The systematic science of alloys(SSA) is a framework of the total energy and total volume able to be separated. The potential energy sequences of characteristic atoms at the central sites of the basic clusters in the fcc-based lattice Au-Cu system are separated out from smaller experimental heats of formation of L10-AuCu and L1_2-AuCu_3 compounds only, by nine potential energy E-functions and through the use of structural unit inversion method. From these potential energy sequences, the potential energies and heats of formation of the disordered Au1-xCux alloys at 0 K are calculated. The potential energies, heats of formation and Tc-temperatures of order-disorder transitions of the L1_0-AuCu, L1_2-Au_3Cu and L1_2-AuCu_3 compounds, as well as the Au_3Cu-, AuCu- and AuCu_3~- type ordered alloys with maximal ordering degrees are calculated too. The results show that the 5th E-function may be chosen for developing it into the free energy-, enthalpy-, vibrational energy- and vibrational entropy-functions for describing thermodynamic properties of the compounds, ordered and disordered phases and for establishing the phase diagram of the Au-Cu system in the future.