## Abstract

Adsorbed 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*_{ad}^{0}) linearly track the entropy of the gas-phase
molecule at the same temperature (*T*), such that
*S*_{ad}^{0}(*T*) = 0.70 *S*_{gas}^{0}(*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.

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