  Hybrid exchange-correlation functionals provide superior electronic structure
and optical properties of semiconductors or insulators as compared to semilocal
exchange-correlation potentials due to admixing a portion of the non-local
exact exchange potential from a Hartree-Fock theory. Since the non-local
potential does not commute with the position operator, the momentum matrix
elements do not fully capture the oscillator strength, while the length-gauge
velocity matrix elements do. So far, length-gauge velocity matrix elements were
not accessible in the all-electron full-potential WIEN2k package. We
demonstrate the feasibility of computing length-gauge matrix elements in WIEN2k
for a hybrid exchange-correlation functional based on a finite difference
approach. To illustrate the implementation we determined matrix elements for
optical transitions between the conduction and valence bands in GaAs, GaN,
(CH$_3$NH$_3$)PbI$_3$ and a monolayer MoS$_2$. The non-locality of the
Hartree-Fock exact exchange potential leads to a strong enhancement of the
oscillator strength as noticed recently in calculations employing
pseudopotentials [Laurien and Rubel: arXiv:2111.14772 (2021)]. We obtained an
analytical expression for the enhancement factor in terms of the difference in
eigenvalues not captured by the kinetic energy. It is expected that these
results can also be extended to other non-local potentials, e.g., a many-body
$GW$ approximation.
