J. Phys. Chem. A 1998, 102, 4857-4862

4857

Comparison of Various Quantum Chemistry Methods for the Computation of Equilibrium Constants Fre´ de´ ric Bohr* and Eric Henon Laboratoire de Chimie Physique, GSMA, UPRES-A 6089, Faculte´ des Sciences de Reims, Moulin de la Housse, B.P. 1039, 51687 REIMS Cedex 2, France ReceiVed: October 14, 1997; In Final Form: February 6, 1998

Ab initio as well as density functional computations have been carried out to test their ability to reproduce experimental equilibrium constants. Three kinds of equilibriums in the gaseous phase have been studied: equilibriums involving nitrogenized compounds or methanol or chlorinated compounds. The basis set effect is also examined. In this work, we show that hybrid HF-DFT and G2 methods seem to be the best adapted to compute this thermodynamic parameter.

I. Introduction The knowledge of equilibrium constants is important in the study of chemical reaction mechanisms. In addition to allowing the prediction of the composition of a mixture, the equilibrium constant is also connected to rate constants in two ways: (1) the existence of equilibrium between stable species in multiplestep processes and (2) the equilibrium between reactants and activated complexes in transition state theory.1 Experimentally, the equilibrium constant determination is not always easy, particularly for equilibrium observable only at high pressure. Indeed, even in recent years, there are relatively few experimental studies of gaseous equilibrium.2-15 Thus, to provide theoretical equilibrium constants is of great interest for experimenters. This kind of calculation requires both energetic and entropic effect determinations. To our knowledge, in the gaseous phase, there are no theoretical studies concerning this kind of parameter (equilibrium constant or Gibbs free energy), comparing various recent quantum chemistry methods with experimental results. Indeed, most theoretical papers concerning thermodynamics predictions from quantum results present only ∆H results, more often than not ∆H at 0 K (i.e., ∆E only with ZPE correction).16-23 Nevertheless, the equilibrium constant is a practical indicator to test theoretical methods because it is very sensitive both to the energy quality and to geometrical parameters and also because the electronic structure of each compound that takes part in the equilibrium is extremely different from the others. Moreover, the ability of theoretical methods to give good equilibrium constants is important to study next the nonideality effect of gases at high pressure.24 In this work, we have examined 12 equilibriums in the gaseous phase, divided in three groups, computing the constants with ab initio (HF, MPn, G2, BAC-MP4) and density functional (local and nonlocal level as well as hybrid HF-DFT) methods. II. Computational Details HF and post-HF computations (MPn, G2) have been done with the Gaussian 94 program.25 Density functional com* Corresponding author. Fax: (33) (0)3-26-05-33-33. E-mail: frederic. [email protected].

putations have been carried out with Gaussian 9425 and deMon-KS 3.226 packages. BAC-MP4 computations, which take as a starting point the MP4/6-31G**//HF/6-31G* values of the energies, have been carried out with the program of Melius.27 In density functional computations with deMon, we have used only the TZVP basis set (equivalent to a 6-311G** Gaussian set), which is the following: (41/1) for hydrogen; (7111/411/ 1) for carbon, nitrogen, and oxygen.28 The auxiliary basis sets, used in the fitting of the charge density and the exchangecorrelation potential, were (4; 4) for H and (4, 4; 4, 4) for C, N, and O. The charge density was fitted analytically, whereas the exchange-correlation potential was fitted numerically on a grid, as proposed in deMon. The FINE grid was employed. In calculations using the local density approximation, the Vosko, Wilk, and Nusair29 parametrization of the correlation energy in the homogeneous electron gas was used. These calculations will be labeled VWN. Nonlocal corrections to the exchangecorrelation potential were included self-consistently using density gradient corrections. Three functionals have been employed: PP, BP, and BLAP. In calculations labeled PP, the approximations proposed by Perdew30,31 for the exchange and correlation parts were used. In computations labeled BP, the functional of Becke32 for the exchange and that of Perdew31 for correlation were employed. Concerning the last labeled BLAP, the functional of Becke32 and that of Proynov et al.33 for correlation were used. All the geometries obtained with deMon were fully optimized using the Versluis-Ziegler correction.34 In computations using Gaussian 94, for two equilibriums, several basis sets have been employed: 6-31G**,35-39 6-311G**,40,41 6-311++G**,40-42 cc-pVTZ,43-45 and AUG-ccpVTZ (cc-pVTZ with diffuse functions).43-45 Otherwise, we have used 6-311G**. DFT calculations with Gaussian 94 have been carried out using the BLYP32,46,47 functional. For HFDFT computations, we have used B3LYP,46-48 B3PW91,48,49 and B3P8648,31 functionals. All energy as well as frequency computations have been done with the geometry obtained by a full optimization in the same basis set. Frequencies are obtained analytically with Gaussian and numerically with deMon.

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