Standard Gibbs energies of formation and equilibrium constants from ab-initio calculations: Covalent dimerization of NO2 and synthesis of NH3

Standard quantum chemical methods are used for accurate calculation of thermochemical properties such as enthalpies of formation, entropies and Gibbs energies of formation. Equilibrium reactions are widely investigated and experimental measurements often lead to a range of reaction Gibbs energies and equilibrium constants. It is useful to calculate these equilibrium properties from quantum chemical methods in order to address the experimental differences. Furthermore, most standard calculation methods differ in accuracy and feasibility of the system size. Hence, a systematic comparison of equilibrium properties calculated with different numerical algorithms would provide a useful reference. We select two well-known gas phase equilibrium reactions with small molecules: covalent dimer formation of NO2 (2NO2 ⇌ N2O4) and the synthesis of NH3 (N2 + 3 H2 ⇌ 2NH3). We test four quantum chemical methods denoted by G3B3, CBS-APNO, W1 and CCSD(T) with aug-cc-pVXZ basis sets (X = 2, 3, and 4), to obtain thermochemical data for NO2, N2O4, and NH3. The calculated standard formation Gibbs energies ΔfG° are used to calculate standard reaction Gibbs energies ΔrG° and standard equilibrium constants Keq for the two reactions. Standard formation enthalpies ΔfH° are calculated in a more reliable way using high-level methods such as W1 and CCSD(T). Standard entropies S° for the molecules are calculated well within the range of experiments for all methods, however, the values of standard formation Gibbs energies ΔfG° show some dependence on the choice of the method. High-level methods perform better for the calculation of molecular energies, however, simpler methods such as G3B3 and CBS-APNO perform quite well in the calculation of total reaction energies and equilibrium constants, provided that the chemical species involved do not exhibit molecular geometries that are difficult to handle by the applied method. The temperature dependence of standard reaction Gibbs energy ΔrG° for the NH3 reaction is discussed by using the calculated standard formation Gibbs energies ΔfG° of the reaction species at 298.15 K. The corresponding equilibrium constant Keq as a function of temperature is found to be close to experimental values.