Hyperfine structure-tunneling coupling in trans-1,2-cyclohexanediamine revealed by rotational spectroscopy

The microwave spectrum of the non-rigid trans-cyclohexanediamine (C₆H₁₀(NH₂)₂) is investigated. It displays a large amplitude interconversion motion during which both amino groups are rotated through 117° leading to tunneling splittings on the order of 21 MHz and line splittings on the order of 42 MHz for b- and c-type transitions. The tunneling is mediated by the quadrupole coupling hyperfine structure arising from both nitrogen atoms which leads to splittings on the same order of magnitude. The frequencies of the rotation-tunneling-hyperfine transitions are analyzed using a new theoretical model in which the large amplitude motion and the quadrupole coupling are treated simultaneously. Hyperfine matrix elements between (within) tunneling sublevels depend on the difference (sum) of the quadrupole coupling of the two nitrogen atoms. Using the theoretical formalism, 249 experimental frequencies are reproduced with an RMS value of 10 kHz, close to the experimental uncertainty. The spectroscopic parameters determined include usual rotational and distortion parameters; tunneling parameters describing the magnitude of the tunneling and its rotational dependence; and various components of the effective quadrupole coupling tensors.