  Selected configuration interaction (sCI) methods including second-order
perturbative corrections provide near full CI (FCI) quality energies with only
a small fraction of the determinants of the FCI space. Here, we introduce both
a state-specific and a multi-state sCI method based on the CIPSI (Configuration
Interaction using a Perturbative Selection made Iteratively) algorithm. The
present method revises the reference (internal) space under the effect of its
interaction with the outer space via the construction of an effective
Hamiltonian, following the shifted-Bk philosophy of Davidson and coworkers. In
particular, the multi-state algorithm removes the storage bottleneck of the
effective Hamiltonian via a low-rank factorization of the dressing matrix.
