# GROUP THEORETICAL TREATMENT OF THE PLANAR INTERNAL ROTATION PROBLEM IN $(HF)_{2}$

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 Title: GROUP THEORETICAL TREATMENT OF THE PLANAR INTERNAL ROTATION PROBLEM IN $(HF)_{2}$ Creators: Hougen, Jon T.; Ohashi, N. Issue Date: 1984 Publisher: Ohio State University Abstract: The $(HF)_{2}$ dimer is believed to exhibit an internal rotation tunneling process between two planar but nonlinear equilibrium configurations, during which tunneling the roles of the hydrogen-bonded and the free hydrogen atoms are interchanged. This process can be represented schematically with labeled atoms as $H_{1} F_{a} H_{2} F_{b}\leftrightarrows F_{a} H_{1} F_{b} H_{2}$, and gives rise to a permutation-tunneling problem in $(HF)_{2}$ has been treated group theoretically in three ways: (i) by allowing tunneling only through a trans planar $C_{2h}$ intermediate, (ii) by allowing tunneling only through a cis planar $C_{2h}$ intermediate, and (iii) by considering the trans and cis tunneling processes to both occur, though not necessarily to the same extent. The several molecular symmetry groups used in these treatments are: (i) the point group $C_{2h}$ (ii) the point group $C_{2v}$, and (iii) a double group, which might be thought of as $G_{4}{^{\dag}} = C_{2h}{^{\dag}} = C_{2v}^{\dag}$. Nonplanar tunneling paths have not been considered, since the internal axis smethod (IAM) coordinate system used here cannot easily be adapted to nonplanar internal rotation motions in this molecule. Various details of energy level diagrams, symmetry species for operators, selection rules for spectroscopic transitions, and statistical weights will be presented for the $(HF)_{2}$ tunneling problem, as well as some speculation on the general question of the conditions under which it is preferable to use point groups, permutation-inversion groups, or double groups. Description: Author Institution: Molecular Spectroscopy Division, National Bureau of Standards; Department of Physics, Kanazawa University URI: http://hdl.handle.net/1811/16853 Other Identifiers: 1984-WF-4