  Doubly occupied configuration interaction (DOCI) with optimized orbitals
often accurately describes strong correlations while working in a Hilbert space
much smaller than that needed for full configuration interaction. However, the
scaling of such calculations remains combinatorial with system size. Pair
coupled cluster doubles (pCCD) is very successful in reproducing DOCI
energetically, but can do so with low polynomial scaling ($N^3$, disregarding
the two-electron integral transformation from atomic to molecular orbitals). We
show here several examples illustrating the success of pCCD in reproducing both
the DOCI energy and wave function, and show how this success frequently comes
about. What DOCI and pCCD lack are an effective treatment of dynamic
correlations, which we here add by including higher-seniority cluster
amplitudes which are excluded from pCCD. This frozen pair coupled cluster
approach is comparable in cost to traditional closed-shell coupled cluster
methods with results that are competitive for weakly correlated systems and
often superior for the description of strongly correlated systems.
