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Graphene Quantum Dots in Various Many-Electron π-Models

  • Anatoliy LuzanovEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 210)

Abstract

We make use of various quantum chemistry approaches to understand π-electronic properties of a number of graphene quantum dots (GQDs) and at the same time to clarify the possibilities of fairly simple and feasible models for complex carbon-containing systems. Most of the studied systems turn out to be electronically unstable and requiring a good account for electron correlation. Here we investigate the ground state properties of GQDs in the framework of Löwdin’s extended Hartree-Fock method for π-shells. Additionally, GQD-excited states are modeled by the restricted active space configuration interaction (RAS-CI) method. In particular, it is shown that RAS-CI allows to get reasonable singlet-triplet energy gaps whereas the conventional single CI method gives mostly incorrect results for the same systems. Special focuses are given to aromaticity, effective electron unpairing, and the behavior of graphene networks in strong electric fields.

References

  1. 1.
    Jiang DE, Chen Z (eds) (2013) Graphene chemistry: theoretical perspectives. Wiley, Puerto RicoGoogle Scholar
  2. 2.
    Güçlü AD, Potasz P, Korkusinski M, Hawrylak P (2014) Graphene quantum dots. Springer, Berlin/Heidelberg/New YorkCrossRefGoogle Scholar
  3. 3.
    Kheirabadi N, Shafiekhani A, Fathipour M (2014) Review on graphene spintronic, new land for discovery. Superlattice Microst 74:123CrossRefADSGoogle Scholar
  4. 4.
    Yin PT, Shah S, Chhowalla M, Lee K-B (2015) Design, synthesis, and characterization of graphene–nanoparticle hybrid materials for bioapplications. Chem Rev 115:2483CrossRefGoogle Scholar
  5. 5.
    Georgakilas V, Perman JA, Tucek J, Zboril R (2015) Broad family of carbon nanoallotropes: classification, chemistry, and applications of fullerenes, carbon dots, nanotubes, graphene, nanodiamonds, and combined superstructures. Chem Rev 115:4744CrossRefGoogle Scholar
  6. 6.
    Luzanov AV (2014) Measures of unpaired electrons for large conjugated systems. J Struct Chem 55:799CrossRefGoogle Scholar
  7. 7.
    Luzanov AV (2014) Effectively unpaired electrons in bipartite lattices within the generalized tight-binding approximation: application to graphene nanoflakes. Funct Mater 21:414CrossRefGoogle Scholar
  8. 8.
    Luzanov AV (2016) Effectively unpaired electrons for singlet states: from diatomics to graphene nanoclusters. In: Leszczynski J, Shukla MK (eds) Practical aspects of computational chemistry IV. Springer, Boston, p 151Google Scholar
  9. 9.
    Luzanov AV (2017) About theoretical peculiarities of lowest excitations in modified nanodiamond color centers. Funct Funct Mater 24:127CrossRefGoogle Scholar
  10. 10.
    Luzanov AV, Plasser F, Das A, Lischka H (2017) Evaluation of the quasi correlated tight-binding (QCTB) model for describing polyradical character in polycyclic hydrocarbons. J Chem Phys 146:064106CrossRefADSGoogle Scholar
  11. 11.
    Luzanov AV (2017) Localization of orbitals and electronic properties in nanodiamonds with color centers: semiempirical models. In: Fesenko O, Yatsenko L (eds) Nanophysics, nanomaterials, and applications, Springer proceedings in physics 195. Springer, Cham, p 115CrossRefGoogle Scholar
  12. 12.
    Zdetsis AD, Economou EN (2015) A pedestrian approach to the aromaticity of graphene and nanographene: significance of Hückel’s (4n+2)π electron rule. J Phys Chem C 119:16991CrossRefGoogle Scholar
