EFFECTIVE ROTATION-PSEUDOROTATION HAMILTONIAN FOR $X_{3}$-TYPE MOLECULES IN THE HIGH-BARRIER LIMIT

Abstract

The rotation-pseudorotation problem in $X_{3}$-type molecules has been treated group-theoretically for the high-barrier tunneling case. Explicit expressions for rotation-pseudorotation Hamiltonian matrix elements, which take into account interaction of overall rotation both with the rotation of principal axes accompanying pseudorotation motion and with the angular momentum generated by pseudorotation motion, have been derived using an m-fold extended group of the $G_{12}$ permutation-inversion group. Illustrative pseudorotation tunneling splitting patterns have been derived by numerically diagonalizing the resulting Hamiltonian matrix for J = 5 using rotational constants appropriate for $Na_{3}$ in the B $state^{1,2}$ together with various sets of tunneling parameters. These tunneling splittings can be qualitatively understood using the concept of two-fold energy level clusters in asymmetic rotor molecules. This high-barrier formalism may be applicable to the two lowest (j=0 and j=1) pseudorotation states of the lowest (u=0) vibrational level of the B state of $Na_{3}$, if the presently available medium resolution $spectra^{1}$ can be recorded at high resolution. Work on a more general formalism, which will hopefully be applicable to the u=1 low-barrier pseudorotation states involved in existing $Na_{3}$ high-resolution $spectra^{1}$, is also underway.