The ability of a ring-shaped molecule to sustain a global aromatic or antiaromatic ring current when placed in a magnetic field indicates that its electronic wave function is coherently delocalized around its whole circumference. Large molecules that display this behavior are attractive components for molecular electronic devices, but this phenomenon is rare in neutral molecules with circuits of more than 40 π-electrons. Here, we use theoretical methods to investigate how the global ring currents evolve with increasing ring size in cyclic molecular nanobelts built from edge-fused porphyrins. Our results indicate that a global ring current persists in neutral nanobelts with Hückel circuits of 220 π-electrons (22 porphyrin units, circumference 18.6 nm). Our predictions are validated by using coupled clusters to construct a density functional approximation (denoted as OX-B3LYP) that accurately describes these nanobelts and by checking compliance with Koopmans' theorem.

Chemistry Research Laboratory Department of Chemistry University of Oxford Oxford OX1 3TA U K

Department of Chemistry The University of Manchester Oxford Road Manchester M13 9PL U K

Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences Flemingovo nám 542 2 Prague 6 160 00 Czechia

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Shalf J. The Future of Computing Beyond Moore’s Law. Philos. Trans. R. Soc. A 2020, 378, 20190061.10.1098/rsta.2019.0061. PubMed DOI

Chen Z.; Grace I. M.; Woltering S. L.; Chen L.; Gee A.; Baugh J.; Briggs G. A. D.; Bogani L.; Mol J. A.; Lambert C. J.; et al. Quantum Interference Enhances the Performance of Single-Molecule Transistors. Nat. Nanotechnol. 2024, 19, 986–992. 10.1038/s41565-024-01633-1. PubMed DOI PMC

Cheung K. Y.; Watanabe K.; Segawa Y.; Itami K. Synthesis of a Zigzag Carbon Nanobelt. Nat. Chem. 2021, 13, 255–259. 10.1038/s41557-020-00627-5. PubMed DOI

Imoto D.; Yagi A.; Itami K. Carbon Nanobelts: Brief History and Perspective. Precis. Chem. 2023, 1, 516–523. 10.1021/prechem.3c00083. DOI

Lin J.; Wang S.; Zhang F.; Yang B.; Du P.; Chen C.; Zang Y.; Zhu D. Highly Efficient Charge Transport across Carbon Nanobelts. Sci. Adv. 2022, 8, eade469210.1126/sciadv.ade4692. PubMed DOI PMC

Deng J.-R.; González M. T.; Zhu H.; Anderson H. L.; Leary E. Ballistic Conductance through Porphyrin Nanoribbons. J. Am. Chem. Soc. 2024, 146, 3651–3659. 10.1021/jacs.3c07734. PubMed DOI PMC

Tsuda A.; Osuka A. Fully Conjugated Porphyrin Tapes with Electronic Absorption Bands That Reach into Infrared. Science 2001, 293, 79–82. 10.1126/science.1059552. PubMed DOI

Chen Z.; Deng J.-R.; Hou S.; Bian X.; Swett J. L.; Wu Q.; Baugh J.; Bogani L.; Briggs G. A. D.; Mol J. A.; et al. Phase-Coherent Charge Transport through a Porphyrin Nanoribbon. J. Am. Chem. Soc. 2023, 145, 15265–15274. 10.1021/jacs.3c02451. PubMed DOI PMC

Yamaguchi Y. Theoretical Prediction of Electronic Structures of Fully π-Conjugated Zinc Oligoporphyrins with Curved Surface Structures. J. Chem. Phys. 2004, 120, 7963–7970. 10.1063/1.1690759. PubMed DOI

Gershoni-Poranne R.; Stanger A. Magnetic Criteria of Aromaticity. Chem. Soc. Rev. 2015, 44, 6597–6615. 10.1039/C5CS00114E. PubMed DOI

Steiner E.; Fowler P. W. Four- and Two-Electron Rules for Diatropic and Paratropic Ring Currents in Monocyclic π Systems. ChemComm 2001, 2220–2221. 10.1039/b104847n. PubMed DOI

Jirásek M.; Anderson H. L.; Peeks M. D. From Macrocycles to Quantum Rings: Does Aromaticity Have a Size Limit?. Acc. Chem. Res. 2021, 54, 3241–3251. 10.1021/acs.accounts.1c00323. PubMed DOI

