Bounds of HOMO-LUMO Gap for Certain Nanotubes and Nanotori

Authors

  • Uzma Ahmad Department of Mathematics, University of the Punjab, Lahore
  • Saira Hameed Department of Mathematics, University of the Punjab, Lahore

DOI:

https://doi.org/10.26713/jims.v10i3.807

Keywords:

Molecular graph, Eigenspectrum, HOMO-LUMO gap, Bipartite graphs, Hermitian matrix

Abstract

The eigenspectrum \(\mu_1 \ge \mu_2\le \cdots \ge \mu_m\) with the middle eigenvalues \(\mu_h\) and \(\mu_l\), where \(h = \lfloor(m + 1)=2\rfloor\) and \(l = \rceil(m + 1)=2\rceil\) of simple connected graph \(G'\) with \(m\) number of vertices contribute significantly in the Huuckel Molecular Theory. The HOMO-LUMO gap \(\Delta_{G'}\) is defined as \(\Delta_{G'}= \mu_h-\mu_l\) subject to the condition that the number of electrons are in one to one correspondence with the number of vertices. In this article, the upper bounds for the HOMO-LUMO gap corresponding to the connected graphs of nanotube \(TUC_4C_8(S)\) and \(C_4C_8\) nanotorus by using matrix theory are estimated.

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References

S. Ahmad, U. Ahmad, M. Imran and N. Farah, The Omega and Sadhana polynomials of nanotube TUC4[p, q], Can. J. Chem. 94 (2016), 490.

P.W. Fowler and T. Pisanski, HOMO-LUMO map for fullerenes, Acta Chim. Slov. 57 (2010), 513.

P.W. Fowler and T. Pisanski, HOMO-LUMO map for chemical graphs, MATCH Commun. Math. Comput. Chem. 64 (2010), 373.

P.W. Fowler, P. Hansen, G. Capoross and A. Soncini, Polyenes with maximum HOMO-LUMO gap, Chem. Phys. Lett. 342 (2001), 105. DOI: 10.1016/S0009-2614(01)00570-X.

M. Gallo, A. Favila and D. Glossman-Mitnik, DFT studies of functionalized carbon nanotubes and fullerenes as nanovectors for drug delivery of antitubercular compounds, Chemical Physics Letters 447 (2007), 105–109.

I. Gutman, Note on a topological property of the HOMO-LUMO separation, Z. Naturforsch. 35 (1980), 458, DOI: 10.1515/zna-1980-0419.

I. Gutman, J.V. Knop and N. Trinajsti, A graph-theoretical analysis of the HOMO LUMO separation in conjugated hydrocarbons, Z. Naturforsch. 29B (1974), 80, DOI: 10.1515/znb-1974-1-225.

M. Hesabi and M. Hesabi, The interaction between carbon nanotube and skin anti-cancer drugs: a DFT and NBO approach, Journal of Nanostructure in Chemistry 3 (2013), 22.

A. Heydari, On the modified Schultz index of C4C8(S) nanotori and nanotube, Digest. J. Nanomater. Bios. 5(1) (2010), 51.

Y. Huo, J. Liu, S. Ahmad, N. Farah, U. Ahmad, M.R. Farahani and M. Imran, On certain topological indices of TUC5C8 nanotubes, Journal of Computational and Theoretical Nanoscience 13 (2016), 9158.

G. Jakli, P.W. Fowler and T. Pisanski, HL-index of a graph, Ars Math. Contemp. 5 (2012), 99.

D.J. Klein, Y. Yang and D. Ye, HOMO-LUMO gap for sub-graphenic and sub-buckytubic species, Proc. R. Soc. A 471: 20150183 (2015).

X. Li, Y. Li, Y. Shi and I. Gutman, Note on the HOMO-LUMO index of graphs, MATCH Commun. Math. Comput. Chem. 70(2013), 85.

B. Mohar, Median eigenvalues and the HOMO-LUMO index of graphs, J. Comb. Theory B. 112 (2015), 78, DOI: 10.1016/j.jctb.2014.12.001.

A. Rochefort, D.R. Salahub and P. Avouris, Effects of finite length on the electronic structure of carbon nanotubes, J. Phys. Chem. B 103 (1999), 641 – 646.

F.J. Zhang and A. Chang, Acyclic molecules with greatest HOMO LUMO separation, Discrete Appl. Math. 98 (1999), 165, DOI: 10.1016/S0166-218X(99)00119-5.

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Published

2018-09-30
CITATION

How to Cite

Ahmad, U., & Hameed, S. (2018). Bounds of HOMO-LUMO Gap for Certain Nanotubes and Nanotori. Journal of Informatics and Mathematical Sciences, 10(3), 391–398. https://doi.org/10.26713/jims.v10i3.807

Issue

Vol. 10 No. 3 (2018)

Section

Research Articles

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