  Surface fluorination of TiO$_2$ (F-TiO$_2$) has complicate photocatalytic
behavior in degradation of organic compounds. This work attempts to establish
an elegant scenario based on the band model to understand this behavior.
Density functional theory (DFT) calculations show that fluorination of the
rutile TiO$_2$(110) surface (F-TiO$_2$${110}$) results in the falling of band
edges. The falling of valence band edge (VBE) facilitates production of free
$\cdot$OH radicals, whereas the falling of conduction band edge (CBE) lowers
the reducing power of photo-electrons and inhibits reductive reactions mediated
by them. As a result, the photo-electrons are built up in the conduction band
which depresses photo-holes in the valence band to produce $\cdot$OH radicals
due to the requirement of electrical neutrality and thus leads to a low
degradation rate of organic compounds. Even though, our model suggests a route
to improve the degradation efficiency, by introducing a scavenger of
photo-electrons to promote formation of $\cdot$OH radicals.
