AN AB INITIO SEMIRIGID BENDER CALCULATION OF THE ROTATION AND TRANS-TUNNELLING SPECTRA OF $(HF)_{2}$ AND $(DF)_{2}$

Abstract

$^{1}$ P.R. Bunker et al., J. Chem. Phys. 89, 3002 (1988). $^{2}$W.J. Lafferty et al., J. Mol. Spectrosc. 123, 434 (1987). $^{3}$A.S. Pine et al., J. Chem. Phys. 81, 2939 (1984).Author Institution: Herzberg Institute of Astrophysics, National Research Council of Canada; Department of Chemistry, Amherst College; Institut fur Theoretische Chemie and Strahlenchemie der Universitat Wien, Wahringerstrasse 17, A-1090 Wien, Austria.Using a purely ab initio minimum energy $path^{1}$ for the trans-tunnelling motion in the HF dimer the energy levels for the K-type rotation and trans-tunnelling motion for $(HF)_{2}$ and $(DF)_{2}$ are calculated with a one-dimensional Semirigid Bender Hamiltonian and no adjustable parameters. The transition moments for rotation-tunnelling transitions are calculated, using our ab initio value for the dipole moment of an isolated HF molecule, and we also calculate $\bar{B}$ values. The energy levels we obtain are in close agreement with $experiment;^{2}$ for example the K-O tunnelling splitting in s$(HF)_{2}$ is calculated as $0.65 cm^{-1}$ compared to the experimental value of $0.65869 cm^{-1}.$ As well as showing that our ab initio minimum energy path is very good, the calculation demonstrates that the Semirigid Bender formalism is able to account quantitatively for the unusual K-dependence of the rotational energies resulting from the quasilinear $behaviour,^{3}$ and that the trans-tunnelling motion is separable from the other degrees of freedom. We use the results to predict the locations, and transition moments, of the $\Delta K=0$ and $\pm 1$ subbands in the tunnelling spectra of $(HF)_{2}$ and $(DF)_{2}$, many of which have not yet been observed