Peeks M. D.; Jirasek M.; Claridge T. D. W.; Anderson H. L. Global Aromaticity and Antiaromaticity in Porphyrin Nanoring Anions. Angew. Chem., Int. Ed. 2019, 58, 15717–15720. 10.1002/anie.201909032. PubMed DOI PMC

Rickhaus M.; Jirasek M.; Tejerina L.; Gotfredsen H.; Peeks M. D.; Haver R.; Jiang H.-W.; Claridge T. D. W.; Anderson H. L. Global Aromaticity at the Nanoscale. Nat. Chem. 2020, 12, 236–241. 10.1038/s41557-019-0398-3. PubMed DOI PMC

Majewski M. A.; Stawski W.; Van Raden J. M.; Clarke M.; Hart J.; O’Shea J. N.; Saywell A.; Anderson H. L. Covalent Template-Directed Synthesis of a Spoked 18-Porphyrin Nanoring. Angew. Chem., Int. Ed. 2023, 62, e20230211410.1002/anie.202302114. PubMed DOI PMC

Kopp S. M.; Gotfredsen H.; Hergenhahn J.; Rodríguez-Rubio A.; Deng J.-R.; Zhu H.; Stawski W.; Anderson H. L. Charge Delocalization and Global Aromaticity in a Partially Fused 12-Porphyrin Nanoring. Chem. 2024, 10, 3410–3427. 10.1016/j.chempr.2024.06.034. DOI

Bradley D.; Jirásek M.; Anderson H. L.; Peeks M. D. Disentangling Global and Local Ring Currents. Chem. Sci. 2023, 14, 1762–1768. 10.1039/D2SC05923A. PubMed DOI PMC

Shaik S.; Shurki A.; Danovich D.; Hiberty P. C. A Different Story of π-Delocalization the Distortivity of π-Electrons and Its Chemical Manifestations. Chem. Rev. 2001, 101, 1501–1540. 10.1021/cr990363l. PubMed DOI

Jug K.; Hiberty P. C.; Shaik S. σ–π Energy Separation in Modern Electronic Theory for Ground States of Conjugated Systems. Chem. Rev. 2001, 101, 1477–1500. 10.1021/cr990328e. PubMed DOI

Heilbronner E. Why Do Some Molecules Have Symmetry Different from That Expected?. J. Chem. Educ. 1989, 66, 471.10.1021/ed066p471. DOI

Pavlak I.; Matasović L.; Buchanan E. A.; Michl J.; Rončević I. Electronic Structure of Metalloporphenes, Antiaromatic Analogues of Graphene. J. Am. Chem. Soc. 2024, 146, 3992–4000. 10.1021/jacs.3c12079. PubMed DOI PMC

Longuet-Higgins H. C.; Salem L. The Alternation of Bond Lengths in Long Conjugated Chain Molecules. Philos. Trans. R. Soc. A 1959, 251, 172–185. 10.1098/rspa.1959.0100. DOI

Bao J. L.; Gagliardi L.; Truhlar D. G. Self-Interaction Error in Density Functional Theory: An Appraisal. J. Phys. Chem. Lett. 2018, 9, 2353–2358. 10.1021/acs.jpclett.8b00242. PubMed DOI

Becke A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648–5652. 10.1063/1.464913. DOI

Zhao Y.; Truhlar D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215–241. 10.1007/s00214-007-0310-x. DOI

Casademont-Reig I.; Guerrero-Avilés R.; Ramos-Cordoba E.; Torrent-Sucarrat M.; Matito E. How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring. Angew. Chem., Int. Ed. 2021, 60, 24080–24088. 10.1002/anie.202108997. PubMed DOI PMC

Deng J.-R.; Bradley D.; Jirásek M.; Anderson H. L.; Peeks M. D. Correspondence on “How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring”. Angew. Chem., Int. Ed. 2022, 61, e20220123110.1002/anie.202201231. PubMed DOI

Valiev R. R.; Baryshnikov G. V.; Nasibullin R. T.; Sundholm D.; Ågren H. When Are Antiaromatic Molecules Paramagnetic?. J. Phys. Chem. C 2020, 124, 21027–21035. 10.1021/acs.jpcc.0c01559. DOI

Mahmood A.; Dimitrova M.; Sundholm D. Current-Density Calculations on Zn-Porphyrin40 Nanorings. J. Phys. Chem. A 2023, 127, 7452–7459. 10.1021/acs.jpca.3c03564. PubMed DOI PMC

