The induced hyperpolarizability Cartesian components have been ab initio computed for the H-2-Kr and H-2-Xe pairs, for three relative orientations and 17 intermolecular distances. Spherical symmetry-adapted components were deduced numerically from the ab initio data sets. The analytical model formulas for the symmetry-adapted vector and septor part of induced hyperpolarizability have been derived. The analytical model behavior of the hyperpolarizability symmetry-adapted components has been compared with the numerical ab initio data. A good comparison was observed in the long-range distance of induced hyperpolarizability. (C) 2013 Elsevier B. V. All rights reserved.