Knowledge Bank

Takami and $Jo¨rissen1$ have observed an infrared diode-laser spectrum of $Ar-SiF4$ showing complicated features which may arise from internal motions. Analysis of the spectrum is hindered at present, however, by strong overlapping lines from the $SiF4$ monomer. Kawashima and $Hirota2$ have studied the microwave spectrum of $Na-BH4$ in the gas phase. Although this spectrum does not appear to show tunneling splittings in the ground vibrational state, such splittings may well appear in vibrationally excited states. Motivated by these observations we have undertaken a theoretical study to parameterize tunneling-rotational energy level expressions and predict tunneling splitting patterns in weakly bound $A-BX4$ type complexes, provided that the internal motions correspond to tunneling through relatively high barriers separating the various equilibrium frameworks. Because the spherical top subunit can internally rotate about axes pointing in a number of different directions, this type of complex is well suited for application of the formalism originally developed for the water dimer. The number of frameworks between which tunneling occurs will depend on the equilibrium geometry of the complex, possible numbers of frameworks being 4, 6, 12, or 24. The lowest number of frameworks arises when the complex has the highest $(C3v)$ symmetry, i.e., when atom A is located at the center of a face of the $BX4$ tetrabedron, or directly above one vertex. The highest number of frameworks arises when the complex has no symmetry, i.e., when the atom A is located off-center on a face or not directly above a vertex. In the present study we consider only the $C3v$ case, with its four equilibrium frameworks. We further assume that the tetrahedral structure of the $BX4$ subunit remains unaltered during the large-amplitude internal-rotation tunneling motion. In the talk we describe a coordinate system for the large-amplitude motion, together with the associated $C24$ group theoretical formalism, basis set functions, and Hamiltonian matix. We also present some possible two-parameter splitting patterns.