Hindered Translator and Hindered Rotor Models for Adsorbates: Partition Functions and Entropies

Abstract

Abstract 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 we present a fast and accurate new method to estimate the partition functions and entropies of adsorbates based on quantum mechanical estimates of the potential energy surface. As with previous approaches, it uses the harmonic oscillator (HO) approximation for most of the modes of motion of the adsorbate. However, it uses hindered translator and hindered rotor models for the three adsorbate modes associated with motions parallel to the surface and evaluates these using an approach based on a method that has proven accurate in modeling the internal hindered rotations of gas molecules. The adsorbate entropies were calculated with this method for four adsorbates (methanol, propane, ethane, and methane) on Pt(111) using density functional theory (DFT) to evaluate the potential energy surface and are shown to be in very good agreement with experiments, better than using only the HO approximation. The translational and rotational contributions to the entropy of a hindered translator/hindered rotor are very closely approximated by the corresponding harmonic oscillator entropy (within 0.46 R) when the barrier exceeds kT and by the entropy of an ideal 2D monatomic gas of the same mass and a free 1D rotor with the same moment of inertia, respectively (within 0.12 R), when the barrier is less than kT. However, the harmonic oscillator/lattice gas model severely overestimates the entropy when kT exceeds the barrier.