Exact exchange-correlation potentials of singlet two-electron systems

 

Ilya G. Ryabinkin¹, Egor Ospadov², and Viktor N. Staroverov^2,a)

 

 

ABSTRACT

 

We suggest a non-iterative analytic method for constructing the exchange-correlation potential, 𝑣XC(𝐫)

, of any singlet ground-state two-electron system. The method is based on a convenient formula for 𝑣XC(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 𝑣XC(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, H+3) using common ab initio methods and Gaussian basis sets.

 

https://sci-hub.se/https://aip.scitation.org/doi/10.1063/1.5003825