Rapid Detection of Strong Correlation with Machine Learning for Transition-Metal Complex High-Throughput Screening
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Abstract
Despite its widespread use in chemical discovery, approximate density functional theory (DFT) is poorly suited to many targets, such as those containing open-shell, 3d transition metals that can be expected to have strong multireference (MR) character. For discovery workflows to be predictive, we need automated, low-cost methods that can distinguish the regions of chemical space where DFT should be applied from those where it should not. We curate more than 4800 open-shell transition-metal complexes up to hundreds of atoms in size from prior high-throughput DFT studies and evaluate affordable, finite-temperature DFT fractional occupation number (FON)-based MR diagnostics. We show that intuitive measures of strong correlation (i.e., the HOMO–LUMO gap) are not predictive of MR character as judged by FON-based diagnostics. Analysis of independently trained machine learning (ML) models to predict HOMO–LUMO gaps and FON-based diagnostics reveals differences in the metal and ligand sensitivity of the two quantities. We use our trained ML models to rapidly evaluate MR character over a space of ∼187000 theoretical complexes, identifying large-scale trends in spin-state-dependent MR character and finding small HOMO–LUMO gap complexes while ensuring low MR character.
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Liu et al. observed that although multireference character is expected to be higher in low-spin states, this trend is seen for only some metals (e.g., Cr or Mn).
“Through this analysis, Liu et al. (44) observed that although multireference character is expected to be higher in low-spin states, this trend is seen for only some metals (e.g., Cr or Mn) (Figure 3).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [44]
Liu et al. applied an ANN trained to predict the multireference diagnostic r_ND to 3% mean absolute percent error (i.e., 0.018) to a theoretical space of 187.2k new complexes, only 1% of which had been seen in training data.
“Starting from a data set of 4,865 complexes, they applied an ANN trained to predict the multireference diagnostic r ND to 3% mean absolute percent error (i.e., 0.018) to a theoretical space of 187.2k new complexes, only 1% of which had been seen in training data.”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [44]
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 [44]
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Self-citationSears, J. S., & Sherrill, C. D. (2008) · The Journal of Physical Chemistry A · doi:10.1021/jp802249n · Cited by 35 · see citing works
Shen, J., Xu, E., Kou, Z., et al. (2011) · Physical Chemistry Chemical Physics · doi:10.1039/c0cp01103g · Cited by 17 · see citing works
Süß, D., Huber, S. E., & Mauracher, A. (2020) · The Journal of Chemical Physics · doi:10.1063/1.5143495 · Cited by 12 · see citing works
Quantitative estimation of uncertainties from wavefunction diagnostics
Sprague, M. K., & Irikura, K. K. (2015) · Highlights in theoretical chemistry · doi:10.1007/978-3-662-47051-0_28 · Cited by 8 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Nandy, A., Duan, C., Taylor, M. G., Liu, F., Steeves, A. H., & Kulik, H. J. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.1c00347 · Cited by 358 · see citing works
Self-citationMachine Learning for the Discovery, Design, and Engineering of Materials.
Duan, C., Nandy, A., & Kulik, H. J. (2022) · Annual Review of Chemical and Biomolecular Engineering · doi:10.1146/annurev-chembioeng-092320-120230 · Cited by 69 · see citing works
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
- Liu, F., Duan, C., & Kulik, H. J.
- Affiliations
- Massachusetts Institute of Technology (US)
- Corresponding author
- Kulik, Heather J.
- Venue
- The Journal of Physical Chemistry Letters
- Publisher
- American Chemical Society (ACS)
- Published
- 2020-08-31
- Volume
- 11
- Issue
- 19
- Pages
- 8067-8076
- ISSN
- 1948-7185 (ISSN-L)
- OpenAlex
- W3082636798
- Cited by
- 58
- References
- 109
- Citations by year
- 2026: 6 · 2025: 7 · 2024: 6 · 2023: 12 · 2022: 17 · 2021: 10
- FWCI
- 3.97
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Licence
- Locations
- The Journal of Physical Chemistry Letters (publishedVersion)
- ChemRxiv (acceptedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- Royal College of Surgeons in Ireland (submittedVersion, cc-by-nc-nd)
- Funders
- Defense Advanced Research Projects Agency (D18AP00039)
- American Association for the Advancement of Science (Marion Milligan Mason Award)
- Basic Energy Sciences (DE-SC0018096)
- Office of Naval Research (N00014-18-1-2434, N00014-20-1-2150)
- Division of Advanced Cyberinfrastructure (ACI-1547580 (MolSSI postdoctoral fellowship))
- Burroughs Wellcome Fund (Career Award at the Scientific Interface)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Keywords
- multireference character, transition metal complexes, open-shell systems, strong correlation, fractional occupation numbers, HOMO-LUMO gap, machine learning prediction, high-throughput screening, 3d transition metals, chemical space
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.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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