  Scalar products and density matrix elements of closed-shell pair geminal
wavefunctions are evaluated directly in terms of the pair amplitudes, resulting
in an analogue of Wick's theorem for fermions or bosons. This expression is in
general intractable, but it is shown how it becomes feasible in three distinct
ways for Richardson-Gaudin (RG) states, the antisymmetrized geminal power, and
the antisymmetrized product of strongly-orthogonal geminals. Dissociation
curves for hydrogen chains are computed with off-shell RG states and the
antisymmetrized product of interacting geminals. Both are near exact suggesting
that the incorrect results observed with ground state RG states are fixable
using a different RG state.