  13. 13.
    Saha B, Bhattacharyya PK (2016) Understanding reactivity, aromaticity and absorption spectra of carbon cluster mimic to graphene: a DFT study. RSC Advance 6:79768CrossRefGoogle Scholar
  14. 14.
    Nishino N, Makino M, Aihara J-i (2016) Aromatic character of irregular-shaped nanographenes. J Phys Chem A 120:2431; Aihara J-i (2016) Graph theory of aromatic stabilization. Bull Chem Soc Jap 89:1425Google Scholar
  15. 15.
    Luzanov AV (2011) Quantum fidelity for analyzing atoms and fragments in molecule: APPLICATION to similarity, chirality, and aromaticity. Int J Quant Chem 111:2197Google Scholar
  16. 16.
    Čížek J, Paldus J (1967) Stability conditions for the solutions of the Hartree—Fock equations for atomic and molecular systems. Application to the pi-electron model of cyclic polyenes. J Chem Phys 47:3976CrossRefADSGoogle Scholar
  17. 17.
    Helgaker T, Jorgensen P, Olsen J (2000) Molecular electronic-structure theory. Wiley, New YorkCrossRefGoogle Scholar
  18. 18.
    Olsen J, Roos BO, Jorgensen P, HJAa J (1988) Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces. J Chem Phys 89:2185CrossRefADSGoogle Scholar
  19. 19.
    McWeeny R (1992) Methods of molecular quantum mechanics. Academic Press, LondonGoogle Scholar
  20. 20.
    Koutecký J (1967) Unrestricted Hartree—Fock solutions for closed-shell molecules. J Chem Phys 46:2443CrossRefADSGoogle Scholar
  21. 21.
    Löwdin P-O (1955) Quantum theory of many-particle systems. III. Extension of the Hartree-Fock scheme to include degenerate systems and correlation effects. Phys Rev 97:1505MathSciNetADSGoogle Scholar
  22. 22.
    Mayer I (1980) The spin-projected extended Hartree-Fock method. Adv Quant Chem 12:189CrossRefGoogle Scholar
  23. 23.
    Mestechkin MM, Vaiman GE, Klimo V, Tino J (1983) Extended Hartree-Fock method and its application to molecules [in Russian]. Naukova Dumka, KievGoogle Scholar
  24. 24.
    Jiménez-Hoyos CA, Henderson TM, Tsuchimochi T, Scuseria GE (2012) Projected Hartree-Fock theory. J Chem Phys 136:164109CrossRefADSGoogle Scholar
  25. 25.
    Luzanov AV, Ivanov VV (1991) Configuration interaction of states of the quasi-one-electron type. Theor Exp Chem 26:363CrossRefGoogle Scholar
  26. 26.
    Yan X, Li B, Lim L-S (2013) Colloidal graphene quantum dots with well-defined structures. Acc Chem Res 46:2224Google Scholar
  27. 27.
    Clar E (1964) Polycyclic hydrocarbons. Academic Press, New YorkGoogle Scholar
  28. 28.
    Bofill JM, Pulay P (1989) The unrestricted natural orbital–complete active space (UNO–CAS) method: an inexpensive alternative to the complete active space–self-consistent-field (CAS–SCF) method. J Chem Phys 90:3637CrossRefADSGoogle Scholar
  29. 29.
    Ovchinnikov AA (1978) Multiplicity of the ground state of large alternant organic molecules with conjugated bonds. Theor Chim Acta 47:297CrossRefGoogle Scholar
  30. 30.
    Lieb EH (1989) Two theorems on the Hubbard model. Phys Rev Lett 62:1201MathSciNetCrossRefADSGoogle Scholar
  31. 31.
    Head-Gordon M (2003) Characterizing unpaired electrons from the one-particle density matrix. Chem Phys Lett 372:508CrossRefADSGoogle Scholar
  32. 32.
    Feixas F, Matito E, Poater J, Sola M (2015) Quantifying aromaticity with electron delocalisation measures. Chem Soc Rev 44:6434CrossRefGoogle Scholar
  33. 33.
