Quantum effects in thermal reaction rates at metal surfaces

Abstract

There is wide interest in developing accurate theories for predicting rates of chemical reactions that occur at metal surfaces, especially for applications in industrial catalysis. Conventional methods contain many approximations that lack experimental validation. In practice, there are few reactions where sufficiently accurate experimental data exist to even allow meaningful comparisons to theory. Here, we present experimentally derived thermal rate constants for hydrogen atom recombination on platinum single-crystal surfaces, which are accurate enough to test established theoretical approximations. A quantum rate model is also presented, making possible a direct evaluation of the accuracy of commonly used approximations to adsorbate entropy. We find that neglecting the wave nature of adsorbed hydrogen atoms and their electronic spin degeneracy leads to a 10× to 1000× overestimation of the rate constant for temperatures relevant to heterogeneous catalysis. These quantum effects are also found to be important for nanoparticle catalysts.

Adsorption and Absorption Energies of Hydrogen with Palladium

“…The insensitivity to steps of the hydrogen recombination rate constant on Pd contrasts behavior reported for Pt. 29 H recombination on Pt(332) was found to be significantly faster than on Pt(111) under similar experimental conditions to the current study. This is consistent with the non-zero step stabilization energy of H on Pt and a facet-dependent partition function.…”

“…With similar partition functions and binding energies, the rate constants are predicted to be nearly equal as observed in the experiment. The insensitivity to steps of the hydrogen recombination rate constant on Pd contrasts behavior reported for Pt . H recombination on Pt(332) was found to be significantly faster than on Pt(111) under similar experimental conditions to the current study.…”

“…We also employ a model of isotope specific recombination rate constants k rec AB ( T ) described by eq 8 , which has been shown to be highly accurate for H and D recombination on Pt. 29 Here, S 0 AB ( T ) is the thermal sticking coefficient obtained by averaging known energy-dependent sticking probabilities 30 , 31 over a Maxwell Boltzmann distribution at temperature T , see SI Section 6 . Q AB gas is the partition function for the gas-phase molecule and is well known, eq S26 of the SI.…”

“…Q A ads is the adsorbate partition function and is computed as previously reported, where electronic-spin is properly accounted for and adsorbate wavefunctions and eigen energies are computed within the static surface approximation using a DFT-based potential energy surface (PES). 29 E 0, ads AB is the dissociative adsorption energy of isotopologue AB. See SI Section 7 for more details.…”

“…Q AB gas is the partition function for the gas-phase molecule and is well known, eq S26 of the SI. Q A ads is the adsorbate partition function and is computed as previously reported, where electronic-spin is properly accounted for and adsorbate wavefunctions and eigen energies are computed within the static surface approximation using a DFT-based potential energy surface (PES) …”