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Triangulene
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<h2 id="ntriangulenes">[<i>n</i>]Triangulenes</h2> <p>Triangulene, as defined here, is a member of a wider class of [<i>n</i>]triangulenes, where <i>n</i> is the number of hexagons along an edge of the molecule. Thus, triangulene may also be referred to as [3]triangulene. </p> <h3>Theory</h3> <p>A <a href="/facts/Tight_binding/1Iq7SSzo">tight-binding</a> description of the <a href="/facts/Molecular_orbitals/0dP30jaa">molecular orbitals</a> of [<i>n</i>]triangulenes predicts<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> that [<i>n</i>]triangulenes have (<i>n</i> − 1) unpaired electrons, which are associated to (<i>n</i> − 1) non-bonding states. When electron–electron interactions are included, theory predicts<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a><a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a><a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> that the ground state total spin quantum number <i>S</i> of [<i>n</i>]triangulenes is <i>S</i> = <i>n</i> − 1/2. Thus, [3]triangulenes are predicted to have an <i>S</i> = 1 ground state. The intramolecular exchange interaction in triangulene, which determines the energy difference between the <i>S</i> = 1 ground state and the <i>S</i> = 0 excited state, is predicted to be the largest<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> among all <a href="/facts/Polycyclic_aromatic_hydrocarbon/K52xSfNC">polycyclic aromatic hydrocarbon</a> (PAH) diradicals, due to maximum overlap of the wave function of the unpaired electrons. </p><p>The ground state spin of [<i>n</i>]triangulenes can be rationalized<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> in terms of a theorem<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> by <a href="/facts/Elliott_H._Lieb/Vr4mrmtb">Elliot H. Lieb</a>, which relates, for a bipartite lattice, the ground state spin of the <a href="/facts/Hubbard_model/5pphLNde">Hubbard model</a> at half filling to the sublattice imbalance. </p> <h3>Experiments</h3> <p>So far, the ultra-high vacuum on-surface syntheses of [<i>n</i>]triangulenes with <i>n</i> = 3,<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> 4,<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> 5<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> and 7<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> (the hitherto largest triangulene homologue) have been reported. In addition, the on-surface synthesis of [3]triangulene dimers<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> has also been reported, where <a href="/facts/Inelastic_electron_tunneling_spectroscopy/V9v3kP06">inelastic electron tunneling spectroscopy</a> provides a direct evidence of a strong antiferromagnetic coupling between the triangulenes. In 2021, an international team of researchers reported the fabrication of [3]triangulene-based quantum spin chains on a gold surface,<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a> where signatures of both spin fractionalization and Haldane gap were observed. </p> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "biradical". doi:10.1351/goldbook.B00671 <a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" target="_blank">/wiki/International_Union_of_Pure_and_Applied_Chemistry</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>"triangulene | C22H12 | ChemSpider". www.chemspider.com. Retrieved 2017-02-19. <a href="http://www.chemspider.com/Chemical-Structure.58825768.html" target="_blank">http://www.chemspider.com/Chemical-Structure.58825768.html</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Ball, Philip (February 2017). "Elusive triangulene created by moving atoms one at a time". Nature. 