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A transferable recommender approach for selecting the best density functional approximations in chemical discovery

Nature Computational Science volume 3, pages 38–47 (2023)Cite this article

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A preprint version of the article is available at arXiv.

Abstract

Approximate density functional theory has become indispensable owing to its balanced cost–accuracy trade-off, including in large-scale screening. To date, however, no density functional approximation (DFA) with universal accuracy has been identified, leading to uncertainty in the quality of data generated from density functional theory. With electron density fitting and Δ-learning, we build a DFA recommender that selects the DFA with the lowest expected error with respect to the gold standard (but cost-prohibitive) coupled cluster theory in a system-specific manner. We demonstrate this recommender approach on the evaluation of vertical spin splitting energies of transition metal complexes. Our recommender predicts top-performing DFAs and yields excellent accuracy (about 2 kcal mol−1) for chemical discovery, outperforming both individual Δ-learning models and the best conventional single-functional approach from a set of 48 DFAs. By demonstrating transferability to diverse synthesized compounds, our recommender potentially addresses the accuracy versus scope dilemma broadly encountered in computational chemistry.

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Fig. 1: Workflow for the DFA recommender.
Fig. 2: Performance of Δ-learning models and the recommender on the VSS-452 set.
Fig. 3: Analysis of Δ-learning model focus using virtual adversarial attack.
Fig. 4: Recommended DFAs by ligand field strength.
Fig. 5: Performance of Δ-learning models and the recommender on the CSD-76 set.

Data availability

Source data for Figs. 2–5 are available with this manuscript. All structures and energies used to train the models along with the trained machine learning models are available at ref. 56 (https://doi.org/10.5281/zenodo.7350957).

Code availability

All models and Python scripts to reproduce results reported in this work can be found at Ref. 56 (https://doi.org/10.5281/zenodo.7350957).

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Acknowledgements

This work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing, Office of Basic Energy Sciences, via the Scientific Discovery through Advanced Computing program (R.M.) as well as by the Office of Naval Research under grant nos. N00014-18-1-2434 (A.N.) and N00014-20-1-2150 (C.D.). N.A. was partially supported by the U.S. Department of Energy under grant no. DE-NA0003965. C.D. was partially supported by a seed fellowship from the Molecular Sciences Software Institute under NSF grant OAC-1547580. A.N. and N.A. were partially supported by a National Science Foundation Graduate Research Fellowship under grants nos. 1122374 and 1745302, respectively. The authors thank A. H. Steeves for a critical reading of the manuscript.

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Authors and Affiliations

  1. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Chenru Duan, Aditya Nandy, Ralf Meyer, Naveen Arunachalam & Heather J. Kulik

  2. Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA

    Chenru Duan, Aditya Nandy & Heather J. Kulik

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Contributions

C.D.: conceptualization, methodology, software, validation, investigation, data curation, writing of original draft, review and editing, and visualization. A.N.: data curation, software, and review and editing. R.M. data curation, software, validation, and review and editing. N.A.: software, and review and editing. H.J.K.: conceptualization, supervision, project administration, funding acquisition, and review and editing.

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Correspondence to Heather J. Kulik.

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Nature Computational Science thanks Jan Hermann, Stefan Vuckovic and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Handling editor: Kaitlin McCardle, in collaboration with the Nature Computational Science team.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–16, Section 1, Tables 1–9 and references.

Source data

Source Data Fig. 2.

Part a: MAEs of all 48 DFAs and recommender MAE. Part B: the recommender error by point for the histogram. Part d: likelihood of occurring in top five from recommender and ground truth to build histogram.

Source Data Fig. 3.

Part A: virtual adversarial attack scores by element. Part B files: value over all 452 points for the contribution of metal, first coordination sphere, second coordination sphere and global features for each of the functionals shown to compute the mean and s.d.

Source Data Fig. 4.

Part A and B file: binned performance of the functionals by the DLPNO-CCSD(T) spin splitting: overall MAE in the bin, s.d. in the bin, recommender MAE and recommender s.d. in the bin along with the fraction selected for each of 48 DFAs.

Source Data Fig. 5.

Part A: MAE of each transfer learning model on the CSD-76 data set and the recommender (VSS-452 data are from Fig. 2). Part B: data for histogram of errors for the CSD-76 data set. Part C: likelihood of being in top five for CSD-76 from ground truth and from recommender (data from VSS-452 are from Fig. 2).

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Duan, C., Nandy, A., Meyer, R. et al. A transferable recommender approach for selecting the best density functional approximations in chemical discovery. Nat Comput Sci 3, 38–47 (2023). https://doi.org/10.1038/s43588-022-00384-0

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