Vydrov O. A.; Heyd J.; Krukau A. V.; Scuseria G. E. Importance of Short-Range Versus Long-Range Hartree-Fock Exchange for the Performance of Hybrid Density Functionals. J. Chem. Phys. 2006, 125, 074106.10.1063/1.2244560. PubMed DOI

Santra G.; Calinsky R.; Martin J. M. L. Benefits of Range-Separated Hybrid and Double-Hybrid Functionals for a Large and Diverse Data Set of Reaction Energies and Barrier Heights. J. Phys. Chem. A 2022, 126, 5492–5505. 10.1021/acs.jpca.2c03922. PubMed DOI PMC

Szczepanik D. W.; Solà M.; Andrzejak M.; Pawełek B.; Dominikowska J.; Kukułka M.; Dyduch K.; Krygowski T. M.; Szatylowicz H. The Role of the Long-Range Exchange Corrections in the Description of Electron Delocalization in Aromatic Species. J. Comput. Chem. 2017, 38, 1640–1654. 10.1002/jcc.24805. PubMed DOI

Yanai T.; Tew D. P.; Handy N. C. A New Hybrid Exchange–Correlation Functional Using the Coulomb-Attenuating Method (CAB-B3LYP). Chem. Phys. Lett. 2004, 393, 51–57. 10.1016/j.cplett.2004.06.011. DOI

Casademont-Reig I.; Soriano-Agueda L.; Ramos-Cordoba E.; Torrent-Sucarrat M.; Matito E. Reply to the Correspondence on “How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring”. Angew. Chem., Int. Ed. 2022, 61, e20220683610.1002/anie.202206836. PubMed DOI

Binsch G.; Heilbronner E.; Murrell J. N. The Theory of Double Bond Fixation in Conjugated Hydrocarbons. Mol. Phys. 1966, 11, 305–320. 10.1080/00268976600101141. DOI

Fowler P. W. Symmetry Aspects of Distortivity in π Systems. Adv. Quantum Chem. 2003, 44, 219–237. 10.1016/S0065-3276(03)44014-8. DOI

Stawski W.; Zhu Y.; Rončević I.; Wei Z.; Petrukhina M. A.; Anderson H. L. The Anti-Aromatic Dianion and Aromatic Tetraanion of [18]Annulene. Nat. Chem. 2024, 16, 998–1002. 10.1038/s41557-024-01469-1. PubMed DOI PMC

Woller T.; Banerjee A.; Sylvetsky N.; Santra G.; Deraet X.; De Proft F.; Martin J. M. L.; Alonso M. Performance of Electronic Structure Methods for the Description of Hückel–Möbius Interconversions in Extended π-Systems. J. Phys. Chem. A 2020, 124, 2380–2397. 10.1021/acs.jpca.9b10880. PubMed DOI PMC

Tučková L.; Jaroš A.; Foroutan-Nejad C.; Straka M. A Quest for Ideal Electric Field-Driven MX@C70 Endohedral Fullerene Memristors: Which MX Fits the Best?. Phys. Chem. Chem. Phys. 2023, 25, 14245–14256. 10.1039/D3CP01149F. PubMed DOI

Park K. H. K.; Frank N.; Duarte F.; Anderson E. A. Collective Synthesis of Illudalane Sesquiterpenes Via Cascade Inverse Electron Demand (4 + 2) Cycloadditions of Thiophene S,S-Dioxides. J. Am. Chem. Soc. 2022, 144, 10017–10024. 10.1021/jacs.2c03304. PubMed DOI PMC

Perdew J. P.; Burke K.; Ernzerhof M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. 10.1103/PhysRevLett.77.3865. PubMed DOI

Lin Y.-S.; Li G.-D.; Mao S.-P.; Chai J.-D. Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections. J. Chem. Theory Comput. 2013, 9, 263–272. 10.1021/ct300715s. PubMed DOI

Kong L.; Bischoff F. A.; Valeev E. F. Explicitly Correlated R12/F12 Methods for Electronic Structure. Chem. Rev. 2012, 112, 75–107. 10.1021/cr200204r. PubMed DOI

Belosludov R. V.; Nevonen D. E.; Nemykin V. N. Accurate Prediction of the Excited States in the Fully Conjugated Porphyrin Tapes across the Full Spectral Range: A Story of the Interplay between π–π* and Intramolecular Charge-Transfer Transitions in Soft Chromophores. J. Phys. Chem. A 2021, 125, 2480–2491. 10.1021/acs.jpca.1c00217. PubMed DOI

