TUNNELING SPLITTINGS IN (XY3)2-TYPE DIMERS

Tunneling-rotational energy level expressions are derived for (XY3)2-type dimers using an internal-axis-method-like formalism previously developed for high-barrier tunneling problems involving several large-amplitude motions. The tunneling-rotational Hamiltonian matrix is set up and block diagonalized using symmetry considerations from G36, the permutation-inversion group known to be appropriate when ammonia-like inversion within either XY3 subunit and exchange of Y atoms between subunits are both absent. It is shown that only 10 different tunneling matrix elements arise, corresponding to one nontunneling motion, five twofold or sixfold "interconversion" motions, which exchange the roles of the two inequivalent XY3 subunits, and four threefold noninterconverting motions, which just rotate one or both XY3 subunits about the appropriate threefold symmetry axis. More than 10 tunneling paths can contribute to these 10 matrix elements, and a number of these paths are described, assuming a non-hydrogen-bonded equilibrium configuration similar to that found experimentally for (NH3)2. The rotational dependence of all 10 tunneling matrix elements is determined, and three tunneling motions are selected, on the basis of chemical intuition, as probably the most feasible for (NH3)2 and (ND3)2. The resultant formalism is then applied to obtain qualitative tunneling-rotational energy level patterns for the fully protonated and fully deuterated ammonia dimer species. © 1991.