A correlation of exchange energy-exchange potential at the nucleus in atoms

We report the results of numerical tests on atom He-Lu, which suggest that the exchange energy calculated within the spin-polarized exchange-only optimized potential model for atoms can be expressed as a power-law in terms of the local effective exchange potential evaluated at the nucleus. The total effective exchange potential increases linearly with the atomic number. These results are useful in improving the energy density functionals at the small r region where most of the popularly used energy functionals provide rather poor functional derivatives. The significance of the present results in obtaining detailed information on the correlation-kinetic energy of the Kohn-Sham model is discussed.(C) 2002 American Institute of Physics.