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Center for Nonlinear Studies |
With the recent explosion in computational catalysis and related microkinetic modeling, the need for a fast, yet accurate, way to predict equilibrium and rate constants for surface reactions has become more important. Here a method to calculate partition functions and entropy of adsorbed species and equilibrium constants is presented. Instead of using the vibrational frequencies estimated from DFT and the harmonic oscillator approximation to calculate all modes of motion in the partition function, we use a hindered translator and hindered rotor model for the three modes of motion parallel to the surface, one for each of the two translations in the directions parallel to the surface and one for rotation about the axis perpendicular to the surface. This hindered translator and hindered rotor model joins the two limiting cases for adsorbates on a surface, the 2D ideal lattice gas (harmonic oscillator) model and the 2D ideal gas (free translator) model, making it valid over large temperature range. At the limit of low temperature, or high energy barrier, only vibrations are present and this model is the same as the harmonic oscillator approximation, while at high temperature, or low energy barrier, translations and rotations readily occur and this model becomes identical to the 2D ideal gas model for translations or the 1D free rotor model for rotations. The transition between the 2D ideal lattice gas (harmonic oscillator) model and the 2D ideal gas (free translator) model is surprisingly sharp, but modeled very closely by the hindered translator/rotor model. To verify this model, density functional theory was used to calculate the translations and rotations of four adsorbates on a platinum surface: methanol, propane (adsorbed via middle C2 or end C1 carbon), ethane, and methane. These entropies were combined with the vibrational entropy contributions and the concentration related entropy contributions to give the total entropies of the adsorbates and were found to agree well with experimental results, with an average absolute value of the error of only 1.1R or 8% for the four adsorbates.
Host: Enrique Batista