Multidimensional Assembly of Polynuclear Osmium–Organic π-Clusters: Aromatic Synergy-Driven Enhancement of Third-Order Nonlinear Optical Responses

Abstract

Third-order nonlinear optical (NLO) materials are critical for applications such as optical limiting, all-optical switching, and ultrafast photonic devices, yet their performance remains constrained by the intricate balance between electronic delocalization and dimensional synergy. This study demonstrates a multidimensional assembly strategy to engineer aromatic synergy in osmium–organic π-clusters, achieving unprecedented enhancement of third-order NLO response. Guided by the concept of metal–organic π-cluster, we design a prototypical Os₃-plane unit as a foundational building block. Through horizontal covalent extension (C─C bonding) and vertical metallophilic stacking (Os─Os interactions), four hierarchical architectures (Os₆-prism, Os₆-plane, Os₉-prism, and Os₉-plane) are constructed, each exhibiting amplified NLO properties. Systematic analysis reveals that horizontal assembly enhances in-plane π-conjugation through quasi-two-dimensional π-delocalization, while vertical stacking facilitates interlayer π-orbital overlap. The novel structure, constructed via a multidimensional assembly strategy, exhibits a narrow HOMO–LUMO gap. The expanded π-delocalization reduces exciton binding energy, promotes electron delocalization, and consequently yields a stronger third-order NLO response. The Os₉-plane exhibits excellent third-order NLO response coefficient (γ = 2.93 × 10⁷ a.u.), which is two orders of magnitude higher than that of the Os₃-plane. This work establishes a paradigm of synergistic integration between multidimensional assembly and aromatic π-conjugation for enhanced NLO performance, opening new avenues for optoelectronic material design.

Keywords

aromaticity / DFT / electron delocalization / metal–organic π-cluster / third-order nonlinear optics

References

[1] T. M. Lowry, “The Electronic Theory of Valency,” Nature 121 (1928): 527–531.

[2] J. Liu, J. Li, Z. Xu, et al., “On-Surface Preparation of Coordinated Lanthanide-Transition-Metal Clusters,” Nature Communications 12 (2021): 1619.

[3] L. Lu, L. Shengqiu, L. Jin, et al., “Spatiotemporal Studies of Molecular Clusters With Neutron Scattering Methodology,” Chinese Journal of Structural Chemistry 42 (2023): 100102.

[4] Z. Wang, Y. Yan, J. Chen, Q.-H. Li, and J. Zhang, “Designed Metal–Organic π-Clusters Combining the Aromaticity of the Metal Cluster and Ligands for a Third-Order Nonlinear Optical Response,” Materials Horizons 11 (2024): 297–302.

[5] Z. Wang, W. Yan, G. Zhao, et al., “Novel Third-Order Nonlinear Optical Materials With Craig-Möbius Aromaticity,” Journal of Physical Chemistry Letters 12 (2021): 11784–11789.

[6] Y. Yan, J. Chen, Z. Wang, et al., “Novel Flexible Aromatic Cu₃ Metal-Organic π-Cluster for Electrocatalytic CO₂ Reduction Reaction,” Surfaces and Interfaces 48 (2024): 104349.

[7] X. Kong, P.-P. Zhou, and Y. Wang, “Chalcogen⋅ ⋅π Bonding Catalysis,” Angewandte Chemie International Edition 60 (2021): 9395–9400.

[8] T. Nishiuchi, K. Kisaka, and T. Kubo, “Synthesis of Anthracene-Based Cyclic π-Clusters and Elucidation of Their Properties Originating From Congested Aromatic Planes,” Angewandte Chemie International Edition 60 (2021): 5400–5406.

[9] Z. Wang, Y.-H. Fang, H. Lin, et al., “Bucket Effect to Improve Third-Order Nonlinear Optical Response on Metal-Heteroaromatic Compounds,” Chinese Journal of Chemistry 40 (2022): 2611–2617.

[10] G. Jiang, J. Yu, J. Wang, and B. Z. Tang, “Ion−π Interactions for Constructing Organic Luminescent Materials,” Aggregate 3 (2022): e285.

