Startseite From Hückel to Clar: a block-localized description of aromatic systems
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

From Hückel to Clar: a block-localized description of aromatic systems

  • Fabien Barrois , Yannick Carissan , Nicolas Goudard , Denis Hagebaum-Reignier und Stéphane Humbel ORCID logo EMAIL logo
Veröffentlicht/Copyright: 16. Juni 2025
Pure and Applied Chemistry
Aus der Zeitschrift Pure and Applied Chemistry Band 97 Heft 9

Abstract

We report a local description of extended aromatic systems using Clar formalism embedded in Valence Bond-like calculations. We disclose a new implementation of our HuLiS (Hückel/Lewis) program that considers blocks of electrons in addition to bonds and lone pairs/radical centers. The method is based on the Hückel approximation for both the empirical hamiltonian and the atomic orbital orthogonality constraint.

Keywords: Aromaticity; computational chemistry; electronic structures; quantum chemistry; quantum science and technology
Corresponding author: Stéphane Humbel, Aix Marseille Univ, CNRS, Centrale Med, ISM2, UMR 7313: Institut des Sciences Moléculaires de Marseille 13397, Marseille, Cedex 20, France, e-mail:
Article note: A collection of invited papers to celebrate the UN’s proclamation of 2025 as the International Year of Quantum Science and Technology.

Acknowledgments

Wei Wu is gratefully acknowledged for the XMVB programs. The authors acknowledge the French Research Ministry, Aix-Marseille Université (PhD grant for F.B.) for financial support.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: YC and NG made most of the implementation. FB made most of the calculations. DHR and SH built the project and wrote the paper.

  4. Use of Large Language Models, AI and Machine Learning Tools: To improve language.

  5. Conflict of interest: The author states no conflict of interest.

  6. Research funding: French Research Ministry.

  7. Data availability: Software availability: HuLiS is available on https://ctomism2.github.io/hulis/hulis_v3_4_0.jar.

Appendix I: Wavefunctions at the Hückel level

In the Hückel approach, the σ skelleton is disregarded, and we use the basis of the atomic p orbitals that make the π system (and π electrons, 1 per carbon atom for instance). Other atoms are of course available and the parameters are the usual Hückel parameters, 68 which can be modified in the interface. In the following, the p atomic orbitals are noted by their atom’s numbering {1, 2, 3}.

A specific localized structure |ψ i ⟩ is represented as one (or two) Slater determinant(s) using π orbitals that are built on the relevant atoms. For a bond between atoms a and b, an orbital π a b = 1 2 ( a + b ) is bioccupied: | ψ i 〉 = | … π a b π a b ¯ … | . In the block algorithm such a bioccupied π ab is the solution of the isolated {a = b} subsystem and 2 electrons. For a sextet located on atoms a − f, the subsystem is made of the 6 atomic orbitals connected together to form the ring, solved at the Hückel level, and the lowest orbitals of the subsystem (π 1 π 2 π 3) are filled with 6 electrons. The blocks coexist with the former bond, lone pair and radical definitions (6).

(6) | ψ i 〉 = | π 1 π 1 ¯ π 2 π 2 ¯ π 3 π 3 ¯ … π a b π a b ¯ … |

Singlet coupled radicals are considered with two coupled determinants | a b ¯ | + | b a ¯ | . We allow two blocks of a single electron to be coupled together, but only one pair of coupled electrons are implemented. Besides, an atomic orbital must belong to a single block as it is the case in the Block Localized Wavefunction (BLW) method. 47

Appendix II: Overlaps at the Hückel level

To show how the overlap between structures is computed in the Hückel framework, we take the example, of the two main resonant structures of the allyl cation, ⟨ ψ I | ψ I I ⟩ = ⟨ | π 12 π 12 ¯ | | | π 23 π 23 ¯ | ⟩ .

This overlap should involve several permutations, but the result is obtained when the left-hand side determinant is considered as a spin-orbital product, 69 and the permutations that operate in the right-hand side determinant are restricted to those between electrons of the same spin. Each term is signed by − 1 t , where t is the total number of permutations in the term.

In our simple two-electron case with no pair of the same spin, there is no permutation and the expansion of the overlap is given by eq. 7. It is found that S I , I I = 1 4 , thanks to the orthonormality of the atomic orbitals in the Hückel approximation.

