The recent development of a new excess Gibbs function G(E) by Twu, Sim and Tassone allows infinite-pressure cubic of equations of state/A(E) (CEOS/A(E)) mixing rules to transition smoothly to the conventional van der Waals one-fluid mixing rules. The incorporation of their proposed G(E) model into a cubic equation-of-state allows an equation-of-state to describe both van der Waals fluids and highly non-ideal mixtures over a broad range of temperatures and pressures in a consistent and unified framework. We continue our work to develop a versatile excess Gibbs free energy function for zero-pressure CEOS/A(E) mixing rules, in addition to the infinite-pressure CEOS/A(E) mixing rules. An optimal two-parameter cubic equation-of-state TST (Twu-Sim-Tassone) has been found to allow better prediction of liquid densities for heavy hydrocarbons and polar components. The alpha function of the TST cubic equation-of-state is generalized here, The generalized alpha function is a linear function of the acentric factor at a constant reduced temperature, not a fourth-order or a sixth-order function as suggested by Soave and other researchers. The advantage of a linear function in the acentric factor is obvious in the extrapolation of the alpha function to heavy hydrocarbons, petroleum fractions, and gas condensates. The new generalized alpha function, when used with the TST, allows very accurate prediction of the vapor pressure from the triple point to the critical point of hydrocarbons. The performance of SRK, PR and TST is examined using the versatile excess Gibbs free energy function in the zero-pressure CEOS/A(E) Mixing rules for the prediction of high pressure and high temperature phase equilibria of highly non-ideal systems.