  The efficient and reliable treatment of both spin-orbit coupling (SOC) and
electron correlation is essential for understanding f-element chemistry. We
analyze two approaches to the problem, the one-step approach where both effects
are treated simultaneously, and the two-step state interaction approach. We
report an implementation of the ab initio density matrix renormalization group
(DMRG) with a one-step treatment of the SOC effect which can be compared to
prior two-step treatments on an equal footing. Using a dysprosium octahedral
complex and bridged dimer as benchmark systems, we identify characteristics of
problems where the one-step approach is beneficial for obtaining the low-energy
spectrum.
