Abstract
Elasticity is ubiquitous and produces a spontaneously reversible response to applied stress1. Despite the utility and importance of this property in regard to scientific and engineering applications, the atomic-scale location of the force that returns an object to its original shape remains elusive in molecular crystals. Here we use a series of density functional theory calculations to locate precisely where the energy is stored when single crystals of three molecular materials are placed under elastic stress. We show for each material that different intermolecular interactions are responsible for the restoring force under both expansive and compressive strain. These findings provide insight into the elastic behaviour of crystalline materials that is needed for more efficient design of flexible technologies and future smart devices.
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Data availability
The results of calculations are provided as Supplementary Data 1–4. Source data are provided with this paper.
Code availability
The Python scripts used to produce the extrapolated atomic coordinates as described in Supplementary Information are available as Supplementary Code 1 or from the authors.
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Acknowledgements
A.J.T. thanks AINSE Limited for providing financial assistance (PGRA Award). B.S.K.C. thanks the University of Queensland for Research Training Program financial support. The University of Queensland Research Computing Centre, Phoenix HPC service at the University of Adelaide and Pawsey Supercomputing Research Centre through the National Computational Merit Allocation Scheme are thanked for providing high-performance, computing resources. This research was supported by the Australian Government’s National Collaborative Research Infrastructure Strategy (NCRIS). B.J.P. thanks the Australian Research Council for financial support (DP181006201). J.D.E. is a recipient of an Australian Research Council Discovery Early Career Award (DE220100163). We thank A. Grosjean for providing input into the design of CrystalExplorer calculations, and for comments on an early version of the paper.
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Contributions
B.S.K.C. performed DFT calculations for [CuL12]. A.J.T. wrote the Python scripts for structure extrapolation and undertook primary data analysis. E.P.K. performed VASP calculations. J.A.P. and A.J.T. performed CrystalExplorer calculations. J.D.E. performed calculations for [CuL22] and [CuL32]. B.J.P., M.A.S., J.C.M. and J.K.C. directed the research. All authors contributed to the analysis of results and writing of the paper.
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Nature Materials thanks Shotaro Hayashi, Satoshi Takamizawa and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Supplementary information
Supplementary Information
Computational methods, extrapolation methodology, calculated mechanical properties, calculation results, curve fitting and single-crystal cantilevers.
Supplementary Data 1
Electronic copy of Supplementary Table 1.
Supplementary Data 2
Electronic copy of Supplementary Table 2.
Supplementary Data 3
Results of calculations for complex of L1.
Supplementary Data 4
Results of calculations for complexes of L2 and L3.
Supplementary Code 1
Python extrapolation scripts.
Supplementary Video 1
Video of cantilever.
Supplementary Video 2
Video of cantilever.
Supplementary Video 3
Video of cantilever.
Supplementary Video 4
Video of cantilever.
Source data
Source Data Fig. 3
Data used for plotting and curve fitting in Fig. 3.
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Thompson, A.J., Chong, B.S.K., Kenny, E.P. et al. Origins of elasticity in molecular materials. Nat. Mater. 24, 356–360 (2025). https://doi.org/10.1038/s41563-025-02133-w
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DOI: https://doi.org/10.1038/s41563-025-02133-w
