  An accurate description of electron correlation is one of the most
challenging problems in quantum chemistry. The exact electron correlation can
be obtained by means of full configuration interaction (FCI). A simple strategy
for approximating FCI at a reduced computational cost is selected CI (SCI),
which diagonalizes the Hamiltonian within only the chosen configuration space.
Recovery of the contributions of the remaining configurations is possible with
second-order perturbation theory. Here, we apply adaptive sampling
configuration interaction (ASCI) combined with molecular orbital optimizations
(ASCI-SCF) corrected with second-order perturbation theory (ASCI-SCF-PT2) for
geometry optimization by implementing the analytical nuclear gradient algorithm
for ASCI-PT2 with the Z-vector (Lagrangian) formalism. We demonstrate that for
phenalenyl radicals and anthracene, optimized geometries and the number of
unpaired electrons can be obtained at nearly the CASSCF accuracy by
incorporating PT2 corrections and extrapolating them. We demonstrate the
current algorithm's utility for optimizing the equilibrium geometries and
electronic structures of 6-ring-fused polycyclic aromatic hydrocarbons and
4-periacene.
