The quadrupole moment of the 3/2(+) nuclear ground state of Au-197 from electric field gradient relativistic coupled cluster and density-functional theory of small molecules and the solid state

An attempt is made to improve the currently accepted muonic value for the Au-197 nuclear quadrupole moment [+0.547(16)x10(-28) m(2)] for the 3/2(+) nuclear ground state obtained by Powers [Nucl. Phys. A230, 413 (1974)]. From both measured Mossbauer electric quadrupole splittings and solid-state density-functional calculations for a large number of gold compounds a nuclear quadrupole moment of +0.60x10(-28) m(2) is obtained. Recent Fourier transform microwave measurements for gas-phase AuF, AuCl, AuBr, and AuI give accurate bond distances and nuclear quadrupole coupling constants for the Au-197 isotope. However, four-component relativistic density-functional calculations for these molecules yield unreliable results for the Au-197 nuclear quadrupole moment. Relativistic singles-doubles coupled cluster calculations including perturbative triples [CCSD(T) level of theory] for these diatomic systems are also inaccurate because of large cancellation effects between different field gradient contributions subsequently leading to very small field gradients. Here one needs very large basis sets and has to go beyond the standard CCSD(T) procedure to obtain any reliable field gradients for gold. From recent microwave experiments by Gerry and co-workers [Inorg. Chem. 40, 6123 (2001)] a significantly enhanced Au-197 nuclear quadrupole coupling constant in (CO)AuF compared to free AuF is observed. Here, these cancellation effects are less important, and relativistic CCSD(T) calculations finally give a nuclear quadrupole moment of +0.64x10(-28) m(2) for Au-197. It is argued that it is currently very difficult to improve on the already published muonic value for the Au-197 nuclear quadrupole moment.