Adsorption Free Energy of a Mobile Physisorbed Molecular Catalyst from Well-Tempered Metadynamics and from the Harmonic Approximation
- 1Department of Chemistry, KU Leuven, Celestijnenlaan 200F, Leuven, Belgium, 3001
Abstract
The adsorption free energy of a molecular catalyst is usually calculated with harmonic frequency analysis of the optimized adsorbed structure, and errors are often blamed on anharmonicity. Here, using fac-Re(bpy)(CO)3Cl on graphene, we show that the main source of error is different. Harmonic analysis treats the complex as vibrating around a single minimum, but at 298 K, the complex can move across the surface, rotate around the surface normal, and rock. In this work, we use multiple-walker well-tempered metadynamics to sample the desorption coordinate and then convert the free-energy profile to a standard-state value, with the gas at 1 bar and the adsorbate at the standard surface concentration as recommended by Campbell et al. The result is ΔG°ads(298 K) = −64.1 ± 2.1 kJ mol−1 at PBE-D3(BJ), while the harmonic approximation gives −26.3 kJ mol−1. Of the 37.8 kJ mol−1 difference, only 1.7 kJ mol−1 comes from the anharmonic shape of the binding well along the surface normal; 36.3 kJ mol−1 is due to the frustrated translations and rotations of the bound complex, which the harmonic model treats as small vibrations around a single minimum. The two exceed the total by the 0.2 kJ mol−1 quantum-to-classical step, which acts in the opposite direction. Insertion-based estimators, which work well for small adsorbates in pores, do not apply here because the ensembles with and without the adsorbate–surface interaction are separated by 34 kBT and do not overlap. The missing entropy cancels out when comparing similar poses of the same adsorbate, but not when referencing the gas phase.
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BibTeX
@misc{sims2026adsorption,
title = {{Adsorption Free Energy of a Mobile Physisorbed Molecular Catalyst from Well-Tempered Metadynamics and from the Harmonic Approximation}},
author = {Joshua M. Sims},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010935/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010935/v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Adsorption Free Energy of a Mobile Physisorbed Molecular Catalyst from Well-Tempered Metadynamics and from the Harmonic Approximation
AU - Joshua M. Sims
PY - 2026
DA - 2026/10/23
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010935/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010935/v1
AB - The adsorption free energy of a molecular catalyst is usually calculated with harmonic frequency analysis of the optimized adsorbed structure, and errors are often blamed on anharmonicity. Here, using fac-Re(bpy)(CO)3Cl on graphene, we show that the main source of error is different. Harmonic analysis treats the complex as vibrating around a single minimum, but at 298 K, the complex can move across the surface, rotate around the surface normal, and rock. In this work, we use multiple-walker well-tempered metadynamics to sample the desorption coordinate and then convert the free-energy profile to a standard-state value, with the gas at 1 bar and the adsorbate at the standard surface concentration as recommended by Campbell et al. The result is ΔG°ads(298 K) = −64.1 ± 2.1 kJ mol−1 at PBE-D3(BJ), while the harmonic approximation gives −26.3 kJ mol−1. Of the 37.8 kJ mol−1 difference, only 1.7 kJ mol−1 comes from the anharmonic shape of the binding well along the surface normal; 36.3 kJ mol−1 is due to the frustrated translations and rotations of the bound complex, which the harmonic model treats as small vibrations around a single minimum. The two exceed the total by the 0.2 kJ mol−1 quantum-to-classical step, which acts in the opposite direction. Insertion-based estimators, which work well for small adsorbates in pores, do not apply here because the ensembles with and without the adsorbate–surface interaction are separated by 34 kBT and do not overlap. The missing entropy cancels out when comparing similar poses of the same adsorbate, but not when referencing the gas phase.
ER -