I'll present our work on H2-He, in which we employ highly accurate cavity-enhanced molecular spectroscopy to study system collisions and interactions . Hydrogen molecule in its ground electronic state perturbed by the helium atom constitutes the simplest system of perturbed molecule (it contains only four electrons). This gives a possibility to make a link between the experiment and the theory from first principles.
In contrast to most of the previous studies, we do not fit spectra with phenomenological line shapes, but directly  superimpose theoretical profiles (originating from our ab initio calculations) on the experimental spectra without fitting any of the line-shape parameters. Within this approach not only the shapes of experimental lines are reliably reproduced, but also the underlying physics of molecular collisions can be traced. Besides the analysis of the basic line-shape effects (such as relaxation or phase changes of the internal states of the molecule), we also analyze the more sophisticated ones such as speed-dependent effects or velocity-changing collisions (complex Dicke parameter) [3, 4], which are particularly pronounced for the H2-He system [1, 5-7]. We achieved good agreement at the below 1% level (relative RMSE) between experimental data and ab initio calculations.
Additionally I'll show, that measured spectral line shapes can be interpolated by recently-introduced as a standard beyond-Voigt line shape model in HITRAN database , i.e. Hartmann-Tran Profile (HTP) , within similar accuracy when it is implemented with beta-correction [5, 10].
 F. Thibault, K. Patkowski et al., J. Quant. Spectrosc. Radiat. T 202, 308 (2017)
 A. D. May, W.-K. Liu et al., Can. J. Phys. 91, 879 (2013)
 S. Hess, Physica 61, 80 (1972)
 R. Ciuryło, D. A. Shapiro et al., Phys. Rev. A 65, 012502 (2002)
 P. Wcisło, H. Tran et al., J. Chem. Phys. 141, 074301 (2014)
 F. Thibault, P. Wcisło et al., Eur. Phys. J. D 70, 236 (2016)
 R. Z. Martínez, D. Bermejo et al., J. Raman Spectrosc. 49(8), 1339 (2018)
 I. E. Gordon, L. S. Rothman et al., J. Quant. Spectrosc. Radiat. T 203, 3 (2017)
 N. Ngo, D. Lisak et al., J. Quant. Spectrosc. Radiat. T 129, 89 (2013)
 M. Konefał, M. Słowiński et al. (submitted)