Kinetic Prefactors of Reactions on Solid Surfaces

Abstract

Surface Reactions / Adsorbate / Kinetics / Kinetic Prefactors / Transition State TheoryAdsorbed molecules are involved in many reactions on solid surfaces that are of great technological importance. As such, there has been tremendous effort worldwide to learn how to theoretically predict rates for reactions involving adsorbed molecules. Theoretical calculations of rate constants require knowing both their activation energy and prefactor. Recent advances in ab initio computational methods (e.g., density functional theory with periodic boundary conditions and van der Waals corrections) promise to soon provide activation energies for surface reactions with sufficient accuracy to have real predictive ability. However, to predict reaction rates, we also need accurate predictions of prefactors. We recently discovered that the standard entropies of adsorbed molecules (S 0 ad ) linearly track the entropy of the gas-phase molecule at the same temperature (T ), such that S 0 ad (T ) = 0.70 S 0 gas (T ) − 3.3 R (R = the gas constant), with a standard deviation of only 2 R over a range of 50 R. This correlation, which applies only to conditions where their surface residence times are shorter than ∼ 1000 s, provides a powerful new method for estimating the partition functions for adsorbates and the kinetic prefactors for their reactions. For desorption, we show that the prefactors obtained with DFT using transition state theory (TST) and the harmonic oscillator approximation to get the partition function predicts prefactors for desorption that are of order 10 3 times larger than experimental values while our approach gives much better estimates. We also explore the applications of this approach to estimate prefactors within TST for the main classes of adsorbate reactions: desorption, diffusion, dissociation and association, and discuss its limitations. We discuss general issues associated with applying TST to rate laws and multi-step mechanisms in surface chemistry, and argue that rates of adsorbate reactions which are often taken to be proportional to coverage (θ) might better be taken as proportional to θ/(1 − θ) (unless the adsorbate forms islands), to account for the configurational entropy or excluded volume effects on the adsorbate's chemical potential.

Detection of adsorbate overlayer structural transitions using sum-frequency generation spectroscopy

“…For the second transition we fitted the increase of the amplitude of the third resonance and obtained ν 0 = 10 9.6 ± 0.9 s −1 and E a = 0.49 ± 0.04 eV. The fitted pre-factors are similar to, or slightly smaller than, the 10 10.1 s − 1 that we estimate for onedimensional CO diffusion based on the translational entropy of CO [40]. When doing the same analysis for the final desorption step we obtain ν 0 = 10 18.2 ± 1 s −1 and E a = 1.38 ± 0.06 eV.…”

CO Oxidation on the Pd(111) Surface

“…However, due to the uncertainty of our DFT-calculated CO adsorption energies and possible missing entropic contributions to our assumed preexponential prefactors, 48 the case for the ER mechanism over LH is not conclusive from the calculations alone. Additional evidence from experiment, however, does make a compelling case.…”

Decomposition Mechanism of Anisole on Pt(111): Combining Single-Crystal Experiments and First-Principles Calculations

“…Although this 0 K study seems to support the selectivity for benzene over phenol, it is very delicate to compare barriers of a reaction at the surface and a desorption step since they involve quite different activation entropies resulting in rates that can be three orders of magnitude different. 53 A more detailed comparison therefore requires including the temperature and entropic contributions.…”