  We introduce a new modelling framework called FLiTs to simulate infrared line
emission spectra from protoplanetary discs. This paper focuses on the mid-IR
spectral region between 9.7 um to 40 um for T Tauri stars. The generated
spectra contain several tens of thousands of molecular emission lines of H2O,
OH, CO, CO2, HCN, C2H2, H2 and a few other molecules, as well as the forbidden
atomic emission lines of SI, SII, SIII, SiII, FeII, NeII, NeIII, ArII and
ArIII. In contrast to previously published works, we do not treat the
abundances of the molecules nor the temperature in the disc as free parameters,
but use the complex results of detailed 2D ProDiMo disc models concerning gas
and dust temperature structure, and molecular concentrations. FLiTs computes
the line emission spectra by ray tracing in an efficient, fast and reliable
way. The results are broadly consistent with R=600 Spitzer/IRS observational
data of T Tauri stars concerning line strengths, colour, and line ratios. In
order to achieve that agreement, however, we need to assume either a high
gas/dust mass ratio of order 1000, or the presence of illuminated disc walls at
distances of a few au. The molecules in these walls cannot be photo-dissociated
easily by UV because of the large densities in the walls which favour their
re-formation. Most observable molecular emission lines are found to be
optically thick, rendering a standard analysis with column densities difficult.
We find that the difference between gas and dust temperatures in the disc
surface is important for the line formation. We briefly discuss the effects of
C/O ratio and choice of chemical rate network on these results. Our analysis
offers new ways to infer the chemical and temperature structure of T Tauri
discs from future JWST/MIRI observations, and to possibly detect secondary
illuminated disc walls based on their specific mid-IR molecular signature.