(7) ⟨ | π a b π a b ¯ | | | π b c π b c ¯ | ⟩ = ⟨ π a b π a b ¯ | π b c π b c ¯ ⟩ = ⟨ 1 2 ( a + b ) 1 2 ( a + b ¯ ) | 1 2 ( b + c ) 1 2 ( b + c ¯ ) ⟩ = 1 4 ⟨ a a ¯ + b b ¯ + a b ¯ + b a ¯ | b b ¯ + c c ¯ + b c ¯ + c b ¯ ⟩ = 1 4 ⟨ a | b ⟩ ⏟ = 0 ⟨ a ¯ | b ¯ ⟩ ⏟ = 0 + ⋯ + ⟨ b | b ⟩ ⟨ b ¯ | b ¯ ⟩ + ⋯ = 1 4

For larger systems, for instance 4 electron systems, the permutations in the right-hand part writes as in eq. 8.

(8) ⟨ | a a ¯ b b ¯ | | | c c ¯ d d ¯ | ⟩ = a a ¯ b b ¯ | c c ¯ d d ¯ − a a ¯ b b ¯ | d c ¯ c d ¯ − a a ¯ b b ¯ | c d ¯ d c ¯ + a a ¯ b b ¯ | d d ¯ c c ¯ = s a c 2 s b d 2 − s a d s a c s b c s b d − s a c s a d s b d s b c + s a d 2 s b c 2

References

1. Merino, G.; Solà, M.; Fernández, I.; Foroutan-Nejad, C.; Lazzeretti, P.; Frenking, G.; Anderson, H. L.; Sundholm, D.; Cossío, F. P.; Petrukhina, M. A.; Wu, J.; Wu, J. I.; Restrepo, A. Aromaticity: Quo Vadis. Chem. Sci. 2023, 14 (21), 5569–5576. https://doi.org/10.1039/d2sc04998h.Suche in Google Scholar PubMed PubMed Central

2. Baird, N. C. Quantum Organic Photochemistry. II. Resonance and Aromaticity in the Lowest 3ππ* State of Cyclic Hydrocarbons. J. Am. Chem. Soc. 1972, 94 (14), 4941–4948. https://doi.org/10.1021/ja00769a025.Suche in Google Scholar

3. von Schleyer, P. R.; Jiao, H. What is Aromaticity? Pure Appl. Chem. 1996, 68 (2), 209–218. https://doi.org/10.1351/pac199668020209.Suche in Google Scholar

4. Karadakov, P. B.; Al-Yassiri, M. A. H. Excited-State Aromaticity Reversals in Naphthalene and Anthracene. J. Phys. Chem. A 2023, 127 (14), 3148–3162. https://doi.org/10.1021/acs.jpca.3c00485.Suche in Google Scholar PubMed PubMed Central

5. Rosenberg, M.; Dahlstrand, C.; Kilså, K.; Ottosson, H. Excited State Aromaticity and Antiaromaticity: Opportunities for Photophysical and Photochemical Rationalizations. Chem. Rev. 2014, 114 (10), 5379–5425. https://doi.org/10.1021/cr300471v.Suche in Google Scholar PubMed

6. Artigas, A.; Hagebaum-Reignier, D.; Carissan, Y.; Coquerel, Y. Visualizing Electron Delocalization in Contorted Polycyclic Aromatic Hydrocarbons. Chem. Sci. 2021, 12 (39), 13092–13100. https://doi.org/10.1039/d1sc03368a.Suche in Google Scholar PubMed PubMed Central

7. El Bakouri, O.; Szczepanik, D. W.; Jorner, K.; Ayub, R.; Bultinck, P.; Solà, M.; Ottosson, H. Three-Dimensional Fully π-Conjugated Macrocycles: When 3D-Aromatic and when 2D-Aromatic-in-3D? J. Am. Chem. Soc. 2022, 144 (19), 8560–8575. https://doi.org/10.1021/jacs.1c13478.Suche in Google Scholar PubMed PubMed Central

8. Clar, E. Polycyclic Hydrocarbons; Springer: Berlin, Heidelberg, 1964.10.1007/978-3-662-01665-7Suche in Google Scholar

9. Clar, E. The Aromatic Sextet. NATO ASI Series; Wiley: New York, 1972.Suche in Google Scholar

10. Solà, M. Forty Years of Clar’s Aromatic π-Sextet Rule. Front. Chem. 2013, 1, 22. https://doi.org/10.3389/fchem.2013.00022.Suche in Google Scholar PubMed PubMed Central

