Rotationally adapted studies of ab initio-computed collision-induced hyperpolarizabilities: The H2-Ar pair

In this work we investigate the collision-induced (CI) dipole moment Delta mu(i)(R), the CI polarizability tensor Delta alpha(ik)(R), and the first dipole-hyperpolarizability tensor Delta beta(ijk)(R) of the H-2-Ar pair as a function of the intermolecular distance R, and the relative orientation of the intermolecular vector R and the H-2 molecule. For each type of spectroscopy the induction operator should be given in the symmetry adapted form. In our case the components of the CI dipole hyperpolarizability are expressed in such a way that their rotational behavior is unambiguously defined. The above description is based on the spherical rotationally adapted method presented here. Spherical rotationally adapted components Delta beta((s,K))(lambda L)(R) of the vector (K=1) and the septor (K=3) parts of the first dipole-hyperpolarizability tensor Delta beta(R) are computed and discussed. Results are applied to the case of H-2-Ar pair. Asymptotic long-range analytical formulas are proposed for the multipole-induced spherical rotationally adapted components Delta beta((s,K))(lambda L)(R) of Delta beta(R), respectively. Reasonable agreement is observed between the long-range analytical and ab initio numerical data.