  We propose a simple first-principles method to describe propagation of
tightly bound excitons. By viewing the exciton as a composite object (an
effective Frenkel exciton in Wannier orbitals), we define an exciton kinetic
kernel to encapsulate the exciton propagation and decay for all binding energy.
Applied to prototypical LiF, our approach produces three exciton bands, which
we verified quantitatively via inelastic x-ray scattering. The proposed
real-space picture is computationally inexpensive and thus enables study of the
full exciton dynamics, even in the presence of surfaces and impurity
scattering. It also provides intuitive understanding to facilitate practical
exciton engineering in semiconductors, strongly correlated oxides, and their
nanostructures.
