A CHALLENGE FOR DENSITY FUNCTIONALS - SELF-INTERACTION ERROR INCREASES FOR SYSTEMS WITH A NONINTEGER NUMBER OF ELECTRONS

The difficulty of widely used density functionals in describing the di ssociation behavior of some homonuclear and heteronuclear diatomic rad icals is analyzed. It is shown that the self-interaction error of thes e functionals accounts for the problem-it is much larger for a system with a noninteger number of electrons than a system with an integer nu mber of electrons. We find the condition for the erroneous dissociatio n behavior described by approximate density functionals: when the ioni zation energy of one dissociation partner differs from the electron af finity of the other partner by a small amount, the self-interaction er ror will lead to wrong dissociation limit. Systems with a noninteger n umber of electrons and hence the large amount of self-interaction erro r in approximate density functionals arise also in the transition stat es of some chemical reactions and in some charge-transfer complexes. I n the course of analysis, we derive a scaling relation necessary for a n exchange-correlation functional to be self-interaction free. (C) 199 8 American Institute of Physics.