11. Kay, M. I.; Okaya, Y.; Cox, D. E. A Refinement of the Structure of the Room-Temperature Phase of Phenanthrene, C14H10, from X-ray and Neutron Diffraction Data. Acta Crystallogr. B Struct. Sci. Cryst. Eng. Mater. 1971, 27 (1), 26–33. https://doi.org/10.1107/s0567740871001663.Suche in Google Scholar

12. Pauling, L.; Sherman, J. The Nature of the Chemical Bond. VI. The Calculation from Thermochemical Data of the Energy of Resonance of Molecules Among Several Electronic Structures. J. Chem. Phys. 1933, 1 (8), 606–617. https://doi.org/10.1063/1.1749335.Suche in Google Scholar

13. Kistiakowsky, G. B.; Ruhoff, J. R.; Smith, H. A.; Vaughan, W. E. Heats of Organic Reactions. IV. Hydrogenation of Some Dienes and of Benzene. J. Am. Chem. Soc. 1936, 58 (1), 146–153. https://doi.org/10.1021/ja01292a043.Suche in Google Scholar

14. Ditchfield, R.; Hehre, W. J.; Pople, J. A.; Radom, L. Molecular Orbital Theory of Bond Separation. Chem. Phys. Lett. 1970, 5 (1), 13–14. https://doi.org/10.1016/0009-2614(70)80116-6.Suche in Google Scholar

15. Mo, Y.; Schleyer, P. V. An Energetic Measure of Aromaticity and Antiaromaticity Based on the Pauling-Wheland Resonance Energies. Chem. Eur. J. 2006, 12 (7), 2009–2020. https://doi.org/10.1002/chem.200500376.Suche in Google Scholar PubMed

16. Suresh, C. H.; Koga, N. An Isodesmic Reaction Based Approach to Aromaticity of a Large Spectrum of Molecules. Chem. Phys. Lett. 2006, 419 (4-6), 550–556. https://doi.org/10.1016/j.cplett.2005.12.028.Suche in Google Scholar

17. Cyrański, M. K. Energetic Aspects of Cyclic Pi-Electron Delocalization: Evaluation of the Methods of Estimating Aromatic Stabilization Energies. Chem. Rev. 2005, 105 (10), 3773–3811. https://doi.org/10.1021/cr0300845.Suche in Google Scholar PubMed

18. Norbeck, J. M.; Gallup, G. A. Valence-Bond Calculation of the Electronic Structure of Benzene. J. Am. Chem. Soc. 1974, 96 (11), 3386–3393. https://doi.org/10.1021/ja00818a008.Suche in Google Scholar

19. Epiotis, N. D. Applications of Molecular Orbital-Valence Bond Theory in Chemistry. Pure Appl. Chem. 1983, 55 (2), 229–236. https://doi.org/10.1351/pac198855020229.Suche in Google Scholar

20. Shaik, S.; Shurki, A.; Danovich, D.; Hiberty, P. C. A Different Story of Benzene. J. Mol. Struct. THEOCHEM 1997, 398-399, 155–167. https://doi.org/10.1016/s0166-1280(96)04934-2.Suche in Google Scholar

21. Aihara, J. A New Definition of Dewar-Type Resonance Energies. J. Am. Chem. Soc. 1976, 98 (10), 2750–2758. https://doi.org/10.1021/ja00426a013.Suche in Google Scholar

22. Gutman, I.; Milun, M.; Trinajstic, N. Graph Theory and Molecular Orbitals. 19. Nonparametric Resonance Energies of Arbitrary Conjugated Systems. J. Am. Chem. Soc. 1977, 99 (6), 1692–1704. https://doi.org/10.1021/ja00448a002.Suche in Google Scholar

23. Randić, M. Aromaticity of Polycyclic Conjugated Hydrocarbons. Chem. Rev. 2003, 103 (9), 3449–3606. https://doi.org/10.1021/cr9903656.Suche in Google Scholar PubMed

24. Chauvin, R.; Lepetit, C. The Fundamental Chemical Equation of Aromaticity. Phys. Chem. Chem. Phys. 2013, 15 (11), 3855. https://doi.org/10.1039/c2cp44075j.Suche in Google Scholar PubMed

