Structure of the Alkali Hydroxides. IV. Interpretation of Vibration–Rotation Interactions in CsOH and RbOH and Refinement of Structures

Abstract

A new formulation of the vibration–rotation interactions in linear triatomic molecules is developed for the purpose of explaining the anomalies found in the microwave spectra of CsOH and RbOH. This formulation, which explicitly takes into account the curvilinear nature of the motions, leads to a some‐what different partitioning of the interaction constant ${\alpha }_2$ into harmonic and anharmonic contributions. The harmonic contribution resulting from direct averaging of the moment of inertia over the bending mode is found to dominate the ${\alpha }_2$ constant in most linear molecules, in contrast to the traditional treatment, which leads to a large anharmonic contribution. In the alkali hydroxides the harmonic and anharmonic parts are comparable in magnitude but of opposite sign; the resulting cancellation is responsible for the unusual vibrational dependence of $B_{\upsilon }$ in these molecules. The deuterium isotope shifts of $B_{\upsilon }$ are in excellent agreement with the predictions of this treatment. All of the microwave and infrared data on CsOH and RbOH are consistent with a reasonable force field, although uncertainties in the harmonic force constants prevent a quantitative determination of anharmonic constants. In the absence of contrary evidence, we conclude that the alkali hydroxides very probably have a linear equilibrium configuration. The equilibrium bond lengths in CsOH are estimated to be: $r_{\mathrm{CsO}}\text{.\hspace{0.17em}=\hspace{0.17em}2.391 Å}$ , $r_{\mathrm{OH}}{\text{\hspace{0.17em}=\hspace{0.17em}0.96}}_0\AA$ ; in RbOH: $r_{\mathrm{RbO}}\text{\hspace{0.17em}=\hspace{0.17em}2.301 Å}$ , $r_{\mathrm{OH}}{\text{\hspace{0.17em}=\hspace{0.17em}0.95}}_7\AA$ .