Knowledge Bank

For the past two decades, nuclear quadrupole hyperfine structure has been a powerful tool in structural determinations of loosely bound complexes. In the present work, we attempt to determine the limits of existing theory by describing hyperfine structure in a molecule which exhibits significant tunneling splittings because of large amplitude inversion and internal rotation motions, but which still has a well defined equilibrium configuration. The approach involves setting up a complete quadrupole Hamiltonian for the two nitrogen atoms in hydrazine $(NH2-NH2)$, which is made dependent upon the three large amplitude coordinates necessary to fully describe the various configurations of the molecule, and which contains all five elements of the electric field gradient tensor (i.e., $2qaa-qbb-qcc,qbb-qcc,qab,qac$, and $qbc$) at one N atom when the molecule is in one of its equilibrium configurations. The mean value of this quadrupole operator is calculated for each tunneling state. One interesting result is that for doubly degenerate E-type levels the hyperfine pattern is expected to be quite different from that for non-degenerate A or B-type levels, because of the influence of the non-diagonal term $qbc$. After the theoretical work, measurements of the hyperfine structure of selected transitions are being carried out on the NBS Fourier transform microwave instrument, and a least square fit of all available data will be performed. Transitions involving either non-degenerate or degenerate levels will allow us to determine the two diagonal terms of the electric field gradient tensor, which should be close to those reported for N2D4 by Harmony and Baron1. Only transitions involving degenerate levels will allow us to determine the non-diagonal term $qbc$. The quality of the overall hyperfine fit in a molecule like hydrazine, where vibrational averaging should not lead to large differences between various expectation values of the form , should be significantly better than the fits obtained for loosely bound complexes, unless our understanding of the tunneling apects of this problem is seriously flawed.