Collision-Induced hyper-Rayleigh light scattering (CIHRS) on super-molecular compounds composed of lighter noble gas atoms (He, Ne and Ar) and linear hydrogen molecules has been recently discussed within theoretical as well as numerical comparative spectral studies. The aim of the present report is to analyze updated results in this field of inter est generalized over the case of two heavier units of H2Kr and H2Xe. The roto-translational collisional profiles are obtained by means of quantum mechanical and semi-classical calculations. Tensorial symmetry adapted components of the first hyperpolarizability, <strong>Δβ</strong> – responsible for occurrence of the CIHRS processes – are applied on the grounds of previously calculated Cartesian quantities, found by means of the quantum chemistry (<i>ab initio</i>) methods. The spectral lines evaluated are partially treated as a benchmarking device to estimate the importance of the long-distance <i>Δβ(R)</i> dependence determined on the basis of the theoretical multipole-induced-multipole analytical model. Moreover, the magnitude of the CIHRS effect is discussed in regard to the experimental feasibility of CIHRS detection.