Nuclear Quadrupole Splittings in Rotational Spectra for the Possible Detection of Fine Structure Constant Variations: The Diatomic Gold Halides and Gold Hydride as Case Studies

The dependence of nuclear quadrupole coupling constants CNQC(α) on the fine-structure constant α for various diatomic gold molecules AuX (X = H, F, Cl, Br, and I) at the density functional level of theory is investigated. While the electric field gradient at gold is very sensitive to the density functional applied, the derivative with respect to α is less sensitive. From this, we can estimate the upper limit for the α variation in time, ∂CNQC/∂t, for the 197Au nuclear quadrupole coupling constant, which is on the order of 10–9 Hz/year. This is currently beyond the limit of high-precision spectroscopy. I demonstrate that α∂CNQC∂α can be estimated from relativistic effects in CNQC, which will be useful in further investigations.