Effect of tunneling motions on the quadrupole hyperfine structure of hydrazine

Abstract

Quadrupole hyperfine structure is described in hydrazine (H 2NNH 2), a molecule which exhibits significant tunneling splittings as a result of large amplitude inversion and internal rotation motions, but which still has a well-defined equilibrium configuration. In this approach the complete quadrupole Hamiltonian for the two nitrogen atoms is expressed as a function of the three large amplitude coordinates needed to describe the eight equivalent equilibrium configurations of the molecule. The mean value of this quadrupole operator is calculated for each tunneling-rotational state, and expressed in terms of all five elements of the equilibrium electric field gradient tensor (2 q zz — q xx — q yy , q xx — q yy , q xz , q yz , and q xy ) at each nitrogen atom. For non-degenerate A or B-type tunneling-rotational levels in the molecular symmetry group G 16 (2) only the sum of the two electric field gradient tensors occurs, while for doubly degenerate E-type levels the difference as well as the sum appears. Since the sum involves only the first three tensor components in parentheses above, while the difference involves only the last two, hyperfine patterns for nondegenerate and degenerate levels show significant qualitative differences. Results of the present treatment are used to perform a least squares global fit of the quadrupole hyperfine structure of selected transitions recorded on our Fourier transform microwave instrument, allowing us to determine the two diagonal quadrupole coupling constants as well as the nondiagonal xy component of this tensor. The possibility is pointed out of drawing erroneous conclusions concerning molecular geometry from a rigid-molecule treatment of hyperfine patterns in molecules exhibiting tunneling motions.