The goal of this work is to develop an open-source code that automatically generates adsorbate partition functions that include anharmonic effects. Specifically, the degrees of freedom that correspond to the motion of the adsorbate relative to the surface are treated as coupled and anharmonic. The coupled partition function is computed using classical phase space representations. The high-dimensional integrals are solved using Monte Carlo Integration (MCI). This code will be a part of the Sandia National Laboratories’ Exascale Catalytic Chemistry (ECC) computational framework for automated chemistry.

The implications of using this method are discussed for hydrogen and methanol on a Cu(111) surface. The anharmonic methanol adsorbate partition function enables the calculation of an accurate equilibrium constant for the desorption of physisorbed methanol, a key reaction in methanol synthesis.

The potential energy surfaces (PESs) are constructed using machine learning in combination with density functional theory (DFT) calculations. We construct minima-preserving neural network (MP-NN) surrogate PESs, which are specifically designed to be accurate at geometries near the optimal position/s of the adsorbate on the surface.

Figure 1 shows that for a H atom on Cu(111), the inclusion of anharmonic effects leads to a larger partition function than the harmonic oscillator (H.O.) approximation, and the effects increase with temperature. The MP-NN partition function is much smaller than predicted by the 2D gas model or the hindered translator in this case. Additionally, there is a good agreement between MCI and direct state counting on the MP-NN PES.

The presented method results in a more accurate depiction of adsorbate partition functions than obtained with the standard analytical methods. The consequently more accurate free energies will lead to improved accuracy of microkinetic mechanisms in heterogeneous catalysis.

<b>Figure 1.</b> Left: The partition function for a H atom on Cu(111) at 290-1400 K, evaluated using the MP-NN surrogate MCI, the 3D classical H.O., the 2D gas model and the hindered translator model. Right: The anharmonic correction factor evaluated with MCI and direct state counting.

Figure 1. Left: The partition function for a H atom on Cu(111) at 290-1400 K, evaluated using the MP-NN surrogate MCI, the 3D classical H.O., the 2D gas model and the hindered translator model. Right: The anharmonic correction factor evaluated with MCI and direct state counting.

David H Bross

Assistant Chemist, Argonne National Laboratory

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