Optimizing adsorption configurations on alloy surfaces using Tensor Train Optimizer

TL;DR

This paper introduces a tensor train optimizer method to efficiently find the most stable adsorption configurations on alloy surfaces by solving a higher-order optimization problem, improving over existing quantum and digital annealing approaches.

Contribution

The paper presents a novel application of tensor train optimization to solve higher-order binary optimization problems in surface chemistry, enabling more accurate modeling of multi-adsorbate interactions.

Findings

Including third-order interaction terms suffices for chemical accuracy.

TTOpt outperforms quadratic-only methods in identifying stable configurations.

The approach is robust across various alloys and adsorbates.

Abstract

Understanding how molecules arrange on surfaces is fundamental to surface chemistry and essential for the rational design of catalytic and functional materials. In particular, the energetically most stable configuration provides valuable insight into adsorption-related processes. However, the search for this configuration is a global optimization problem with exponentially growing complexity as the number of adsorbates and possible adsorption sites increases. To address this, we express the adsorption energy as a sum of multi-adsorbate interaction terms, evaluated using our in-house trained machine learning interatomic potential MACE-Osaka24, and formulate the search for the most stable configuration as a higher-order unconstrained binary optimization (HUBO) problem. We employ a tensor-train-based method, Tensor Train Optimizer (TTOpt), to solve the HUBO problem and identify optimal adsorption configurations of CO and NO molecules on various alloys up to full surface coverage. Our results show that including interaction terms up to third order may be sufficient to approximate adsorption energies within chemical accuracy and to identify optimal configurations. We also observed that TTOpt performs better with the HUBO formulation, suggesting that third-order terms help preserve correlations between adsorption sites, which allow TTOpt to optimize configurations more effectively. The extensive benchmarks across various alloys, surface geometries, and adsorbates demonstrate the robustness and applicability of using TTOpt to solve HUBO-type global optimization problems in surface chemistry. In contrast to quantum and digital annealers, which have recently been applied to similar global optimization tasks but are restricted to cost functions with at most quadratic terms, our approach can incorporate higher-order terms in a straightforward manner and does not require specialized hardware.