25. Randić, M. Benzenoid Rings Resonance Energies and Local Aromaticity of Benzenoid Hydrocarbons. J. Comput. Chem. 2019, 40 (5), 753–762. https://doi.org/10.1002/jcc.25760.Suche in Google Scholar

26. Varet, A.; Prcovic, N.; Terrioux, C.; Hagebaum-Reignier, D.; Carissan, Y. BenzAI: A Program to Design Benzenoids with Defined Properties Using Constraint Programming. J. Chem. Inf. Mod. 2022, 62 (11), 2811–2820. https://doi.org/10.1021/acs.jcim.2c00353.Suche in Google Scholar PubMed

27. Schleyer, P. V. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; Van Eikema Hommes, N. J. R. Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe. J. Am. Chem. Soc. 1996, 118 (26), 6317–6318. https://doi.org/10.1021/ja960582d.Suche in Google Scholar PubMed

28. Stanger, A. Nucleus-Independent Chemical Shifts (NICS): Distance Dependence and Revised Criteria for Aromaticity and Antiaromaticity. J. Org. Chem. 2006, 71 (3), 883–893. https://doi.org/10.1021/jo051746o.Suche in Google Scholar PubMed

29. Geuenich, D.; Hess, K.; Köhler, F.; Herges, R. Anisotropy of the Induced Current Density (ACID), A General Method to Quantify and Visualize Electronic Delocalization. Chem. Rev. 2005, 105 (10), 3758–3772. https://doi.org/10.1021/cr0300901.Suche in Google Scholar PubMed

30. Fliegl, H.; Taubert, S.; Lehtonen, O.; Sundholm, D. The Gauge Including Magnetically Induced Current Method. Phys. Chem. Chem. Phys. 2011, 13 (46), 20500. https://doi.org/10.1039/c1cp21812c.Suche in Google Scholar PubMed

31. Islas, R.; Heine, T.; Merino, G. The Induced Magnetic Field. Acc. Chem. Res. 2012, 45 (2), 215–228. https://doi.org/10.1021/ar200117a.Suche in Google Scholar PubMed

32. Krygowski, T. M. Crystallographic Studies of Inter- and Intramolecular Interactions Reflected in Aromatic Character of .pi.-Electron Systems. J. Chem. Inf. Comput. Sci. 1993, 33 (1), 70–78. https://doi.org/10.1021/ci00011a011.Suche in Google Scholar

33. Poater, J.; Fradera, X.; Duran, M.; Solà, M. The Delocalization Index as an Electronic Aromaticity Criterion: Application to a Series of Planar Polycyclic Aromatic Hydrocarbons. Chem. Eur. J. 2003, 9 (2), 400–406. https://doi.org/10.1002/chem.200390041.Suche in Google Scholar PubMed

34. Portella, G.; Poater, J.; Solà, M. Assessment of Clar’s Aromatic π-Sextet Rule by Means of PDI, NICS and HOMA Indicators of Local Aromaticity. J. Phys. Org. Chem. 2005, 18 (8), 785–791. https://doi.org/10.1002/poc.938.Suche in Google Scholar

35. Karadakov, P. B.; Hearnshaw, P.; Horner, K. E. Magnetic Shielding, Aromaticity, Antiaromaticity, and Bonding in the Low-Lying Electronic States of Benzene and Cyclobutadiene. J. Org. Chem. 2016, 81 (22), 11346–11352. https://doi.org/10.1021/acs.joc.6b02460.Suche in Google Scholar PubMed

36. Kleinpeter, E.; Koch, A. Identification and Quantification of Local Antiaromaticity in Polycyclic Aromatic Hydrocarbons (PAHs) Based on the Magnetic Criterion. Org. Biomol. Chem. 2024, 22 (15), 3035–3044. https://doi.org/10.1039/d4ob00114a.Suche in Google Scholar PubMed

37. Lampkin, B. J.; Karadakov, P. B.; VanVeller, B. Detailed Visualization of Aromaticity Using Isotropic Magnetic Shielding. Angew. Chem., Int. Ed. 2020, 59 (43), 19275–19281. https://doi.org/10.1002/anie.202008362.Suche in Google Scholar PubMed

