New efficient algorithm for solving thermodynamic chemistry

Modeling thermodynamic equilibrium of complex nonlinear chemical systems with the most used Newton‐Raphson method can lead to nonconvergence. From the mathematical properties of the set of equations, a chemically permitted interval is defined. By imposing this interval, the robustness of the Newton‐Raphson method is increased at a low computing time cost. The new method, the positive continuous fraction, does not depend on the first derivative of the objective function to find the solution. A new algorithm is thus built by the association of this very robust method with the fast Newton‐Raphson method and the definition of the chemically allowed interval. This combined algorithm is very impressive in terms of reliability, robustness, and speed.