Infrared spectrum of H${}_5{}^{+}$ and D${}_5{}^{+}$: The simplest shared-proton model

We present a two-dimensional collinear, adiabatic model to describe the motion of a proton in between two hydrogen molecules which adjust their elongation to trace a minimum-energy path. Together with bound states, the predissociative, vibrationally excited states involved in the electric dipole transitions are characterized. The main qualitative features of the infrared spectra of H${}_5{}^{+}$ and its deuterated variant are discussed, and the effect of the temperature of the clusters is analyzed.

Figure 1

Potential energy $V(r,R)$ (solid lines, left-hand vertical axis), and its derivative with respect to $R$ (dashed lines, right-hand vertical axis), for three selected values of $R$ (bohr).

Figure 2

H${}_5{}^{+}$ adiabatic effective potentials $W_v\left(R\right)$ obtained by solving Eq. (6), and $E_{vn}$ energy-level diagram.

Figure 3

ir spectra of H${}_5{}^{+}$ (left-hand panel) and D${}_5{}^{+}$ (right-hand panel) obtained at $T=1$ and 300 K. They are compared to the experiments of Ref. [6]. The insets show the spectra at higher frequencies (H${}_5{}^{+}$) and around the experimental main peaks (D${}_5{}^{+}$).