Application of Machine-Learned Exchange-Correlation Functionals to Surface Chemistry

The accurate determination of adsorption energies remains one of the most challenging tasks in density-functional theory. This is despite the fact that having reliable methods to calculate adsorption energies might have significant implications to materials design and engineering for catalysis applications. To address this challenge, we develop machine-learned (ML) exchange-correlation (XC) functionals based on the CIDER formalism [1,2], focusing on molecular adsorption on transition metal surfaces. This is motivated by the promising performance of CIDER in learning the non-local Fock exchange at semilocal DFT cost [2], as well as the generally good performance of the EXX+RPA approach in describing adsorption energies [3]. With recent developments in CIDER allowing for full XC training, our aim was to train an ML XC functional to learn the full EXX+RPA reactions energies using the CIDER framework. To this end, we generated an extensive dataset comprised of hundreds of reaction energies at the EXX+RPA level that include molecular atomization energies, metallic cohesive energies, surface energies, and adsorption energies at different coverages. By using EXX+RPA dataset, we are able to train a series of non-local CIDER functionals which yield reaction energies that greatly outperform the baseline PBE performance in terms of mean absolute errors with respect to the RPA+EXX labels. Furthermore, we observe systematic performance improvement with increasing the degree of nonlocality by tuning length scale of the CIDER features, and with increasing GP model covariance. Our results open the door to the accurate prediction of adsorption energies close to EXX+RPA level at semilocal functional cost.

[1] K. Bystrom and B. Kozinsky, “CIDER: an expressive, nonlocal feature set for machine learning density functionals with exact constraints”, Journal of Chemical Theory and Computation 18, 2180–2192 (2022).

[2] K. Bystrom and B. Kozinsky, “Nonlocal machine-learned exchange functional for molecules and solids”, Physical Review B 110, 075130 (2024).

[3] L. Schimka, J. Harl, A. Stroppa, A. Grüneis, M. Marsman, F. Mittendorfer, and G. Kresse, “Accurate surface and adsorption energies from many-body perturbation theory”, Nature Materials 9, 741–744 (2010).