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The dependence of the nuclear quadrupole coupling constants (NQCC) on the interaction between electrons and a nucleus of finite size is theoretically analyzed. A deviation of the ratio of the NQCCs obtained from two different isotopomers of a molecule from the ratio of the corresponding bare nuclear electric quadrupole moments, known as quadrupole anomaly, is interpreted in terms of the logarithmic derivatives of the electric field gradient at the nuclear site with respect to the nuclear charge radius. Quantum chemical calculations based on a Dirac-exact relativistic methodology suggest that the effect of the changing size of the Au nucleus in different isotopomers can be observed for Au-containing molecules, for which the predicted quadrupole anomaly reaches values of the order of 0.1%. This is experimentally detectable and provides an insight into the charge distribution of non-spherical nuclei. [ABSTRACT FROM AUTHOR]