[11] D. R. Kanis, M. A. Ratner, and T. J. Marks, “Design and Construction of Molecular Assemblies With Large Second-Order Optical Nonlinearities. Quantum Chemical Aspects,” Chemical Reviews 94 (1994): 195–242.

[12] Y.-J. Liu, Q.-H. Li, D.-J. Li, X.-Z. Zhang, W.-H. Fang, and J. Zhang, “Designable Al 32-Oxo Clusters With Hydrotalcite-Like Structures: Snapshots of Boundary Hydrolysis and Optical Limiting,” Angewandte Chemie International Edition 60 (2021): 4849–4854.

[13] C.-Y. Zhu, Z. Zhang, J.-K. Qin, et al., “Two-dimensional Semiconducting SnP2Se6 With Giant Second-Harmonic-Generation for Monolithic On-Chip Electronic-Photonic Integration,” Nature Communications 14 (2023): 2521.

[14] X. Han, F. Ge, J. Xu, and X.-H. Bu, “Aggregation-Induced Emission Materials for Nonlinear Optics,” Aggregate 2 (2021): e28.

[15] S.-T. Wang, Y.-J. Liu, C.-C. Feng, W.-H. Fang, and J. Zhang, “The Largest Aluminum Molecular Rings: Phenol-Thermal Synthesis, Photoluminescence, and Optical Limiting,” Aggregate 4 (2023): e264.

[16] X. Liu, Q. Guo, and J. Qiu, “Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics,” Advanced Materials 29 (2017): 1605886.

[17] Z.-Z. Ma, Q.-H. Li, Z. Wang, Z.-G. Gu, and J. Zhang, “Electrically Regulating Nonlinear Optical Limiting of Metal-Organic Framework Film,” Nature Communications 13 (2022): 6347.

[18] S.-J. Bao, Z.-M. Xu, Y. Ju, et al., “The Covalent and Coordination Co-Driven Assembly of Supramolecular Octahedral Cages With Controllable Degree of Distortion,” Journal of the American Chemical Society 142 (2020): 13356–13361.

[19] Z.-K. Wang, M.-H. Du, P. Braunstein, and J.-P. Lang, “A Cut-to-Link Strategy for Cubane-Based Heterometallic Sulfide Clusters With Giant Third-Order Nonlinear Optical Response,” Journal of the American Chemical Society 145 (2023): 9982–9987.

[20] B. Xu, D. Chen, K. Ruan, et al., “Metal-Centred Planar [15]Annulenes,” Nature 641 (2025): 106–111.

[21] M. Luo, D. Chen, Q. Li, and H. Xia, “Unique Properties and Emerging Applications of Carbolong Metallaaromatics,” Accounts of Chemical Research 56 (2023): 924–937.

[22] Z. Wang, G. Zhao, W. Yan, et al., “Tin Metal Cluster Compounds as New Third-Order Nonlinear Optical Materials by Computational Study,” Journal of Physical Chemistry Letters 12 (2021): 7537–7544.

[23] G. A. N. Dong-Er, Z. Zhang, L. I. Qiao-Hong, and L. I. Wen-Mu, “Oligo(Aromatic Ether Sulfone)-F as a Nonlinear Polarized Polymeric Material: An Experiment and DFT Study,” Chinese Journal of Structural Chemistry 40 (2021): 383–393.

[24] C. Zhu, S. Li, M. Luo, et al., “Stabilization of Anti-Aromatic and Strained Five-Membered Rings With a Transition Metal,” Nature Chemistry 5 (2013): 698–703.

[25] R. Herges and D. Geuenich, “Delocalization of Electrons in Molecules,” Journal of Physical Chemistry A 105 (2001): 3214–3220.

[26] D. Geuenich, K. Hess, F. Köhler, and R. Herges, “Anisotropy of the Induced Current Density (ACID), a General Method To Quantify and Visualize Electronic Delocalization,” Chemical Reviews 105 (2005): 3758–3772.

[27] S. Klod and E. Kleinpeter, “Ab Initio Calculation of the Anisotropy Effect of Multiple Bonds and the Ring Current Effect of Arenes—Application in Conformational and Configurational Analysis.” Journal of the Chemical Society, Perkin Transactions 2 10 (2001): 1893–1898.

