Knowledge Bank

We calculate absorption intensities of rotational lines in the $O\to 3\nu 3$ vibrational transition in $SF6$, from wavefunctions obtained by diagonalizing the Hamiltonian in the $(J,\ell 3,R)$ basis, and from a model of the dipole moment containing two inedpendent constants. Although the ""polar"" representation for the dipole moment. [ \mu_{z} = u_{1} f_{1} (\ell_{3} = 1) + \mu_{3} f_{3} (\ell_{3} = 3) ] is most convenient for computation of intensities, we find that the Cartsian $representation,^{2} $ [ \mu_{z} = \mu_{a} q_{3z}{^{3}} + \mu_{b} \cdot 2^{-1/2}(q_{3z}{^{2}} q_{3y}{^{2}} q_{3z}) ] provides a better intuitive concept because the vibrational wavefunctions do not mix much in the Cartesian basis and the spectrum is cansistent with $|\mu a|>>|\mu b|$. A ratio between the two independent coefficients (in either representation) is determined from the observed spectrum.