Adsorbate Partition Functions via Phase Space Integration: Quantifying the Effect of Translational Anharmonicity on Thermodynamic Properties

Abstract

A new method for computing anharmonic thermophysical properties for adsorbates on metal surfaces is presented. Classical Monte Carlo phase space integration is performed to calculate the partition function for the motion of a hydrogen atom on Cu(111). A minima-preserving neural network potential energy surface is used within the integration routine. Two different sampling schema for generating the training data are presented, and two different density functionals are used. The results are benchmarked against direct state counting results by using discrete variable representation. The phase space integration results are in excellent quantitative agreement with the benchmark results. Additionally, both the discrete variable representation and the phase space integration results confirm that the motion of H on Cu( 111) is highly anharmonic. The results were applied to calculate the free energy of dissociative adsorption of H 2 and the resulting Langmuir isotherms at 400, 800, and 1200 K in a partial pressure range of 0−1 bar. It shows that the anharmonic effects lead to significantly higher predicted surface site fractions of hydrogen.

Configuration Space Integration for Adsorbate Partition Functions: The Effect of Anharmonicity on the Thermophysical Properties of CO–Pt(111) and CH3OH–Cu(111)

“…We employ MP-NN surrogate form described in detail in ref and implemented in a light python-based library . The main distinction in this work is the inclusion of angular coordinates.…”

“…The MP-NN surrogate is a weighted linear combination of multiple surrogates of form V MPNN ( x ) = V ( x 0 ) + 1 2 ( x − x 0 ) normalT H ( x 0 ) ( x − x 0 ) .25em normale NN ( x − x 0 ) each “anchored” at a minimum x 0 with a given known Hessian H ( x 0 ). With appropriate transformations of input and output training values (details are provided in ref ), we train a neural network function NN(·) within the PyTorch framework. Note that the form in eq forces the PES surrogate to have the same minimum x 0 as the underlying ‘true’ potential energy, and the trained neural network effectively serves as a multiplicative correction factor to a quadratic approximation.…”

“…It is expected to be accurate except at the lowest temperatures, where continuity of energy levels becomes a poor approximation. This work is an extension of the method proposed in the 2021 Blöndal et al study …”

Calculation of Entropy for a Two-Dimensional (2D) Ideal Gas with a Statistical Thermodynamic Method

“…The above deduction is based on the 2D ideal gas model, which assumes that the adsorbate molecules translate freely in the xy plane. If the free translation in the plane is hindered by the barrier which is formed by the interaction of adsorbate and adsorbent, more accurate numerical results can be obtained by HT or CPES method. − …”

“…It shows that 2D lattice gas model would accurately predict the adsorbate entropy when kT is less than the barrier height and that the 2D ideal gas model would accurately predict these when kT exceeds the barrier height. The barrier in HT model can also be replaced by the complete potential energy sampling (CPES). − It treats the adsorbate motion as a classical continuous system and considers the detailed energy landscape.…”