the ionization energy. Based on the Taylor expansion of the effective potential along the coupling constant path, a density functional perturbation theory is introduced which leads to a formally exact Kohn–Sham KS formalism. To first order, this formalism gives identities for the exchange potential in terms of KS orbitals and orbital eigenvalues. Moreover, higher-order terms give identities for the correlation potential as well as for the exchange potential. These identities are pointwise as well as integrated. Hence, various new requirements for the exchange and correlation functionals are derived. New insight into the optimized effective potential method is gained by discussing it in the light of the results obtained here. © 1995 John Wiley & Sons, Inc.

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