  Even when starting with a very poor initial guess, the iterative
configuration interaction (iCI) approach can converge from above to full CI
very quickly by constructing and diagonalizing a small Hamiltonian matrix at
each macro/micro-iteration. However, iCI scales exponentially with respect to
the numbers of electrons and orbitals. The problem can be mitigated by
observing that a vast number of configurations have little weights in the wave
function and do not contribute to the correlation energy. The real questions
are then (a) how to identify important configurations in the early stage of the
calculation and (b) how to account for the residual contributions of those
unimportant configurations. It is generally true that if a high-quality yet
compact variational space can be determined for describing the static
correlation, a low-order treatment of the residual dynamic correlation would be
sufficient. While this is common to all selected CI schemes, the `iCI with
selection' scheme presented here has the following distinctive features: (1)
Full spin symmetry is maintained. (2) Although the selection is performed on
individual CSFs, it is orbital configurations (oCFG) that are used as the
organizing units. (3) Given a coefficient pruning-threshold, the selection of
important oCFGs/CSFs is performed iteratively until convergence. (4) At each
iteration for the growth of wave function, the first-order interacting space is
decomposed into disjoint subspaces to reduce memory requirement and facilitate
parallelization. (5) Upper bounds for the interactions between oCFG pairs are
used to screen each first-order interacting subspace before the first-order
coefficients of individual CSFs are evaluated. (6) Upon termination of the
selection, dynamic correlation is estimated by using the ENPT2 theory. The
efficacy of the iCIPT2 scheme is demonstrated numerically by taking several
examples.