Jirásek M.; Rickhaus M.; Tejerina L.; Anderson H. L. Experimental and Theoretical Evidence for Aromatic Stabilization Energy in Large Macrocycles. J. Am. Chem. Soc. 2021, 143, 2403–2412. 10.1021/jacs.0c12845. PubMed DOI

Kronik L.; Stein T.; Refaely-Abramson S.; Baer R. Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals. J. Chem. Theory Comput. 2012, 8, 1515–1531. 10.1021/ct2009363. PubMed DOI

Karolewski A.; Kronik L.; Kümmel S. Using Optimally Tuned Range Separated Hybrid Functionals in Ground-State Calculations: Consequences and Caveats. J. Chem. Phys. 2013, 138, 204115.10.1063/1.4807325. PubMed DOI

Manna D.; Blumberger J.; Martin J. M. L.; Kronik L. Prediction of Electronic Couplings for Molecular Charge Transfer Using Optimally Tuned Range-Separated Hybrid Functionals. Mol. Phys. 2018, 116, 2497–2505. 10.1080/00268976.2018.1489084. DOI

Kopp S. M.; Gotfredsen H.; Deng J.-R.; Claridge T. D. W.; Anderson H. L. Global Aromaticity in a Partially Fused 8-Porphyrin Nanoring. J. Am. Chem. Soc. 2020, 142, 19393–19401. 10.1021/jacs.0c09973. PubMed DOI

Stoychev G. L.; Auer A. A.; Izsák R.; Neese F. Self-Consistent Field Calculation of Nuclear Magnetic Resonance Chemical Shielding Constants Using Gauge-Including Atomic Orbitals and Approximate Two-Electron Integrals. J. Chem. Theory Comput. 2018, 14, 619–637. 10.1021/acs.jctc.7b01006. PubMed DOI

Stoychev G. L.; Auer A. A.; Neese F. Efficient and Accurate Prediction of Nuclear Magnetic Resonance Shielding Tensors with Double-Hybrid Density Functional Theory. J. Chem. Theory Comput. 2018, 14, 4756–4771. 10.1021/acs.jctc.8b00624. PubMed DOI

Van Damme S.; Acke G.; Havenith R. W. A.; Bultinck P. Can the Current Density Map Topology Be Extracted from the Nucleus Independent Chemical Shifts?. Phys. Chem. Chem. Phys. 2016, 18, 11746–11755. 10.1039/C5CP07170D. PubMed DOI

Fliegl H.; Taubert S.; Lehtonen O.; Sundholm D. The Gauge Including Magnetically Induced Current Method. Phys. Chem. Chem. Phys. 2011, 13, 20500–20518. 10.1039/c1cp21812c. PubMed DOI

Jusélius J.; Sundholm D.; Gauss J. Calculation of Current Densities Using Gauge-Including Atomic Orbitals. J. Chem. Phys. 2004, 121, 3952–3963. 10.1063/1.1773136. PubMed DOI

Peeks M. D.; Claridge T. D. W.; Anderson H. L. Aromatic and Antiaromatic Ring Currents in a Molecular Nanoring. Nature 2017, 541, 200–203. 10.1038/nature20798. PubMed DOI

Monaco G.; Summa F. F.; Zanasi R. Program Package for the Calculation of Origin-Independent Electron Current Density and Derived Magnetic Properties in Molecular Systems. J. Chem. Inf. Model. 2021, 61, 270–283. 10.1021/acs.jcim.0c01136. PubMed DOI

Szczepanik D. W.; Andrzejak M.; Dominikowska J.; Pawełek B.; Krygowski T. M.; Szatylowicz H.; Solà M. The Electron Density of Delocalized Bonds (EDDB) Applied for Quantifying Aromaticity. Phys. Chem. Chem. Phys. 2017, 19, 28970–28981. 10.1039/C7CP06114E. PubMed DOI

Zhu H.; Chen Q.; Rončević I.; Christensen K. E.; Anderson H. L. Anthracene-Porphyrin Nanoribbons. Angew. Chem., Int. Ed. 2023, 62, e20230703510.1002/anie.202307035. PubMed DOI

