  Most nonrelativistic electron correlation methods can be adapted to account
for relativistic effects, as long as the relativistic molecular spinor
integrals are available, from either a four-, two-, or one-component mean-field
calculation. However, relativistic multireference correlation methods remain a
relatively unexplored area, with mixed evidence regarding the improvements
brought by perturbative treatments. We report, for the first time, the
implementation of state-averaged four-component multireference perturbation
theories to second and third order based on the driven similarity
renormalization group (DSRG). With our methods, named 4c-SA-DSRG-MRPT2 and 3,
we find that the dynamical correlation included on top of 4c-CASSCF references
can significantly improve the spin-orbit splittings in p-block elements and
potential energy surfaces when compared to 4c-CASSCF and 4c-CASPT2 results. We
further show that 4c-DSRG-MRPT2 and 3 are applicable to these systems over a
wide range of the flow parameter, with systematic improvement from second to
third order in terms of both improved error statistics and reduced sensitivity
with respect to the flow parameter.
