  The near-exact iCIPT2 approach for strongly correlated systems of electrons,
which stems from the combination of iterative configuration interaction (iCI,
an exact solver of full CI) with configuration selection for static correlation
and second-order perturbation theory (PT2) for dynamic correlation, is extended
to the relativistic domain. In the spirit of spin separation, relativistic
effects are treated in two steps: scalar relativity is treated by the
infinite-order, spin-free part of the exact two-component (X2C) relativistic
Hamiltonian, whereas spin-orbit coupling (SOC) is treated by the first-order,
Douglas-Kroll-Hess-like SOC operator derived from the same X2C Hamiltonian. Two
possible combinations of iCIPT2 with SOC are considered, i.e., SOiCI and iCISO.
The former treats SOC and electron correlation on an equal footing, whereas the
latter treats SOC in the spirit of state interaction, by constructing and
diagonalizing an effective spin-orbit Hamiltonian matrix in a small number of
correlated scalar states. Both double group and time reversal symmetries are
incorporated to simplify the computation. Pilot applications reveal that SOiCI
is very accurate for the spin-orbit splitting (SOS) of heavy atoms, whereas the
computationally very cheap iCISO can safely be applied to the SOS of light
atoms and even of systems containing heavy atoms when SOC is largely quenched
by ligand fields.
