Abstract
Molecules capable of repeatable, narrow-band spontaneous photon scattering are prized for direct laser cooling and quantum state detection. Recently, large molecules incorporating phenyl rings have been shown to exhibit a high probability of returning to the same vibrational state after photon emission, a behaviour previously observed in small molecules, although it is not yet known if the high vibrational-mode density of even larger species will eventually compromise optical cycling. Here we systematically increase the size of hydrocarbon ligands attached to single alkaline-earth phenoxides from –H to –C14H19 while measuring the vibrational branching fractions of the optical transition. We find that varying the ligand size from one to more than 30 atoms does not systematically reduce the cycle closure, which remains around 90%. Theoretical extensions to larger diamondoids and diamond surfaces suggest that alkaline-earth phenoxides may maintain their desirable scattering behaviour as the system size grows further, with no indication of an upper limit.

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Data availability
The datasets and codes for Figs. 2–5 and Extended Data Figs. 1 and 2 are available from Zenodo via https://doi.org/10.5281/zenodo.14496831. (ref. 72). All other data supporting the findings of this study are available in the Supplementary Information files. Source data are provided with this paper.
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Acknowledgements
This work was supported by the NSF Center for Chemical Innovation Phase I (grant number CHE-2221453, A.A., E.R.H.), AFOSR (grant number FA9550-20-1-0323, E.R.H., W.C.C.), the NSF (grant numbers OMA-2016245, W.C.C., E.R.H.; PHY-2207985, W.C.C.; and DGE-2034835). This research is funded in part by the Gordon and Betty Moore Foundation (DOI: 10.37807/GBMF11566, W.C.C.). Computational resources were provided by XSEDE and UCLA IDRE shared cluster hoffman2. The authors acknowledge computational resources from the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility.
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G.-Z.Z. and G.L. constructed the spectroscopy apparatus. G.-Z.Z. drafted the paper, G.L., T.K., W.C.C. and A.M. contributed to the writing of the paper. G.-Z.Z., G.L., H.Z., T.K. and A.M. acquired the experimental data. T.K., H.W.T.M., R.H.L., R.C. and D.U. performed the calculations. G.-Z.Z., G.L., T.K. and A.M. analysed the data. H.Z., T.K. and A.M. contributed to the data analysis. A.M. developed the synthesis and contributed to the species production. A.N.A., W.C.C. and G.-Z.Z. conceived the idea. W.C.C., E.R.H., G.-Z.Z. and M.A.G.-G. coordinated the experimental research. A.N.A. coordinated the theoretical research.
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Extended data
Extended Data Fig. 1 Dispersed spectra of the \(\widetilde{B}\to \widetilde{X}\) transitions of SrOPh-x.
a, SrOPh-CH3. b,SrOPh-\({\rm{C}}{({{\rm{CH}}}_{3})}_{3}\). c, SrOPh-Ad. d, SrOPh-1diA. e, SrOPh-4diA. The black curves and red dashed curves show the experimental spectra and the Voigt profile fits, respectively. The blue sticks indicate the theoretical predictions of the intensity ratios and harmonic frequencies of the vibrational decays. The two cyan dashed sticks near -200 cm−1 in a represent the vibrational perturbation theory calculation of the Fermi resonance coupling between the fundamental mode ν5 and the combination mode ν2 + ν4. The lines labeled with the + signs correspond to the strontium atomic lines. The vibrational decays are labeled with notation \({n}_{i}^{j}\), where n denotes the vibrational mode νn, i and j are the vibrational quantum numbers in the ground and excited states, respectively. ‘+’ labels denote strontium atomic lines produced from laser ablation of SrH2.
Extended Data Fig. 2 Dispersed spectra of the \(\widetilde{A}/\widetilde{B}\to \widetilde{X}\) transitions of CaOPh-x species.
a-b, CaOPh-CH3. c-d, CaOPh-\({\rm{C}}{({{\rm{CH}}}_{3})}_{3}\). e-f, CaOPh-Ad. g-h, CaOPh-1diA. i-j, CaOPh-4diA. The black curves and red dashed curves show the experimental spectra and the Voigt profile fits, respectively. The blue sticks indicate the theoretical predictions of the intensity ratios and harmonic frequencies of the vibrational decays. The vibrational decays are labeled with notation \({n}_{i}^{j}\), where n represents the vibrational mode νn, i and j are the vibrational quantum numbers in the ground and excited states, respectively. * indicates the calcium atomic lines induced by the laser ablation of the calcium/CaH2 targets.
Supplementary information
Supplementary Information
Supplementary Methods, Tables 1–14 and Figs. 1–19.
Source data
Source Data Fig. 2
Datasets of dispersed spectra of all molecules and MATLAB codes. Source Data Extended Data Fig. 1 Datasets of dispersed spectra of all molecules and MATLAB codes. Source Data Extended Data Fig. 2 Datasets of dispersed spectra of all molecules and MATLAB codes.
Source Data Fig. 3
Data and MATLAB codes.
Source Data Fig. 4
Data and MATLAB codes.
Source Data Fig. 5
Data and MATLAB codes.
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Lao, G., Khvorost, T., Macias, A. et al. Bottom-up approach to making larger hydrocarbon molecules capable of optical cycling. Nat. Chem. (2025). https://doi.org/10.1038/s41557-025-01965-y
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DOI: https://doi.org/10.1038/s41557-025-01965-y