    Nagai H, Nakano M, Yoneda K, Kishi R, Takahashi H, Shimizu A, Kubo T, Kamada K, Ohta K, Botek E, Champagne B (2010) Signature of multiradical character in second hyperpolarizabilities of rectangular graphene nanoflakes. Chem Phys Lett 489:212CrossRefADSGoogle Scholar
  34. 34.
    Nakano M, Champagne B (2016) Nonlinear optical properties in open-shell molecular systems. WIREs Comput Mol Sci 6:198CrossRefGoogle Scholar
  35. 35.
    Zakharov AB, Ivanov VV, Adamowicz L (2016) Optical parameters of π-conjugated oligomer chains from the semiempirical local coupled-cluster theory. In: Leszczynski J, Shukla M (eds) Practical aspects of computational chemistry IV. Springer, Boston, p 57Google Scholar
  36. 36.
    Li H-P, Bi Z-T, Hu R-F, Han K, Li M-X, , Shen X-P, Wu Y-X (2017) Theoretical study on electronic polarizability and second hyperpolarizability of hexagonal graphene quantum dots: effects of size, substituent, and frequency. Carbon 122:756CrossRefGoogle Scholar
  37. 37.
    Pople JA, McIver JW, Ostlund NS (1968) Self-consistent perturbation theory. I. Finite perturbation methods. J Chem Phys 49:2960CrossRefADSGoogle Scholar
  38. 38.
    Pedash YF, Ivanov VV, Luzanov AV (1992) π-Electron hyperpolarizability of even-numbered polyenes in the complete configuration interaction method. Theor Exp Chem 28:19CrossRefGoogle Scholar
  39. 39.
    Pedash VF, Luzanov AV (1981) Separation of the local contributions to the transition moments and the polarizability of a molecule in the self-consistent field method. J Struct Chem 21:439CrossRefGoogle Scholar
  40. 40.
    Lazzeretti P, Zanasi R (1984) Resolution of molecular polarizability into atomic terms. Chem Phys Lett 109:89CrossRefADSGoogle Scholar
  41. 41.
    Bader RFW (1990) Atoms in molecules – a quantum theory. Oxford University Press, OxfordGoogle Scholar
  42. 42.
    Otego N, Aslenoy CV, Pouchan C, Karamais P (2015) Hirshfeld-based intrinsic polarizability density representations as a tool to analyze molecular polarizability. J Comput Chem 36:1831CrossRefGoogle Scholar
  43. 43.
    Chattaraj PK, Sengupta S (1996) Popular electronic structure principles in a dynamical context. J Phys Chem 100:16126CrossRefGoogle Scholar
  44. 44.
    Chattaraj PK, Sarkar U, Roy DR (2007) Electronic structure principles and aromaticity. J Chem Educ 84:354CrossRefGoogle Scholar
  45. 45.
    Santos JC, Contreras M, Merino G (2010) Structure and stability of Si 6 li 6: aromaticity vs polarizability. Chem Phys Lett 496:172CrossRefADSGoogle Scholar
  46. 46.
    Luzanov AV (2013) π-system in a strong electric field. Analysis of electron unpairing. J Struct Chem 54:835CrossRefGoogle Scholar
  47. 47.
    Kryachko ES, Ludeña EV (2014) Density functional theory: foundations reviewed. Phys Rep 544:123MathSciNetCrossRefADSGoogle Scholar
  48. 48.
    McWeeny R (1994) Density functions and density functionals. Philos Mag B 69:727CrossRefADSGoogle Scholar
  49. 49.
    Kaplan IG (2007) Problems in DFT with the total spin and degenerate states. Int J Quantum Chem 107:2595CrossRefADSGoogle Scholar
  50. 50.
    Kaplan IG (2017) The Pauli exclusion principle: origin, verifications and applications. Wiley, ChichesterzbMATHGoogle Scholar
  51. 51.
    Chiappe G, Louis E, San-Fabián E, Vergés AV (2015) Can model Hamiltonians describe the electron-electron interaction in π-conjugated systems? PAH and graphene. J Phys Condens Matter 27:463001CrossRefADSGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Scientific Institution “Institute of Single Crystals”National Academy of Sciences of UkraineKharkivUkraine

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