Strategies and Software for Machine Learning Accelerated Discovery in Transition Metal Chemistry
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Abstract
Machine learning the electronic structure of open shell transition metal complexes presents unique challenges, including robust and automated data set generation. Here, we introduce tools that simplify data acquisition from density functional theory (DFT) and validation of trained machine learning models using the molSimplify automatic design (mAD) workflow. We demonstrate this workflow by training and comparing the performance of LASSO, kernel ridge regression (KRR), and artificial neural network (ANN) models using heuristic, topological revised autocorrelation (RAC) descriptors we have recently introduced for machine learning inorganic chemistry. On a series of open shell transition metal complexes, we evaluate set aside test errors of these models for predicting the HOMO level and HOMO-LUMO gap. The best performing models are ANNs, which show 0.15 and 0.25 eV test set mean absolute errors on the HOMO level and HOMO-LUMO gap, respectively. Poor performing KRR models using the full 153-feature RAC set are improved to nearly the same performance as the ANNs when trained on down-selected subsets of 20-30 features. Analysis of the essential descriptors for HOMO and HOMO-LUMO gap prediction as well as comparison to subsets previously obtained for other properties reveals the paramount importance of non-local, steric properties in determining frontier molecular orbital energetics. We demonstrate our model performance on diverse complexes and in the discovery of molecules with target HOMO-LUMO gaps from a large 15,000 molecule design space in minutes rather than days that full DFT evaluation would require.
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Identifying key descriptors or features in a structure-property relationship mapping has been demonstrated as an approach to revealing design principles and enabling iterative design.
“Identifying key descriptors or features in a structure-property relationship mapping has been demonstrated as an approach to revealing design principles (18,22,32,52) and enabling iterative design (70).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [22]
Section 4a (page unavailable) says feature selection identifies the relative importance of descriptors, while Section 2b (page unavailable) says analyzed results guide iterative discovery in mAD. The paper does not establish that identifying key descriptors itself enables that iterative design; it presents these as separate parts of the workflow. (LLM, conf=0.82)
Experimental — accuracy not yet measuredIn some cases, deep learning models have been developed to predict frontier orbital energies, which can be applied to explain experimental activity of catalysts known to be correlated to such energies.
“In some cases, deep learning models (e.g., ANNs) have been developed to predict frontier orbital energies (22,43,86), which can be applied to explain experimental activity of catalysts known to be correlated to such energies (86).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [22]
The Abstract and Section 5 (page numbers unavailable in our copy) report ANN models that predict HOMO levels and HOMO–LUMO gaps in transition-metal complexes. They do not report using those predictions to explain experimental catalyst activity or establish a correlation between that activity and frontier-orbital energies. (LLM, conf=0.86)
Experimental — accuracy not yet measuredBy applying random forest-ranked recursive feature addition to KRR models, expected heuristics have been reinforced by feature selection approaches, such as the spin splitting of a complex being strongly dependent on the metal-local electronic environment.
“By applying random forest-ranked recursive feature addition to KRR models, expected heuristics have been reinforced by feature selection approaches (22,32,105), such as the spin splitting of a complex being strongly dependent on the metal-local electronic environment (e.g., from the electronegativities of surrounding atoms; Figure 5)”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [22]
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredOne-shot models such as LASSO or random forests are widely used both as ML models for property prediction and for selection of important features.
“In a similar fashion, one-shot models such as least absolute shrinkage and selection operator (LASSO) or random forests are widely used both as ML models for property prediction (61) and for selection of important features (22,32,40,43) (Figure 4).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [22]
When KRR models are applied with tailored feature sets, their prediction accuracy can rival or surpass deep learning models.
“When KRR models are applied with tailored feature sets, their prediction accuracy can rival or surpass (22) deep learning models (e.g., fully connected ANNs or convolutional neural networks).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [22]
Conversely, other properties, such as the frontier orbital energies, band gap, or ionization/redox potential, depend much more on the global structure of the molecule.
“Conversely, other properties, such as the frontier orbital energies (22), band gap (44, 105), or ionization/redox potential (32,52), depend much more on the global structure of the molecule (Figure 5).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [22]
Beyond trial-and-error or ad hoc selection of descriptors, rigorous feature selection with ML models has emerged as a powerful tool for inferring design principles.
“Beyond trial-and-error or ad hoc selection of descriptors, rigorous feature selection with ML models has emerged as a powerful tool for inferring design principles (22,32,43,52,72,90,91).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [22]
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Machine Learning for Catalysis Informatics: Recent Applications and Prospects
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Understanding the diversity of the metal-organic framework ecosystem
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Self-citationSeeing Is Believing: Experimental Spin States from Machine Learning Model Structure Predictions
Taylor, M. G., Yang, T., Lin, S., Nandy, A., Janet, J. P., Duan, C., & Kulik, H. J. (2020) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.0c01458 · Cited by 81 · see citing works
Self-citationMachine Learning for the Discovery, Design, and Engineering of Materials.
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Self-citationLiu, F., Duan, C., & Kulik, H. J. (2020) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.0c02288 · Cited by 58 · see citing works
Self-citationEnumeration of <i>de novo</i> inorganic complexes for chemical discovery and machine learning
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Self-citationDuan, C., Chen, S., Taylor, M. G., Liu, F., & Kulik, H. J. (2021) · Chemical Science · doi:10.1039/d1sc03701c · Cited by 40 · see citing works
Self-citation
- Authors
- Nandy, A., Duan, C., Janet, J. P., Gugler, S., & Kulik, H. J.
- Affiliations
- Massachusetts Institute of Technology (US)
- ETH Zurich (CH)
- Corresponding author
- Kulik, Heather J.
- Venue
- Industrial & Engineering Chemistry Research
- Publisher
- American Chemical Society (ACS)
- Published
- 2018-09-24
- Volume
- 57
- Issue
- 42
- Pages
- 13973-13986
- ISSN
- 0888-5885 (ISSN-L)
- 1520-5045
- OpenAlex
- W2892439819
- Cited by
- 161
- References
- 98
- Citations by year
- 2026: 12 · 2025: 19 · 2024: 18 · 2023: 20 · 2022: 21 · 2021: 30 · 2020: 21 · 2019: 18 · 2018: 2
- FWCI
- 6.63
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Licence
- cc-by-nc-nd
- Locations
- Industrial & Engineering Chemistry Research (publishedVersion)
- ChemRxiv (acceptedVersion, cc-by-nc-nd)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- Royal College of Surgeons in Ireland (submittedVersion, cc-by-nc-nd)
- Funders
- Defense Advanced Research Projects Agency (D18AP00039)
- Massachusetts Institute of Technology (2014, 2017)
- Office of Naval Research (N00014-17-1-2956, N00014-18-1-2434)
- U.S. Department of Energy (DE-SC0018096)
- Division of Chemical, Bioengineering, Environmental, and Transport Systems (CBET-1704266)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Keywords
- machine learning, electronic structure prediction, HOMO energy level, HOMO-LUMO gap, descriptor selection, artificial neural networks, kernel ridge regression, LASSO, frontier molecular orbitals, steric effects, density functional theory
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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