The ab initio induced first hyperpolarizability of several pairs of dissimilar atomic rare gases: Ne-He, Ar-He, Xe-Kr as well as the angular independent part of the induced first hyperpolarizability of H-2-He and H-2-Ne have been compared against the predictions of the model long-range induced first hyperpolarizability. The induced hyperpolarizability mechanism is of the R-ab(-4) order and can be described by way of the dipole polarizability alpha of one monomer interacting with the dipole(2)-quadrupole hyperpolarizability B of another microsystem and vice versa. We have designated this mechanism as the alpha B model. At the long-range very good agreement is observed between the ab initio data and the model alpha B induced hyperpolarizability. (C) 2010 Elsevier B.V. All rights reserved.