Knowledge Bank

The molecular ion $H+5+$ can be thought of as an $H2$ molecule weakly bound to an $H3\mathrm{<mrow\; data-mjx-texclass="ORD">+</mrow>}$ ion. However, ab initio calculations have shown that this picture is inaccurate and that this ion is fairly non-rigid. It exhibits at least three tunneling motions; the most feasible one, involving intramolecular proton transfer, corresponds to the isomerization $H3\mathrm{<mrow\; data-mjx-texclass="ORD">+</mrow>}-H2\leftrightarrows H2\mathrm{<mrow\; data-mjx-texclass="ORD">-</mrow>}H3\mathrm{<mrow\; data-mjx-texclass="ORD">+</mrow>}$. This along with the fact that this ion has 60 equilibrium configurations leads to a complicated energy level diagram. Determining this energy pattern in order to understand the infrared spectrum of this ion is one of the motivations of the present investigation. In this work the formalism developed for the water dimer has been applied to the determination of the splitting pattern of the H5+ ion. Although applying this formalism is fairly straightforward, it is worthwhile mentioning that the large number of equilibrium configurations leads to a very large tunneling Hamiltonian matrix. It is also worhtwhile pointing out that we were led to use the permotation group $S5$ to label the tunneling sublevels. This group, because it contains operations equivalent to rotation about a 5-fold axis of symmetry, has only been used in a small number of cases, for instance, in the Berry pseudo rotation of phosphorus pentafluoride. The validity of the present approach has not yet been demonstrated. The theoretical formalism was originally designed for hindered Lunneling motions, and it may not apply to a light molecule like the H5+ ion, but certainly to the heavier species $D5\mathrm{<mrow\; data-mjx-texclass="ORD">+</mrow>}$.