The main effort in this study is focused on devising a numerical model procedure capable of providing reliable values of collisionally induced microscopic properties of importance in processes of light radiation interactions with molecular media. Special attention is devoted to the anisotropic polarizability of the weakly bound H2-H compounds, although broader applicability of the routines proposed is anticipated as well. To this end, Cartesian components of the collision-induced anisotropic polarizability, Δαij [-], are obtained for the L- (linear, 0°), S- (45°), and T-shape (90°) configurations of the supermolecular systems. The quantum chemistry ab initio numerical method is applied to determine the values of the quantities within the range of the separations between H2 and H moieties reaching 3 < R < 20 bohrs. This approach is then combined with long-range approximate computing routines in order to formulate an overall uniform modeling algorithm including the influence of the exchange, dispersion, and induction interactions on the collisional induced (CI) effects. The validity and precision of the tool is thoroughly assessed. The polarizabilities are then transformed so as to be expressed in terms of the so-called symmetry adapted (SA) components of the spherical tensor representation, ΔαλL (2). Applicability of the modeling scheme is evidenced with regard to the effective evaluation of symmetry adapted parameters for an extended range of intramolecular angularities, separations, and indices. The importance of the procedure for foreseeable CI spectral profile analyses is discussed.