  We investigate the effects of spin-orbit coupling on the optical response of
materials. In particular, we study the effects of the commutator between the
spin-orbit coupling part of the potential and the position operator on the
optical matrix elements. Using a formalism that separates a fullyrelativistic
Kleinman-Bylander pseudopotential into the scalar-relativistic and
spin-orbit-coupling parts, we calculate the contribution of the commutator
arising from spin-orbit coupling to the squared optical matrix elements of
isolated atoms, monolayer transition metal dichalcogenides, and topological
insulators. In the case of isolated atoms from H ($Z = 1$) to Bi ($Z = 83$),
the contribution of spin-orbit coupling to the squared matrix elements can be
as large as 14 %. On the other hand, in the cases of monolayer transition metal
dichalcogenides and topological insulators, we find that this contribution is
less than 1 % and that it is sufficient to calculate the optical matrix
elements and subsequent physical quantities without considering the commutator
arising from spin-orbit coupling.
