  A quasi-relativistic two-component approach for an efficient calculation of
$\mathcal{P,T}$-odd interactions caused by a permanent electric dipole moment
of the electron (eEDM) is presented. The approach uses a (two-component)
complex generalized Hartree-Fock (cGHF) and a complex generalized Kohn-Sham
(cGKS) scheme within the zeroth order regular approximation (ZORA). In
applications to select heavy-elemental polar diatomic molecular radicals, which
are promising candidates for an eEDM experiment, the method is compared to
relativistic four-component electron-correlation calculations and confirms
values for the effective electrical field acting on the unpaired electron for
RaF, BaF, YbF and HgF. The calculations show that purely relativistic effects,
involving only the lower component of the Dirac bi-spinor, are well described
by treating only the upper component explicitly.
