Linear coupled-cluster method. I. Exchange-correlation effects in atoms

Abstract

The linear coupled-cluster method and a hierarchy of its approximations are employed to investigate the Slater Xα method and to study the exchange-correlation effects in the beryllium atom. An analysis of the various contributions to the exchange-correlation corrections to the total energy is made using the approximations to the coupled-cluster model. The total dominance of the valenceshell exchange-correlation corrections, the role of the single-particle excitation terms, and the relative importance of the ring- and ladder-diagram terms are gleaned from these calculations. The exchange parameter α, for the calculation of the reference state, i.e., the Xα orbitals, is chosen using the criterion that the total energy computed by the Xα method be equal to the Hartree-Fock total energy for the atom. For this reference state, the total energy of the beryllium atom, with the inclusion of the exchange-correlation correction, is found to be - 14.663 598 hartrees, a value very close to the experimental energy of - 14.669 hartress. The Xα method is seen to provide good single-particle reference states for many-body calculations.