Exact exchange-correlation potentials of singlet two-electron systems

We suggest a non-iterative analytic method for constructing the exchange-correlation potential, v_XC(r), of any singlet ground-state two-electron system. The method is based on a convenient formula for v_XC(r) in terms of quantities determined only by the system's electronic wave function, exact or approximate, and is essentially different from the Kohn-Sham inversion technique. When applied to Gaussian-basis-set wave functions, the method yields finite-basis-set approximations to the corresponding basis-set-limit v_XC(r), whereas the Kohn-Sham inversion produces physically inappropriate (oscillatory and divergent) potentials. The effectiveness of the procedure is demonstrated by computing accurate exchange-correlation potentials of several two-electron systems (helium isoelectronic series, H₂, H₃⁺) using common ab initio methods and Gaussian basis sets.