The equilibrium geometry and two measures (the equilibrium dissociation energy in the complete basis set limit, D-e(CBS) and the intermolecular stretching force constant k(sigma)) of the strength of the non-covalent interaction of each of six Lewis acids M-X (M = Cu, Ag, Au) with each of nine simple Lewis bases B (B = N-2, CO, HCCH, CH2CH2, H2S, PH3, HCN, H2O, and NH3) have been calculated at the CCSD(T)/aug-cc-pVTZ level of theory in a systematic investigation of the coinage-metal bond. Unlike the corresponding series of hydrogen-bonded B center dot center dot center dot HX and halogen-bonded B center dot center dot center dot XY complexes (and other series involving non-covalent interactions), D-e is not directly proportional to k(sigma). Nevertheless, as for the other series, it has been possible to express D-e in terms of the equation D-e = cN(B).E-MX, where N-B and E-MX are the nucleophilicities of the Lewis bases B and the electrophilicities of the Lewis acids M-X, respectively. The order of the E-MX is determined to be E-AuF > E-AuCl > E-CuF > E-CuCl > E-AgF approximate to E-AgCl. A reduced electrophilicity defined as (E-MX/sigma(max)) is introduced, where sigma(max) is the maximum positive value of the molecular electrostatic surface potential on the 0.001 e/bohr(3) iso-surface. This quantity is, in good approximation, independent of whether F or Cl is attached to M.