542 (7641): 284–285. Bibcode:2017Natur.542..284B. doi:10.1038/nature.2017.21462. PMID 28202993. S2CID 4398214. <a href="https://doi.org/10.1038%2Fnature.2017.21462" target="_blank">https://doi.org/10.1038%2Fnature.2017.21462</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Pavliček, Niko; Mistry, Anish; Majzik, Zsolt; Moll, Nikolaj; Meyer, Gerhard; Fox, David J.; Gross, Leo (April 2017). "Synthesis and characterization of triangulene" (PDF). Nature Nanotechnology. 12 (4): 308–311. Bibcode:2017NatNa..12..308P. doi:10.1038/nnano.2016.305. PMID 28192389. <a href="http://wrap.warwick.ac.uk/86722/1/WRAP_ch-030317-wrap_-cusersdavid_foxdesktop40triangulene_complete_accepted.pdf" target="_blank">http://wrap.warwick.ac.uk/86722/1/WRAP_ch-030317-wrap_-cusersdavid_foxdesktop40triangulene_complete_accepted.pdf</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Morita, Yasushi; Suzuki, Shuichi; Sato, Kazunobu; Takui, Takeji (2011). "Synthetic organic spin chemistry for structurally well-defined open-shell graphene fragments". Nature Chemistry. 3 (3): 197–204. Bibcode:2011NatCh...3..197M. doi:10.1038/nchem.985. PMID 21336324. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Pavliček, Niko; Mistry, Anish; Majzik, Zsolt; Moll, Nikolaj; Meyer, Gerhard; Fox, David J.; Gross, Leo (April 2017). "Synthesis and characterization of triangulene" (PDF). Nature Nanotechnology. 12 (4): 308–311. Bibcode:2017NatNa..12..308P. doi:10.1038/nnano.2016.305. PMID 28192389. <a href="http://wrap.warwick.ac.uk/86722/1/WRAP_ch-030317-wrap_-cusersdavid_foxdesktop40triangulene_complete_accepted.pdf" target="_blank">http://wrap.warwick.ac.uk/86722/1/WRAP_ch-030317-wrap_-cusersdavid_foxdesktop40triangulene_complete_accepted.pdf</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Fernández-Rossier, J.; Palacios, J. J. (23 October 2007). "Magnetism in Graphene Nanoislands". Physical Review Letters. 99 (17): 177204. arXiv:0707.2964. Bibcode:2007PhRvL..99q7204F. doi:10.1103/PhysRevLett.99.177204. hdl:10045/25254. PMID 17995364. S2CID 9697828. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Fernández-Rossier, J.; Palacios, J. J. (23 October 2007). "Magnetism in Graphene Nanoislands". Physical Review Letters. 99 (17): 177204. arXiv:0707.2964. Bibcode:2007PhRvL..99q7204F. doi:10.1103/PhysRevLett.99.177204. hdl:10045/25254. PMID 17995364. S2CID 9697828. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Wang, Wei L.; Meng, Sheng; Kaxiras, Efthimios (1 January 2008). "Graphene NanoFlakes with Large Spin". Nano Letters. 8 (1): 241–245. Bibcode:2008NanoL...8..241W. doi:10.1021/nl072548a. PMID 18052302. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Güçlü, A. D.; Potasz, P.; Voznyy, O.; Korkusinski, M.; Hawrylak, P. (10 December 2009). "Magnetism and Correlations in Fractionally Filled Degenerate Shells of Graphene Quantum Dots". Physical Review Letters. 103 (24): 246805. arXiv:0907.5431. Bibcode:2009PhRvL.103x6805G. doi:10.1103/PhysRevLett.103.246805. PMID 20366221. S2CID 18754119. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Ortiz, Ricardo; Boto, Roberto A.; García-Martínez, Noel; Sancho-García, Juan C.; Melle-Franco, Manuel; Fernández-Rossier, Joaquı́n (11 September 2019). "Exchange Rules for Diradical π-Conjugated Hydrocarbons". Nano Letters. 19 (9): 5991–5997. arXiv:1906.08544. Bibcode:2019NanoL..19.5991O. doi:10.1021/acs.nanolett.9b01773. PMID 31365266. S2CID 195218794. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Fernández-Rossier, J.; Palacios, J. J. (23 October 2007). "Magnetism in Graphene Nanoislands". Physical Review Letters. 