  The simplest picture of excitons in materials with atomic-like localization
of electrons is that of Frenkel excitons, where electrons and holes stay close
together, which is associated with a large binding energy. Here, using the
example of the layered oxide V$_2$O$_5$ , we show how localized charge-transfer
excitations combine to form excitons that also have a huge binding energy but,
at the same time, a large electron-hole distance, and we explain this seemingly
contradictory finding. The anisotropy of the exciton delocalization is
determined by the local anisotropy of the structure, whereas the exciton
extends orthogonally to the chains formed by the crystal structure. Moreover,
we show that the bright exciton goes together with a dark exciton of even
larger binding energy and more pronounced anisotropy. These findings are
obtained by combining first principles many-body perturbation theory
calculations, ellipsometry experiments, and tight binding modelling, leading to
very good agreement and a consistent picture. Our explanation is general and
can be extended to other materials.

Materials Science;Computational Physics