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Directional multiobjective optimization of metal complexes at the billion-system scale

A preprint version of the article is available at ChemRxiv.

Abstract

The discovery of transition metal complexes (TMCs) with optimal properties requires large ligand libraries and efficient multiobjective optimization algorithms. Here we provide the tmQMg-L library, containing 30k diverse and synthesizable ligands with robustly assigned charges and metal coordination modes. tmQMg-L enabled the generation of 1.37 million palladium TMCs, which were used to develop and benchmark the Pareto-Lighthouse multiobjective genetic algorithm (PL-MOGA). With fine control over aim and scope, this algorithm maximized both the polarizability and highest occupied molecular orbital–lowest unoccupied molecular orbital gap of the TMCs within selected regions of the Pareto front, without requiring prior knowledge on the objective limits. Instead of genetic operations on small ligand fragments, the PL-MOGA did whole-ligand mutation and crossover operations, which in chemical spaces containing billions of systems, yielded thousands of highly diverse TMCs in an interpretable manner.

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Fig. 1: PL-MOGA algorithm.
Fig. 2: Derivation of the tmQMg-L ligand dataset.
Fig. 3: Size and distribution of the chemical spaces.
Fig. 4: Multiobjective (α, ϵ) optimizations within the 1.37M space.
Fig. 5: Interpretability and diversity.
Fig. 6: Pareto front distributions and samples in the billion spaces.

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Data availability

The tmQMg-L dataset can be accessed at https://github.com/hkneiding/tmQMg-L, including the data for the charge assignment benchmark and the 1.37M space. The dataset is also available via Zenodo at https://doi.org/10.5281/zenodo.10374523 (ref. 64). In addition to the geometric and electronic structure information, it provides Weisfeiler–Lehman graph hashes65. All data are openly available. Source data are provided with this paper. The larger datasets may require Linux software to be visualized.

Code availability

The PL-MOGA code is available from https://github.com/hkneiding/PL-MOGA and Zenodo via https://doi.org/10.5281/zenodo.10663863 (ref. 66), including the DFT geometries of selected TMC hits and the weighted-sum benchmark. The code includes a command line functionality, together with documentation and installation instructions. All code is openly available.

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Acknowledgements

European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement number 945371 (H.K.). This article reflects only the author’s view and the REA is not responsible for any use that may be made of the information it contains. Research Council of Norway (RCN) FRIPRO program supporting the CO2pCat project, with number 314321 (A.N.). RCN FRIPRO program supporting the catLEGOS project, with number 325003 (D.B.). RCN support through the Centers of Excellence program, including the Hylleraas Centre, with project number 262695, and the Sigma2 – National Infrastructure for High Performance Computing and Data Storage in Norway, with grant number NN4654K (H.K., A.N. and D.B.). We also thank M. Strandgaard and T. Linjordet for helpful discussions and for reviewing preliminary versions of this manuscript.

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Contributions

H.K. was the main developer of the tmQMg-L dataset, the 1.37M space and the PL-MOGA algorithm. H.K. also derived the combinatorics of the square planar TMC space and developed the concept of a generative model based on whole-ligand multiple-site genetic operations. A.N. and D.B. developed the concept of extracting the ligand charges from the natural Lewis structures. All authors made substantial contributions to the conception and design of the work. D.B. was the main contributor to the writing and revision of the manuscript, as well as to the definition, supervision and funding of the research project.

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Correspondence to David Balcells.

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Nature Computational Science thanks Jan Jensen, Aditya Nandy and Robert Pollice for their contribution to the peer review of this work. Primary Handling Editor: Kaitlin McCardle, in collaboration with the Nature Computational Science team. Peer reviewer reports are available.

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Supplementary sections, Figs. 1–20, Equations 1–4, Algorithm 1 and Table 1.

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Kneiding, H., Nova, A. & Balcells, D. Directional multiobjective optimization of metal complexes at the billion-system scale. Nat Comput Sci 4, 263–273 (2024). https://doi.org/10.1038/s43588-024-00616-5

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