Vibrationally induced nuclear quadrupole coupling in tetrahedral and octahedral molecules

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Abstract
Hyperfine splittings arising from the presence of a quadrupolar nucleus at the center of a molecule belonging to the point group Td or Oh (e.g., 189OsO4 or 235UF6) are symmetry forbidden to a high degree of approximation. Nevertheless, quadrupole splittings can be induced by either vibrational or rotational distortions of the molecule, i.e., by distortions similar to those responsible for inducing electric dipole moments in Td molecules. Such hyperfine splittings have recently been observed in several laboratories using laser saturation spectroscopy. In this paper we investigate theoretically the quadrupole splittings induced by excitation of doubly and triply degenerate vibrations in Td and Oh molecules. We find that much of the vibration–rotation formalism already present in the methane literature can be applied with only minor changes to the induced-quadrupole-coupling problem, and that rather simple theoretical relationships can be derived between the quadrupole splitting and the tetrahedral or octahedral vibration–rotation splitting of a given level. Values for the scalar and tensor contribution to the quadrupole coupling constant have been derived from the experimental data for 189OsO4 reported by Bordé et al.