The nature of the bonding of molecules to neutral gold atoms or surfaces is of wide interest, particularly with regard to recent molecular electronics experiments involving molecules linked to gold electrodes and nanoclusters. Here, the fundamental problem of accurate calculation of gold atom-ligand interactions is addressed, and a best-possible estimate for the binding energy of AuNH3 is obtained via coupled-cluster and density-functional calculations using series of Gaussian, Slater, and plane-wave basis sets. Poor convergence of both coupled-cluster and density-functional calculations toward the infinite basis-set limit is obtained from the Gaussian basis sets; using Slater basis sets, convergence is more rapid while plane-wave basis sets easily reached convergence. A total of 24 Gaussian basis sets are examined, and a method is introduced for determining if a particular basis set is sufficiently balanced in its treatment of the metal and its ligand. For balanced basis sets, better estimates of the binding energy are obtained neglecting corrections for basis-set superposition error. Various treatment of relativistic effects are examined including the use of relativistic effective core potentials (RECPs), ultrasoft pseudopotentials, and all electron scalar and full spin-orbit zero-order regular approximation calculations. While the use of RECPs has minimal affect, use of ultrasoft pseudopotentials and neglect of spin-orbit coupling both result in underestimation of the binding energy by 2-3 kcal mol-1 (15%-20%), as does the neglect of triples excitations in coupled-cluster theory. The PW91, B3LYP, BLYP, and LDA density functionals were investigated and of these only PW91 predicted binding energies and geometries in qualitative agreement with the coupled-cluster results. The AuNH3 complex is found to be a realistic model for the bonding of NH3 to a gold (111) surface, the primary differences being the prediction of charge transfer within the complex and associated significantly stronger binding. This may have profound implications for molecular electronics applications in which small gold clusters are used to represent macroscopic electrodes.