O’Sullivan M. C.; Sprafke J. K.; Kondratuk D. V.; Rinfray C.; Claridge T. D. W.; Saywell A.; Blunt M. O.; O’Shea J. N.; Beton P. H.; Malfois M.; et al. Vernier Templating and Synthesis of a 12-Porphyrin Nano-Ring. Nature 2011, 469, 72–75. 10.1038/nature09683. PubMed DOI

Hoffmann M.; Wilson C. J.; Odell B.; Anderson H. L. Template-Directed Synthesis of a π-Conjugated Porphyrin Nanoring. Angew. Chem., Int. Ed. 2007, 46, 3122–3125. 10.1002/anie.200604601. PubMed DOI

Gotfredsen H.; Deng J.-R.; Van Raden J. M.; Righetto M.; Hergenhahn J.; Clarke M.; Bellamy-Carter A.; Hart J.; O’Shea J.; Claridge T. D. W.; et al. Bending a Photonic Wire into a Ring. Nat. Chem. 2022, 14, 1436–1442. 10.1038/s41557-022-01032-w. PubMed DOI

Wheeler S. E.; Houk K. N.; Schleyer P. v. R.; Allen W. D. A Hierarchy of Homodesmotic Reactions for Thermochemistry. J. Am. Chem. Soc. 2009, 131, 2547–2560. 10.1021/ja805843n. PubMed DOI PMC

Wiberg K. B. The Concept of Strain in Organic Chemistry. Angew. Chem., Int. Ed. Engl. 1986, 25, 312–322. 10.1002/anie.198603121. DOI

Merino G.; Solà M.; Fernández I.; Foroutan-Nejad C.; Lazzeretti P.; Frenking G.; Anderson H. L.; Sundholm D.; Cossío F. P.; Petrukhina M. A.; et al. Aromaticity: Quo Vadis. Chem. Sci. 2023, 14, 5569.10.1039/D2SC04998H. PubMed DOI PMC

Soya T.; Mori H.; Osuka A. Quadruply Twisted Hückel-Aromatic Dodecaphyrin. Angew. Chem., Int. Ed. 2018, 57, 15882–15886. 10.1002/anie.201811433. PubMed DOI

Ishida S.-I.; Kim J.; Shimizu D.; Kim D.; Osuka A. Synthesis of (Bis)Silicon Complexes of [38], [37], and [36]Octaphyrins: Aromaticity Switch and Stable Radical Cation. Angew. Chem., Int. Ed. 2018, 57, 5876–5880. 10.1002/anie.201801986. PubMed DOI

Anand V. G.; Saito S.; Shimizu S.; Osuka A. Internally 1,4-Phenylene-Bridged Meso Aryl-Substituted Expanded Porphyrins: The Decaphyrin and Octaphyrin Cases. Angew. Chem., Int. Ed. 2005, 44, 7244–7248. 10.1002/anie.200502769. PubMed DOI

Hod O.; Rabani E.; Baer R. Magnetoresistance of Nanoscale Molecular Devices. Acc. Chem. Res. 2006, 39, 109–117. 10.1021/ar0401909. PubMed DOI

Bannwarth C.; Ehlert S.; Grimme S. GFN2-XTB—an Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions. J. Chem. Theory Comput. 2019, 15, 1652–1671. 10.1021/acs.jctc.8b01176. PubMed DOI

Frisch M. J.; Trucks G. W.; Schlegel H. B.; Scuseria G. E.; Robb M. A.; Cheeseman J. R.; Scalmani G.; Barone V.; Petersson G. A.; Nakatsuji H.; et al.Gaussian 16. Rev. C.01: Wallingford, CT, 2016.

Neese F.; Wennmohs F.; Becker U.; Riplinger C. The Orca Quantum Chemistry Program Package. J. Chem. Phys. 2020, 152, 224108.10.1063/5.0004608. PubMed DOI

Grimme S. Improved Second-Order Møller–Plesset Perturbation Theory by Separate Scaling of Parallel- and Antiparallel-Spin Pair Correlation Energies. J. Chem. Phys. 2003, 118, 9095–9102. 10.1063/1.1569242. DOI

Balasubramani S. G.; Chen G. P.; Coriani S.; Diedenhofen M.; Frank M. S.; Franzke Y. J.; Furche F.; Grotjahn R.; Harding M. E.; Hättig C.; et al. Turbomole: Modular Program Suite for Ab Initio Quantum-Chemical and Condensed-Matter Simulations. J. Chem. Phys. 2020, 152, 184107.10.1063/5.0004635. PubMed DOI PMC