Density-functional study of small molecules within the Krieger-Li-Iafrate approximation

We report density-functional studies of several small molecules $({\mathrm{H}}_2,$ ${\mathrm{N}}_2,$ CO, ${\mathrm{H}}_2\mathrm{O},$ and ${\mathrm{CH}}_4)$ within the Krieger-Li-Iafrate (KLI) approximation to the exact Kohn-Sham local exchange potential, using a three-dimensional real-space finite-difference pseudopotential method. It is found that the exchange-only KLI approximation leads to markedly improved eigenvalue spectra compared to those obtained within the standard local-density approximation (LDA), the generalized gradient approximation (GGA), and the Hartree-Fock (HF) method. For structural properties, exchange-only KLI approximation results are close to the corresponding HF values. We find that the addition of LDA or GGA correlation energy functionals does not lead to systematic improvements.