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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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).
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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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.
The authors declare no competing financial interest.
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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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