Exact Expressions for Exchange-Correlation Potentials

The Baerends and Staroverov groups have devised various exact expressions for the exchange-correlation potential in terms of wave-function and Kohn--Sham ingredients. We show that all these expressions can be obtained as special cases of one general approach. One particular expression derived by us involves at most the two-electron reduced density matrix and is ideally suited for practical calculations of exchange-correlation potentials from many-electron wave functions, as demonstrated by numerical examples. Interesting identities emerging from our derivation are also presented and discussed.