99 (17): 177204. arXiv:0707.2964. Bibcode:2007PhRvL..99q7204F. doi:10.1103/PhysRevLett.99.177204. hdl:10045/25254. PMID 17995364. S2CID 9697828. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Lieb, Elliott H. (6 March 1989). "Two theorems on the Hubbard model". Physical Review Letters. 62 (10): 1201–1204. Bibcode:1989PhRvL..62.1201L. doi:10.1103/PhysRevLett.62.1201. PMID 10039602. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Pavliček, Niko; Mistry, Anish; Majzik, Zsolt; Moll, Nikolaj; Meyer, Gerhard; Fox, David J.; Gross, Leo (April 2017). "Synthesis and characterization of triangulene" (PDF). Nature Nanotechnology. 12 (4): 308–311. Bibcode:2017NatNa..12..308P. doi:10.1038/nnano.2016.305. PMID 28192389. <a href="http://wrap.warwick.ac.uk/86722/1/WRAP_ch-030317-wrap_-cusersdavid_foxdesktop40triangulene_complete_accepted.pdf" target="_blank">http://wrap.warwick.ac.uk/86722/1/WRAP_ch-030317-wrap_-cusersdavid_foxdesktop40triangulene_complete_accepted.pdf</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Mishra, Shantanu; Beyer, Doreen; Eimre, Kristjan; Liu, Junzhi; Berger, Reinhard; Gröning, Oliver; Pignedoli, Carlo A.; Müllen, Klaus; Fasel, Roman; Feng, Xinliang; Ruffieux, Pascal (10 July 2019). "Synthesis and Characterization of π-Extended Triangulene" (PDF). Journal of the American Chemical Society. 141 (27): 10621–10625. doi:10.1021/jacs.9b05319. PMID 31241927. S2CID 195696890. <a href="https://boris.unibe.ch/141648/2/Postprint.pdf" target="_blank">https://boris.unibe.ch/141648/2/Postprint.pdf</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Su, Jie; Telychko, Mykola; Hu, Pan; Macam, Gennevieve; Mutombo, Pingo; Zhang, Hejian; Bao, Yang; Cheng, Fang; Huang, Zhi-Quan; Qiu, Zhizhan; Tan, Sherman J. R.; Lin, Hsin; Jelínek, Pavel; Chuang, Feng-Chuan; Wu, Jishan; Lu, Jiong (July 2019). "Atomically precise bottom-up synthesis of π-extended [5]triangulene". Science Advances. 5 (7): eaav7717. Bibcode:2019SciA....5.7717S. doi:10.1126/sciadv.aav7717. PMC 6660211. PMID 31360763. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6660211" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6660211</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Mishra, Shantanu; Xu, Kun; Eimre, Kristjan; Komber, Hartmut; Ma, Ji; Pignedoli, Carlo A.; Fasel, Roman; Feng, Xinliang; Ruffieux, Pascal (2021). "Synthesis and characterization of [7]triangulene". Nanoscale. 13 (3): 1624–1628. doi:10.1039/d0nr08181g. PMID 33443270. S2CID 231605335. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>Mishra, Shantanu; Beyer, Doreen; Eimre, Kristjan; Ortiz, Ricardo; Fernández-Rossier, Joaquín; Berger, Reinhard; Gröning, Oliver; Pignedoli, Carlo A.; Fasel, Roman; Feng, Xinliang; Ruffieux, Pascal (13 July 2020). "Collective All-Carbon Magnetism in Triangulene Dimers". Angewandte Chemie International Edition. 59 (29): 12041–12047. arXiv:2003.00753. doi:10.1002/anie.202002687. PMC 7383983. PMID 32301570. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7383983" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7383983</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>Mishra, Shantanu; Catarina, Gonçalo; Wu, Fupeng; Ortiz, Ricardo; Jacob, David; Eimre, Kristjan; Ma, Ji; Pignedoli, Carlo A.; Feng, Xinliang; Ruffieux, Pascal; Fernández-Rossier, Joaquín; Fasel, Roman (13 October 2021). "Observation of fractional edge excitations in nanographene spin chains". Nature. 598 (7880): 287–292. arXiv:2105.09102. Bibcode:2021Natur.598..287M. doi:10.1038/s41586-021-03842-3. PMID 34645998. S2CID 234777902. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> </ol>