[28] Z. Liu, T. Lu, and Q. Chen, “An sp-Hybridized All-Carboatomic Ring, Cyclo[18]Carbon: Bonding Character, Electron Delocalization, and Aromaticity,” Carbon 165 (2020): 468–475.

[29] P. R. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, and N. J. R. van Eikema Hommes, “Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe,” Journal of the American Chemical Society 118 (1996): 6317–6318.

[30] Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta, and P. V. R. Schleyer, “Nucleus-Independent Chemical Shifts (NICS) as an Aromaticity Criterion,” Chemical Reviews 105 (2005): 3842–3888.

[31] D. Y. Zubarev and A. I. Boldyrev, “Developing Paradigms of Chemical Bonding: Adaptive Natural Density Partitioning,” Physical Chemistry Chemical Physics 10 (2008): 5207–5217.

[32] M.-Y. Gao, Z. Wang, Q.-H. Li, et al., “Black Titanium-Oxo Clusters With Ultralow Band Gaps and Enhanced Nonlinear Optical Performance,” Journal of the American Chemical Society 144 (2022): 8153–8161.

[33] K. Sasagane, F. Aiga, and R. Itoh, “Higher-Order Response Theory Based on the Quasienergy Derivatives: The Derivation of the Frequency-Dependent Polarizabilities and Hyperpolarizabilities,” Journal of Chemical Physics 99 (1993): 3738–3778.

[34] M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al. “Gaussian 16 Rev. B.01,” 2016, 54, Gaussian, Inc., Wallingford.

[35] P. J. Hay and W. R. Wadt, “Ab Initio Effective Core Potentials for Molecular Calculations. Potentials for the Transition Metal Atoms Sc to Hg,” Journal of Chemical Physics 82 (1985): 270–283.

[36] W. R. Wadt and P. J. Hay, “Ab Initio Effective Core Potentials for Molecular Calculations. Potentials for Main Group Elements Na to Bi,” Journal of Chemical Physics 82 (1985): 284–298.

[37] P. J. Hay and W. R. Wadt, “Ab Initio Effective Core Potentials for Molecular Calculations. Potentials for K to Au Including the Outermost Core Orbitals,” Journal of Chemical Physics 82 (1985): 299–310.

[38] A. D. Becke, “Density-Functional Exchange-Energy Approximation With Correct Asymptotic Behavior,” Physical Review A 38 (1988): 3098–3100.

[39] C. Lee, W. Yang, and R. G. Parr, “Development of the Colle-Salvetti Correlation-Energy Formula Into a Functional of the Electron Density,” Physical Review B 37 (1988): 785–789.

[40] B. Miehlich, A. Savin, H. Stoll, and H. Preuss, “Results Obtained With the Correlation Energy Density Functionals of Becke and Lee, Yang and Parr,” Chemical Physics Letters 157 (1989): 200–206.

[41] A. D. Becke, “A New Mixing of Hartree–Fock and Local Density-Functional Theories,” Journal of Chemical Physics 98 (1993): 1372–1377.

[42] P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, “Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields,” Journal of Physical Chemistry 98 (1994): 11623–11627.

[43] S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, “A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu,” Journal of Chemical Physics 132 (2010): 154104.

[44] F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, “Electric Field Modulated Nonlinear Optical Properties of Donor-Acceptor Polyenes: Sum-Over-States Investigation of the Relationship Between Molecular Polarizabilities (.alpha., .beta., and .gamma.) and Bond Length Alternation,” Journal of the American Chemical Society 116 (1994): 10703–10714.

[45] T. Lu and F. Chen, “Multiwfn: A Multifunctional Wavefunction Analyzer,” Journal of Computational Chemistry 33 (2012): 580–592.

[46] W. Humphrey, A. Dalke, and K. Schulten, “VMD: Visual Molecular Dynamics,” Journal of Molecular Graphics 14 (1996): 33–38.

RIGHTS & PERMISSIONS

2025 The Author(s). Aggregate published by SCUT, AIEI, and John Wiley & Sons Australia, Ltd.