Unified non-fitting formulation representation of thermodynamic properties for diatomic substances

•We report a unified non-fitting formulation representation of the Gibbs free energy for diatomic substances.•The developed explicit formulation representation only involve experimental data of four molecular constants.•The predicted Gibbs free energy values for 36 substances are in excellent agreement with the NIST data.•The predicted isobaric heat capacity values are in good agreement with the NIST data.