  (Abridged) Organic molecules are important constituents of protoplanetary
disks. Their ro-vibrational lines observed in the near- and mid-infrared are
commonly detected toward T Tauri disks. These lines are the only way to probe
the chemistry in the inner few au where terrestrial planets form. To understand
this chemistry, accurate molecular abundances have to be determined. This is
complicated by excitation effects. Most analyses so far have made the
assumption of local thermal equilibrium (LTE).
  Starting from estimates for the collisional rate coefficients of HCN, non-LTE
slab models of the HCN emission were calculated to study the importance of
different excitation mechanisms. Using a new radiative transfer model, the HCN
emission from a full two-dimensional disk was then modeled to study the effect
of the non-LTE excitation, together with the line formation. We ran models
tailored to the T Tauri disk AS 205 (N) where HCN lines in both the 3 {\mu}m
and 14 {\mu}m bands have been observed by VLT-CRIRES and the Spitzer Space
Telescope.
  Reproducing the observed 3 {\mu}m / 14 {\mu}m flux ratios requires very high
densities and kinetic temperatures ($n > 10^{14}$ cm$^{-3}$ and $T > 750$ K),
if only collisional excitation is accounted for. Radiative pumping can,
however, excite the lines easily out to considerable radii $\sim$ 10 au.
Consequently, abundances derived from LTE and non-LTE models do not differ by
more than a factor of about 3. Models with both a strongly enhanced abundance
within $\sim$ 1 au (jump abundance) and constant abundance can reproduce the
current observations, but future observations with the MIRI instrument on JWST
and METIS on the E-ELT can easily distinguish between the scenarios and test
chemical models. Depending on the scenario, ALMA can detect rotational lines
within vibrationally excited levels.
