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Influence of broken-pair excitations on the exact pair wavefunction

Doubly occupied configuration interaction (DOCI), the exact diagonalization of the Hamiltonian in the paired (seniority zero) sector of the Hilbert space, is a combinatorial cost wave function that can be very efficiently approximated by pair coupled cluster doubles (pCCD) at mean-field computational cost. As such, it is a very interesting candidate as a starting point for building the full configuration interaction (FCI) ground state eigenfunction belonging to all (not just paired) seniority sectors. The true seniority zero sector of FCI (referred to here as FCI${}_0$) includes the effect of coupling between all seniority sectors rather than just seniority zero, and is, in principle, different from DOCI. We here study the accuracy with which DOCI approximates FCI${}_0$. Using a set of small Hubbard lattices, where FCI is possible, we show that DOCI $\sim$ FCI${}_0$ under weak correlation. However, in the strong correlation regime, the nature of the FCI${}_0$ wavefunction can change significantly, rendering DOCI and pCCD a less than ideal starting point for approximating FCI.