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 scali ng of the electron-electron interaction is reviewed. The effective pot ential along the coupling constant path which connects a noninteractin g and a fully interacting system with the same electron density is con sidered. The effective potential for an arbitrary coupling constant is here expressed in terms of the exchange-correlation potential at a co upling 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 Tayl or expansion of the effective potential along the coupling constant pa th, a density functional perturbation theory is introduced which leads to a formally exact Kohn-Sham KS formalism. To first order, this form alism gives identities for the exchange potential in terms of Ks orbit als and orbital eigenvalues. Moreover, higher-order terms give identit ies for the correlation potential as well as for the exchange potentia l. These identities are pointwise as well as integrated. Hence, variou s new requirements for the exchange and correlation functionals are de rived. New insight into the optimized effective potential method is ga ined by discussing it in the light of the results obtained here. (C) 1 995 John Wiley & Sons, Inc.