  Recently developed pair coupled cluster doubles (pCCD) theory successfully
reproduces doubly occupied configuration interaction (DOCI) with mean field
cost. However, the projective nature of pCCD makes the method non-variational
and thus hard to improve systematically. As a variational alternative, we
explore the idea of coupled-cluster-like expansions based on amplitude
determinants and develop a specific theory similar to pCCD based on
determinants of pairwise doubles. The new ansatz admits a variational treatment
through Monte Carlo methods while remaining size-consistent and, crucially,
polynomial cost. In the dissociations of LiH, HF, H2O and N2, the method
performs very similarly to pCCD and DOCI, suggesting that coupled-cluster-like
ansatzes and variational evaluation may not be mutually exclusive.