38. Carissan, Y.; Hagebaum-Reignier, D.; Goudard, N.; Humbel, S. Hückel-Lewis Projection Method: A “Weights Watcher” for Mesomeric Structures. J. Phys. Chem. A 2008, 112 (50), 13256–13262. https://doi.org/10.1021/jp803813e.Suche in Google Scholar PubMed

39. Humbel, S. Getting the Weights of Lewis Structures Out of Hückel Theory: Hückel–Lewis Configuration Interaction (HL-CI). J. Chem. Educ. 2007, 84 (6), 1056. https://doi.org/10.1021/ed084p1056.Suche in Google Scholar

40. Carissan, Y.; Hagebaum-Reignier, D.; Goudard, N.; Benzidi, H.; Humbel, S. Local Description with Lewis Structures at the Hückel Level. In Comprehensive Computational Chemistry; Yáñez, M.; Boyd, R. J., Eds.; Elsevier: Oxford, 2024, 1st ed.; pp. 605–616.10.1016/B978-0-12-821978-2.00036-2Suche in Google Scholar

41. Carissan, Y.; Hagebaum-Reignier, D.; Goudard, N.; Humbel, S. Weight Watchers électronique : calculez votre poids de formes résonantes, ou les bienfaits du numérique, même approximatif. Act. Chim. 2016, 406, 36.Suche in Google Scholar

42. Chirgwin, B. H.; Coulson, C. A. The Electronic Structure of Conjugated Systems. VI. Proc. R. Soc. Lond. Math. Phys. Eng. Sci. 1950, 201 (1065), 196.10.1098/rspa.1950.0053Suche in Google Scholar

43. Racine, J.; Hagebaum-Reignier, D.; Carissan, Y.; Humbel, S. Recasting Wave Functions into Valence Bond Structures: A Simple Projection Method to Describe Excited States. J. Comput. Chem. 2016, 37 (8), 771–779. https://doi.org/10.1002/jcc.24267.Suche in Google Scholar PubMed

44. Hiberty, P. C.; Leforestier, C. Expansion of Molecular Orbital Wave Functions into Valence Bond Wave Functions. A Simplified Procedure. J. Am. Chem. Soc. 1978, 100 (7), 2012–2017. https://doi.org/10.1021/ja00475a007.Suche in Google Scholar

45. Thorsteinsson, T.; Cooper, D. L.; Gerratt, J.; Karadakov, P. B.; Raimondi, M. Modern Valence Bond Representations of CASSCF Wavefunctions. Theor. Chim. Acta 1996, 93 (6), 343. https://doi.org/10.1007/s002140050158.Suche in Google Scholar

46. Hirao, K.; Nakano, H.; Nakayama, K.; Dupuis, M. A Complete Active Space Valence Bond (CASVB) Method. J. Chem. Phys. 1996, 105 (20), 9227–9239. https://doi.org/10.1063/1.472754.Suche in Google Scholar

47. Mo, Y.; Song, L.; Lin, Y. Block-Localized Wavefunction (BLW) Method at the Density Functional Theory (DFT) Level. J. Phys. Chem. A 2007, 111 (34), 8291–8301. https://doi.org/10.1021/jp0724065.Suche in Google Scholar PubMed

48. Hiberty, P. C.; Humbel, S.; Byrman, C. P.; van Lenthe, J. H. Compact Valence Bond Functions with Breathing Orbitals: Application to the Bond Dissociation Energies of F2 and FH. J. Chem. Phys. 1994, 101 (7), 5969–5976. https://doi.org/10.1063/1.468459.Suche in Google Scholar

49. Malrieu, J.-P.; Angeli, C.; Cimiraglia, R. On the Relative Merits of Non-Orthogonal and Orthogonal Valence Bond Methods Illustrated on the Hydrogen Molecule. J. Chem. Educ. 2008, 85 (1), 150. https://doi.org/10.1021/ed085p150.Suche in Google Scholar

50. Da Silva, E. C.; Gerratt, J.; Cooper, D. L.; Raimondi, M. Study of the Electronic States of the Benzene Molecule Using Spin-Coupled Valence Bond Theory. J. Chem. Phys. 1994, 101 (5), 3866–3887. https://doi.org/10.1063/1.467505.Suche in Google Scholar

