Evaluating Thermal Corrections for Adsorption Processes at the Metal/Gas Interface

Adsorption
and desorption steps are key for active catalysts and
rely on a subtle balance between enthalpic and entropic terms. While
the enthalpic term is becoming ever more accurate through density
functional development, the entropic term remains underrated and its
precise determination a great challenge. In this work, we have performed
extensive first-principles thermodynamic integration (TI) simulations
for the adsorption of small (e.g., CO) to larger (e.g., phenol) molecules
at metallic surfaces and compared their adsorption free energies to
the values obtained by vertical, static statistical mechanics approximations
to thermal corrections invoking three different approximations for
the low-frequency modes. We have found an excellent agreement between
the vertical corrections and the TI for minima, for both weakly bound
systems (e.g., CO2 and formic acid) and strongly chemisorbed
molecules such as phenol or CO. While the treatment of the low-frequency
modes has a minor impact on the agreement with TI, all vertical corrections
systematically overestimate activation energies by 0.1–0.2
eV compared to TI, demonstrating a noticeable lowering of activation
barriers. As a result of this study, we suggest that the vertical
corrections and in particular the standard harmonic approximation
can be safely applied to chemisorption minima, while the activation
energies are likely to be overestimated. Hence, if a greater accuracy
than ∼0.2 eV is required for activation free energies, we recommend
to use thermodynamic integration, which for small- to medium-sized
molecules in the gas phase is accessible with a reasonable computational
effort but requires a dense sampling in the transition state region.