Linear coupled-cluster method. II. Analysis of local exchange-correlation potentials in beryllium and its isoelectronic series

Abstract

The Slater Xα method and its local-potential modifications are examined with reference to the many-electron exchange-correlation effects in the beryllium atom and its isoelectronic series. The linear coupled-cluster method and a hierarchy of approximations to it are employed for this purpose. The role of the exchange parameter α in providing an accurate description of the exchange-correlation effects is analyzed in the light of the electron-gas model. It is found that for Be atoms an α value of 0.768, that which causes the local potential to mimic the Hartree-Fock potential, is the best suited reference state for many-body calculations. The impact of the.α variation on the exchange-correlation corrections in the Be isoelectronic series is assessed. With increase in the nuclear charge Z, exchange-correlation corrections favor the use of α values closer to 2/3, the Gaspar-Kohn-Sham limit, in the Xα model. The instabilities in the cluster equations induced by ringdiagram terms are also noted. The futility of using gradient corrections to the Xα model to account for exchange-correlation effects is brought out in the calculations. It is found that a simple scaling of the electron-gas potential results in excellent single-particle reference states for many-body calculations.