We provide a rigorous model-free definition and a detailed theoretical analysis of the electron-charge displacements making up the donation and back-donation components of the Dewar-Chatt-Duncanson model in some realistic catalytic intermediates of formula L-Au(I)-S in which L is an N-heterocyclic carbene or Cl(-) and S is an eta(2)-coordinated substrate containing a C-C multiple bond. We thus show, contrary to a widely held view, that the gold-substrate bond is characterized by a large pi back-donation component that is comparable to, and often as large as, the sigma donation. The back-donation is found to be a highly tunable bond component and we analyze its relationship with the nature of the auxiliary ligand L and with structural (interdependent) factors such as metal-substrate bond lengths and carbon pyramidalization.