The current well-known excess Gibbs functions that combine with cubic equations of state (CEOS) all reduce to the ideal solution functions. A new class of excess Gibbs function, which reduces to the van der Waals one-fluid mixing rule, is introduced for application to various asymmetric, highly non-ideal chemical systems. The incorporation of this new excess Gibbs function into a cubic equation of state allows the CEOS/A(E) mixing rule to smoothly transition to the conventional van der Waals one-fluid mixing rules. It is well known that equation's of state with the van der Waals mixing rules work very well for non-polar systems, it is, therefore, desirable that the composition dependent excess Gibbs free energy function reduce to that of the van der Waals fluid. Introducing this capability into a Gibbs energy model ensures the binary interaction parameters for the classical quadratic mixing rules available in many existing data banks for systems involving hydrocarbons and gases can be used directly in the new excess Gibbs function. The new liquid activity model is an excellent GE function and is combined with an equation of state to handle non-ideal systems while still retaining the equation of state capability to handle non-polar systems in the accurate prediction of high pressure and high temperature phase equilibria.