Symmetry-adapted coupled-pair approach to the many-electron correlation problem. II. Application to the Be atom

The analytic forms of both the LS-adapted coupled-pair many-electron theory (CPMET) and its linear version (LCPMET) are applied to the ground state of the Be atom in order to examine the reliability of the analytic coupled-pair approaches. Using CPMET within a ($7s,7p,4d,3f,3g$) set of orbitals, we obtain 97% of the experimental correlation energy. Special attention is paid to the convergence properties for both radial and angular correlation effects. By means of the partial-wave analysis of the various pair energies it is shown that the difference between LCPMET and CPMET is primarily due to the quasidegeneracy of the Be ground state. The role of different types of coupling terms for pair clusters is also examined yielding a basis for an understanding of various approximate coupled-pair theories. The results are compared with other calculations and the role of monoexcited and triexcited clusters is briefly discussed.