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

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 ring-diagram 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