  Richardson-Gaudin (RG) states are employed as a variational wavefunction
ansatz for strongly correlated isomers of H$_4$ and H$_{10}$. In each case a
single RG state describes the seniority-zero sector quite well. Simple natural
orbital functionals offer a cheap and reasonable approximation of the
outstanding weak correlation in the seniority-zero sector, while systematic
improvement is achieved by performing a configuration interaction (CI) in terms
of RG states. Other pair theories (e.g. generalized valence bond and
pair-coupled-cluster doubles) can provide a good description of many of the
geometries considered, but, at short distances, the wavefunctions for the 2D
and 3D structures of H$_{10}$ take the form of an RG state that cannot be
described by these other theories.

Chemical Physics;Strongly Correlated Electrons