Knowledge of near infrared intensities of rovibrational transitions of polyatomic molecules is essential for the modeling of various planetary atmospheres, brown dwarfs and for other astrophysical applications ^{1,2,3}. For example, to analyze exoplanets, atmospheric models have been developed, thus making the need to provide accurate spectroscopic data. Consequently, the spectral characterization of such planetary objects relies on the necessity of having adequate and reliable molecular data in extreme conditions (temperature, optical path length, pressure). On the other hand, in the modeling of astrophysical opacities, millions of lines are generally involved and the line-by-line extraction is clearly not feasible in laboratory measurements. It is thus suggested that this large amount of data could be interpreted only by reliable theoretical predictions. There exists essentially two theoretical approaches for the computation and prediction of spectra. The first one is based on empirically-fitted effective spectroscopic models. Another way for computing energies, line positions and intensities is based on global variational calculations using *ab initio *surfaces. They do not yet reach the spectroscopic accuracy *stricto sensu *but implicitly account for all intramolecular interactions including resonance couplings in a wide spectral range.

The final aim of this work is to provide reliable predictions which could be quantitatively accurate with respect to the precision of available observations and as complete as possible. All this thus requires extensive first-principles quantum mechanical calculations essentially based on three necessary ingredients which are (*i*) accurate intramolecular potential energy surface and dipole moment surface components well-defined in a large range of vibrational displacements and (*ii*) efficient computational methods combined with suitable choices of coordinates to account for molecular symmetry properties and to achieve a good numerical convergence. Because high-resolution *ab initio *spectra predictions for systems with N*>*4 atoms is a very challenging task, the major issue is to minimize the cost of computations and the loss of accuracy during calculations. To this end, a truncation-reduction technique for the Hamiltonian operator as well as an extraction-compression procedure for the basis set functions will be introduced and discussed in detail.

We will give a review on the recent progress in computational methods as well as on existing experimental and theoretical databases ^{4,5,6,7,8,9}. This presentation will be focused on highly symmetric molecules such as methane and phosphine, with the corresponding applications at low-T in relation with Titan’s atmosphere and at high-T with the production of theoretical line lists for astrophysical opacity calculations^{10}. The study of isotopic H→D and ^{12}C→^{13}C substitutions will be also addressed and carried out by means of symmetry and coordinate transformations^{11}. Finally we hope this work will help refining studies of currently available analyses which are not yet finalized. The modeling of non-LTE emissions accounting for contribution of many fundamental and hot bands could also be possible.

Support from PNP (French CNRS national planetology program) is acknowledged.