51. Song, L.; Mo, Y.; Zhang, Q.; Wu, W. XMVB: A Program for Ab Initio Nonorthogonal Valence Bond Computations. J. Comput. Chem. 2005, 26 (5), 514–521. https://doi.org/10.1002/jcc.20187.Suche in Google Scholar PubMed

52. Chen, Z.; Ying, F.; Chen, X.; Song, J.; Su, P.; Song, L.; Mo, Y.; Zhang, Q.; Wu, W. XMVB 2.0: A New Version of Xiamen Valence Bond Program. Int. J. Quantum Chem. 2015, 115 (11), 731–737. https://doi.org/10.1002/qua.24855.Suche in Google Scholar

53. 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.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; MontgomeryJr.J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian 16 Rev. A03, 2016.Suche in Google Scholar

54. Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Self-Consistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions. J. Chem. Phys. 1980, 72 (1), 650–654. https://doi.org/10.1063/1.438955.Suche in Google Scholar

55. Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self – Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian – Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 1972, 56 (5), 2257–2261. https://doi.org/10.1063/1.1677527.Suche in Google Scholar

56. Klug, A. The Crystal and Molecular Structure of Triphenylene, C18H12. Acta Crystallogr. 1950, 3 (3), 165–175. https://doi.org/10.1107/s0365110x50000422.Suche in Google Scholar

57. Howard, S.; Krygowski, T. Benzenoid Hydrocarbon Aromaticity in Terms of Charge Density Descriptors. Can. J. Chem. 1997, 75 (9), 1174–1181. https://doi.org/10.1139/v97-141.Suche in Google Scholar

58. Ciesielski, A.; Cyrański, M. K.; Krygowski, T. M.; Fowler, P. W.; Lillington, M. Super-Delocalized Valence Isomer of Coronene. J. Org. Chem. 2006, 71 (18), 6840–6845. https://doi.org/10.1021/jo060898w.Suche in Google Scholar PubMed

59. Kumar, A.; Duran, M.; Solà, M. Is Coronene Better Described by Clar’s Aromatic π-Sextet Model or by the AdNDP Representation? J. Comput. Chem. 2017, 38 (18), 1606–1611. https://doi.org/10.1002/jcc.24801.Suche in Google Scholar PubMed

60. Schleyer, P. v. R.; Manoharan, M.; Jiao, H.; Stahl, F. The Acenes: Is There a Relationship Between Aromatic Stabilization and Reactivity? Org. Lett. 2001, 3 (23), 3643–3646. https://doi.org/10.1021/ol016553b.Suche in Google Scholar PubMed

61. Fias, S.; Van Damme, S.; Bultinck, P. Multidimensionality of Delocalization Indices and Nucleus Independent Chemical Shifts in Polycyclic Aromatic Hydrocarbons. J. Comput. Chem. 2008, 29 (3), 358–366. https://doi.org/10.1002/jcc.20794.Suche in Google Scholar PubMed

62. Leyva-Parra, L.; Pino-Rios, R.; Inostroza, D.; Solà, M.; Alonso, M.; Tiznado, W. Aromaticity and Magnetic Behavior in Benzenoids: Unraveling Ring Current Combinations. Chem. Eur. J. 2024, 30 (1), e202302415. https://doi.org/10.1002/chem.202302415.Suche in Google Scholar PubMed

63. Colvin, M. E.; Janssen, C. L.; Seidl, E. T.; Nielsen, I. M. B.; Melius, C. F. Energies, Resonance and UHF Instabilities in Polycyclic Aromatic Hydrocarbons and Linear Polyenes. Chem. Phys. Lett. 1998, 287 (5), 537–541. https://doi.org/10.1016/s0009-2614(98)00228-0.Suche in Google Scholar

64. Trinquier, G.; David, G.; Malrieu, J.-P. Qualitative Views on the Polyradical Character of Long Acenes. J. Phys. Chem. A 2018, 122 (34), 6926–6933. https://doi.org/10.1021/acs.jpca.8b03344.Suche in Google Scholar PubMed

65. Andrzejak, M.; Petelenz, P. Vibronic Relaxation Energies of Acene-Related Molecules Upon Excitation or Ionization. Phys. Chem. Chem. Phys. 2018, 20 (20), 14061–14071. https://doi.org/10.1039/c8cp01562g.Suche in Google Scholar PubMed

