Rotationally adapted studies ofab initio–computed collision-induced hyperpolarizabilities: TheH2-Arpair

Abstract

In this work we investigate the collision-induced (CI) dipole moment $\ensuremath{\Delta}{\ensuremath{\mu}}_{i}(R)$, the CI polarizability tensor $\ensuremath{\Delta}{\ensuremath{\alpha}}_{ik}(R)$, and the first dipole-hyperpolarizability tensor $\ensuremath{\Delta}{\ensuremath{\beta}}_{ijk}(R)$ of the ${\text{H}}_{2}\text{-Ar}$ pair as a function of the intermolecular distance $R$, and the relative orientation of the intermolecular vector $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$ and the ${\text{H}}_{2}$ 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 $\ensuremath{\Delta}{\ensuremath{\beta}}_{\ensuremath{\lambda}L}^{(s,K)}(R)$ of the vector $(K=1)$ and the septor $(K=3)$ parts of the first dipole-hyperpolarizability tensor $\ensuremath{\Delta}\mathbit{\ensuremath{\beta}}(R)$ are computed and discussed. Results are applied to the case of ${\text{H}}_{2}\text{-Ar}$ pair. Asymptotic long-range analytical formulas are proposed for the multipole-induced spherical rotationally adapted components $\ensuremath{\Delta}{\ensuremath{\beta}}_{\ensuremath{\lambda}L}^{(s,K)}(R)$ of $\ensuremath{\Delta}\mathbit{\ensuremath{\beta}}(R)$, respectively. Reasonable agreement is observed between the long-range analytical and ab initio numerical data.