The importance of the asymptotic exchange-correlation potential in density functional theory

The importance to density functional theory (DFT) of the integer discontinuity in the exchange-correlation potential is reiterated and further examined. It follows that if generalized gradient approximation (GGA) functional are used, then the asymptotic value of the exchange-correlation potential must be a positive system-dependent constant. Our previously introduced asymptotic correction (AC), which forces the correct behaviour of the potential in the asymptotic region, is further discussed. Three examples are given that demonstrate the importance of the analysis; (i) HOMO eigenvalues lie well above the negative of the ionization energy when GGA functionals are used—this is not detrimental to GGA DFT; (ii) an independent calculation of the GGA asymptotic potentials for some molecules is presented, based on the determination of parametrized GGA functionals; (iii) Rydberg states of He+ and H+ 2 are studied, demonstrating that essentially exact Rydberg potential energy curves can be determined if the AC is used, even though the valence curves may be incorrect.