Automated search for optimal surface phases (ASOPs) in grand canonical ensemble powered by machine learning

Surface phase diagrams from nested sampling

Studies in atomic-scale modeling of surface phase equilibria often focus on temperatures near zero Kelvin due to the challenges in calculating the free energy of surfaces at finite temperatures. The Bayesian-inference-based nested sampling (NS) algorithm allows for modeling phase equilibria at arbitrary temperatures by directly and efficiently calculating the partition function, whose relationship with free energy is well known. This work extends NS to calculate adsorbate phase diagrams, incorporating all relevant configurational contributions to the free energy. We apply NS to the adsorption of Lennard-Jones (LJ) gas particles on low-index and vicinal LJ solid surfaces and construct the canonical partition function from these recorded energies to calculate ensemble averages of thermodynamic properties, such as the constant-volume heat capacity and order parameters that characterize the structure of adsorbate phases. Key results include determining the nature of phase transitions of adsorbed LJ particles on flat and stepped LJ surfaces, which typically feature an enthalpy-driven condensation at higher temperatures and an entropy-driven reordering process at lower temperatures, and the effect of surface geometry on the presence of triple points in the phase diagrams. Overall, we demonstrate the ability and potential of NS for surface modeling.

Accelerating the prediction of inorganic surfaces with machine learning interatomic potentials

The surface properties of solid-state materials often dictate their functionality, especially for applications where nanoscale effects become important. The relevant surface(s) and their properties are determined, in large part, by the material's synthesis or operating conditions. These conditions dictate thermodynamic driving forces and kinetic rates responsible for yielding the observed surface structure and morphology. Computational surface science methods have long been applied to connect thermochemical conditions to surface phase stability, particularly in the heterogeneous catalysis and thin film growth communities. This review provides a brief introduction to first-principles approaches to compute surface phase diagrams before introducing emerging data-driven approaches. The remainder of the review focuses on the application of machine learning, predominantly in the form of learned interatomic potentials, to study complex surfaces. As machine learning algorithms and large datasets on which to train them become more commonplace in materials science, computational methods are poised to become even more predictive and powerful for modeling the complexities of inorganic surfaces at the nanoscale.

An optimal Fe-C coordination ensemble for hydrocarbon chain growth: a full Fischer-Tropsch synthesis mechanism from machine learning

Fischer-Tropsch synthesis (FTS, CO + H2 → long-chain hydrocarbons) because of its great significance in industry has attracted huge attention since its discovery. For Fe-based catalysts, after decades of efforts, even the product distribution remains poorly understood due to the lack of information on the active site and the chain growth mechanism. Herein powered by a newly developed machine-learning-based transition state (ML-TS) exploration method to treat properly reaction-induced surface reconstruction, we are able to resolve where and how long-chain hydrocarbons grow on complex in situ-formed Fe-carbide (FeCx) surfaces from thousands of pathway candidates. Microkinetics simulations based on first-principles kinetics data further determine the rate-determining and the selectivity-controlling steps, and reveal the fine details of the product distribution in obeying and deviating from the Anderson-Schulz-Flory law. By showing that all FeCx phases can grow coherently upon each other, we demonstrate that the FTS active site, namely the A-P5 site present on reconstructed Fe3C(031), Fe5C2(510), Fe5C2(021), and Fe7C3(071) terrace surfaces, is not necessarily connected to any particular FeCx phase, rationalizing long-standing structure-activity puzzles. The optimal Fe-C coordination ensemble of the A-P5 site exhibits both Fe-carbide (Fe4C square) and metal Fe (Fe3 trimer) features.

Benchmark of general-purpose machine learning-based quantum mechanical method AIQM1 on reaction barrier heights

Artificial intelligence-enhanced quantum mechanical method 1 (AIQM1) is a general-purpose method that was shown to achieve high accuracy for many applications with a speed close to its baseline semiempirical quantum mechanical (SQM) method ODM2*. Here, we evaluate the hitherto unknown performance of out-of-the-box AIQM1 without any refitting for reaction barrier heights on eight datasets, including a total of ∼24 thousand reactions. This evaluation shows that AIQM1's accuracy strongly depends on the type of transition state and ranges from excellent for rotation barriers to poor for, e.g., pericyclic reactions. AIQM1 clearly outperforms its baseline ODM2* method and, even more so, a popular universal potential, ANI-1ccx. Overall, however, AIQM1 accuracy largely remains similar to SQM methods (and B3LYP/6-31G* for most reaction types) suggesting that it is desirable to focus on improving AIQM1 performance for barrier heights in the future. We also show that the built-in uncertainty quantification helps in identifying confident predictions. The accuracy of confident AIQM1 predictions is approaching the level of popular density functional theory methods for most reaction types. Encouragingly, AIQM1 is rather robust for transition state optimizations, even for the type of reactions it struggles with the most. Single-point calculations with high-level methods on AIQM1-optimized geometries can be used to significantly improve barrier heights, which cannot be said for its baseline ODM2* method.

Methanol Synthesis from CO2/CO Mixture on Cu-Zn Catalysts from Microkinetics-Guided Machine Learning Pathway Search

Methanol synthesis on industrial Cu/ZnO/Al₂O₃ catalysts via the hydrogenation of CO and CO₂ mixture, despite several decades of research, is still puzzling due to the nature of the active site and the role of CO₂ in the feed gas. Herein, with the large-scale machine learning atomic simulation, we develop a microkinetics-guided machine learning pathway search to explore thousands of reaction pathways for CO₂ and CO hydrogenations on thermodynamically favorable Cu-Zn surface structures, including Cu(111), Cu(211), and Zn-alloyed Cu(211) surfaces, from which the lowest energy pathways are identified. We find that Zn decorates at the step-edge at Cu(211) up to 0.22 ML under reaction conditions with the Zn-Zn dimeric sites being avoided. CO₂ and CO hydrogenations occur exclusively at the step-edge of the (211) surface with up to 0.11 ML Zn coverage, where the low coverage of Zn (0.11 ML) does not much affect the reaction kinetics, but the higher coverages of Zn (0.22 ML) poison the catalyst. It is CO₂ hydrogenation instead of CO hydrogenation that dominates methanol synthesis, agreeing with previous isotope experiments. While metallic steps are identified as the major active site, we show that the [-Zn-OH-Zn-] chains (cationic Zn) can grow on Cu(111) surfaces under reaction conditions, which suggests the critical role of CO in the mixed gas for reducing the cationic Zn and exposing metal sites for methanol synthesis. Our results provide a comprehensive picture on the dynamic coupling of the feed gas composition, the catalyst active site, and the reaction activity in this complex heterogeneous catalytic system.