A Case Study of State-Specific and State-Averaged Brueckner Equation-of-Motion Coupled-Cluster Theory: The Ionic-Covalent Avoided Crossing in Lithium Fluoride

State-specific Brueckner equation-of-motion coupled-cluster theory (SS-B-EOMCC) is summarized, which can be considered an internally contracted version of a state-selective multireference coupled-cluster theory, which, however, is not entirely size-consistent. The method is applicable to general multireference problems, adheres to the space and spin symmetries of the molecular system, is straightforwardly extended to a state-averaged version, and has an associated perturbative variant which yields results close to the full coupled-cluster treatment. A key strength is that Brueckner orbitals are used, such that orbitals are optimized in the presence of dynamic correlation. A number of variations on the theme of SS-EOMCC is applied to study the ionic-covalent avoided crossing in LiF in a 6-311++G(3df,3pd) basis set. While reasonable results are obtained at the state-averaged level, the iterative solution process does not consistently converge for SS-EOMCC, due to the non-Hermiticity of the transformed Hamiltonian which may yield complex eigenvalues upon truncated diagonalization. This leads to an irrevocable breakdown of the state-specific EOMCC approach. We indicate some future directions that can resolve some of the problems with the SS-EOMCC methodology, as revealed by the demanding test case of the LiF potential energy curves.