Sulfuric acid and its gaseous hydrates play a central role in the nucleation processes of the atmosphere. In this study, the thermodynamic properties for the formation of the sulfuric acid monohydrate complex were determined from the results of accurate ab initio calculations by using statistical mechanics. Of the ab initio calculations, geometry optimizations and energy calculations were performed with the explicitly correlated CCSD(T)-F12a/VDZ-F12 method, which was shown to give results comparable to CCSD(T)/aug-cc-pVQZ level calculations. Four different stable geometries were found, and the energies of the two lowest were within 0.41 kJ mol −1 of each other. Harmonic frequencies were calculated both at the DF-SCS-LMP2/aug-cc-pVTZ level and the CCSD-F12/VDZ-F12 level.
Because the harmonic approximation works badly for the high frequency OH stretches and the low frequency intermolecular large amplitude motions, some of the vibrational degrees of freedom were treated by limiting the dimensionality of the potential energy surface to small, two- or three-dimensional subspaces that contained a few strongly coupled vibrational degrees of freedom. In these anharmonic domains, the vibrational problem was solved variationally from a potential energy surface calculated at the CCSD(T)-F12a/VDZ-F12 level. Even though the subspaces are completely decoupled from the rest of the vibrational degrees of freedom, my results indicate that with a careful choice of the domains, the resulting vibrational states are accurate enough for the calculation of thermodynamic properties.
It is shown that with the anharmonic domain approximation it becomes possible to incorporate quantum mechanically the presence of at least some of the other minimum energy structures into the thermodynamic properties, and that the inclusion of these is essential if accurate results are desired. Furthermore, the anharmonic domain approximation makes it relatively easy to calculate vibrational overtones which, especially for the large amplitude motions, have a major impact on the vibrational partition function.
With the inclusion of the anharmonic domains, very uniform results were obtained for the thermodynamic properties with the two different methods used in the harmonic calculation. At one atmosphere and 298 K, the Gibbs free energy was found to have a value of about -8.0 kJ mol −1. The anharmonic domains used in this study had the effect of raising the zero point energy by around 1.7 kJ mol −1. Comparison with the earlier results reveals that one of the most important reasons for the differences in the Gibbs energy is the inaccurate calculation of the electronic energies of the different reaction components. Thus, we recommend that all future studies employ a higher level method for these calculations.
Finally, investigations were carried out on the temperature dependence of the equilibrium constant and on the pressure and temperature dependencies of the Gibbs free energy and entropy. To this effect, the statistical thermodynamic formulae that included the anharmonic domain approximation in calculations of the thermodynamic properties were derived. The temperature dependence of both enthalpies and entropies was predicted to be rather small and, therefore, the Gibbs free energy varied almost linearly with temperature.
