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Complexity of many-body interactions in transition metals via machine-learned force fields from the TM23 data set

Cameron Owen1,2*, Steven Torrisi2*, Yu Xie2*, Simon Batzner2*, Kyle Bystrom2*, Jennifer Coulter2*, Albert Musaelian2*, Lixin Sun2*, Boris Kozinsky2,3*

1 Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA

2 John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA

3 Robert Bosch LLC, Research and Technology Center, Watertown, MA 02472, USA

* Corresponding authors emails: cowen@g.harvard.edu, steven.torrisi@tri.global, xiey@g.harvard.edu, batzner@g.harvard.edu, kylebystrom@g.harvard.edu, jcoulter@g.harvard.edu, albym@g.harvard.edu, lixinsun@microsoft.com, bkoz@g.harvard.edu
DOI10.24435/materialscloud:6c-b3 [version v1]

Publication date: Mar 22, 2024

How to cite this record

Cameron Owen, Steven Torrisi, Yu Xie, Simon Batzner, Kyle Bystrom, Jennifer Coulter, Albert Musaelian, Lixin Sun, Boris Kozinsky, Complexity of many-body interactions in transition metals via machine-learned force fields from the TM23 data set, Materials Cloud Archive 2024.48 (2024), https://doi.org/10.24435/materialscloud:6c-b3


This work examines challenges associated with the accuracy of machine-learned force fields (MLFFs) for bulk solid and liquid phases of d-block elements. In exhaustive detail, we contrast the performance of force, energy, and stress predictions across the transition metals for two leading MLFF models: a kernel-based atomic cluster expansion method implemented using sparse Gaussian processes (FLARE), and an equivariant message-passing neural network (NequIP). Early transition metals present higher relative errors and are more difficult to learn relative to late platinum- and coinage-group elements, and this trend persists across model architectures. Trends in complexity of interatomic interactions for different metals are revealed via comparison of the performance of representations with different many-body order and angular resolution. Using arguments based on perturbation theory on the occupied and unoccupied d states near the Fermi level, we determine that the large, sharp d density of states both above and below the Fermi level in early transition metals leads to a more complex, harder-to-learn potential energy surface for these metals. Increasing the fictitious electronic temperature (smearing) modifies the angular sensitivity of forces and makes the early transition metal forces easier to learn. This work illustrates challenges in capturing intricate properties of metallic bonding with current leading MLFFs and provides a reference data set for transition metals, aimed at benchmarking the accuracy and improving the development of emerging machine-learned approximations.

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File name Size Description
893.2 MiB TM23 data set, including various train-test splits for ease of use.
3.8 KiB Example FLARE and NequIP training scripts.
476 Bytes README describing both of the directories.


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.


density-functional theory machine learned force fields transition metals equivariant neural networks Gaussian processes

Version history:

2024.48 (version v1) [This version] Mar 22, 2024 DOI10.24435/materialscloud:6c-b3