66. Szczepanik, D. W.; Solà, M.; Krygowski, T. M.; Szatylowicz, H.; Andrzejak, M.; Pawełek, B.; Dominikowska, J.; Kukułka, M.; Dyduch, K. Aromaticity of Acenes: The Model of Migrating π-Circuits. Phys. Chem. Chem. Phys. 2018, 20 (19), 13430–13436. https://doi.org/10.1039/c8cp01108g.Suche in Google Scholar PubMed

67. Portella, G.; Poater, J.; Bofill, J. M.; Alemany, P.; Solà, M. Local Aromaticity of [n]Acenes, [n]Phenacenes, and [n]Helicenes (n = 1−9). J. Org. Chem. 2005, 70 (7), 2509. https://doi.org/10.1021/jo0560254.Suche in Google Scholar

68. Van-Catledge, F. A. A Pariser-Parr-Pople-Based Set of Hueckel Molecular Orbital Parameters. J. Org. Chem. 1980, 45 (23), 4801–4802. https://doi.org/10.1021/jo01311a060.Suche in Google Scholar

69. Shaik, S. S.; Hiberty, P. C. A Chemist’s Guide to Valence Bond Theory; John Wiley & Sons, Inc.: Hoboken, New Jersey, USA, 2007.10.1002/9780470192597Suche in Google Scholar

Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/pac-2025-0495).

Received: 2025-04-25
Accepted: 2025-05-22
Published Online: 2025-06-16
Published in Print: 2025-09-25

© 2025 IUPAC & De Gruyter

Artikel in diesem Heft

  1. Frontmatter
  2. IUPAC Technical Report
  3. Acid dissociation constants in selected dipolar non-hydrogen-bond-donor solvents (IUPAC Technical Report)
  4. Preface
  5. Introduction to the Special Issue of “The International Year of Quantum”
  6. Review Articles
  7. Quantum chemistry of molecules in solution. A brief historical perspective
  8. From Hückel to Clar: a block-localized description of aromatic systems
  9. Exploring potential energy surfaces
  10. Unlocking the chemistry facilitated by enzymes that process nucleic acids using quantum mechanical and combined quantum mechanics–molecular mechanics techniques
  11. Hypothetical heterocyclic carbenes
  12. Is relativistic quantum chemistry a good theory of everything?
  13. When theory came first: a review of theoretical chemical predictions ahead of experiments
  14. Research Articles
  15. Exploring reaction dynamics involving post-transition state bifurcations based on quantum mechanical ambimodal transition states
  16. Molecular aromaticity: a quantum phenomenon
  17. Using topology for understanding your computational results
  18. The role of ion-pair on the olefin polymerization reactivity of zirconium bis(phenoxy-imine) catalyst: quantum mechanical study and its beyond
  19. Theoretical insights on the structure and stability of the [C2, H3, P, O] isomeric family
https://doi.org/10.1515/pac-2025-0495
Schlagwörter für diesen Artikel
Aromaticity; computational chemistry; electronic structures; quantum chemistry; quantum science and technology

Artikel in diesem Heft

  1. Frontmatter
  2. IUPAC Technical Report
  3. Acid dissociation constants in selected dipolar non-hydrogen-bond-donor solvents (IUPAC Technical Report)
  4. Preface
  5. Introduction to the Special Issue of “The International Year of Quantum”
  6. Review Articles
  7. Quantum chemistry of molecules in solution. A brief historical perspective
  8. From Hückel to Clar: a block-localized description of aromatic systems
  9. Exploring potential energy surfaces
  10. Unlocking the chemistry facilitated by enzymes that process nucleic acids using quantum mechanical and combined quantum mechanics–molecular mechanics techniques
  11. Hypothetical heterocyclic carbenes
  12. Is relativistic quantum chemistry a good theory of everything?
  13. When theory came first: a review of theoretical chemical predictions ahead of experiments
  14. Research Articles
  15. Exploring reaction dynamics involving post-transition state bifurcations based on quantum mechanical ambimodal transition states
  16. Molecular aromaticity: a quantum phenomenon
  17. Using topology for understanding your computational results
  18. The role of ion-pair on the olefin polymerization reactivity of zirconium bis(phenoxy-imine) catalyst: quantum mechanical study and its beyond
  19. Theoretical insights on the structure and stability of the [C2, H3, P, O] isomeric family
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 30.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/pac-2025-0495/html
Button zum nach oben scrollen