Polarizability and second hyperpolarizability of M@B24N24 cages (M=Li, Na and K)

Document Type : Reasearch Paper


Departments of Physics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.


By applying B3LYP/6-31G* time dependent density functional level of theory and sum-over-state (SOS) approach, the static and frequency dependent polarizability and second hyperpolarizability properties of the , , and  cages have been studied. The polarizability and second hyperpolarizability properties of  cage have been studied by considering effects of Li, Na and K atoms encapsulation in the cage. The type and encapsulation of M atom can greatly impress onpolarizabilities and second hyperpolarizabilities values of cage. As, highest peak value of second hyperpolarizabilities for  is about 23 times larger than that of the , and cages. It seems that cages can be used to produce the semiconductors with various band gaps.


[1] Munn R. W., Ironside C. N., (1993), Principles and Applications of Nonlinear Optical Materials, London: Chapman and Hall.
[2] Han L. A., Chen C. L., (2012), Transport properties and laser irradiation effect in Ca0.8Ce0.2MnO3 film. Indian J. Phys. 86: 877-880.
[3] Gogoi A., Ahmed G. A., Choudhury A., (2009), Nanoparticle size characterization by laser light scattering. Indian J. Phys. 83: 473-477.
[4] Ahmadi R., Pirahan Foroush M., (2014), Fullerene effect on chemical properties of antihypertensive clonidine in water phase. Annals of Military Health Sci. Res.12: 39-43.
[5] Blackmore K. J., Lal N., Ziller J. W., Heyduk A. F., (2008), Catalytic reactivity of a zirconium(IV) redox-active ligand complex with 1, 2-diphenylhydrazine. J. Am. Chem. Soc. 130: 2728–2729.
[6] Yaghobi M., (2014), Effect of carbon doping on polarizability and second hyperpolarizability of B 12 N 12 cage, Indian J. Phys. 88: 237-242.
[7] Marder S. R., Torruellas W. E., Blanchard-Desce M., Ricci V., Stegeman G.  I., Gilmour S.,   Bredas J. –L., Li J., Bublitz G. U., Boxe S. G., (1997), Large molecular third-order optical nonlinearities in polarized carotenoids.Science. 276: 1233-1236.
[8]  Dresselhaus M. S., (1996), Science of Fullerenes and Carbon Nanotubes: Their Properties and Applications, New York: Academic Press.
[9] Heath J. R., Brien S. C. O., Zhang Q., Liu Y., Curl R. F., Tittel F. K., Smalley R. E., (1985), Lanthanum complexes of spheroidal carbon shells. J. Am. Chem. Soc. 107: 7779-7780.
[10] Chai Y., Guo T., Jin C., Haufler R. E., Chibante L. P. F., Fure J., Wang L., Alford J. M., Smalley R. E., (1991), Fullerenes with metals inside.  J. Phys. Chem. 95: 7564–7568.
[11] Johnson R. D., de Vries M. S., Salem J. R., Bethunde D. S., Yannoni C. S., (1992), Electron paramagnetic resonance studies of lanthanum-containing C82. Nature. 355: 239-244.
[12] Andreoni W., Gygi F., Parrinello M., (1992), Impurity states in doped fullerenes: C59B and C59N. Chem. Phys. Lett. 190: 159-162.
[13] Hummelen J. C., Bellavia-Lund C., Wudl F., (1999), Fullerenes and related structures (eds) A Hirsch , Berlin, Heidelberg: Springer.
[14] Hummelen J. C., Knight B., Pavlovich J., Gonzalez R., Wudl F., (1995), Isolation of the heterofullerene C59N as Its dimer (C59N)2. Science 269: 1554-1558.
[15] Forrol L., Mihaly L., (2001), Electronic properties of doped fullerenes. Rep. Prog. Phys. 64: 649-708.
[16] Hou  J. Q.,  Kang H. S., (2007), DFT study on the stabilities of the heterofullerenes Sc3N@C67B, Sc3N@C67N, and Sc3N@C66BN. J. Phys. Chem. A. 111: 1111-1116.
[17] Stevenson S., Rice G., Glass T., Harich K., Cromer F., Jordan M. R., Craft J., Hadju E., Bible R., Olmstead M. M., Maitra K., Fisher A. J., Balch A. L., Dorn H. C., (1999), Small-bandgap endohedral metallofullerenes in high yield and purity. Nature. 401: 55-57.
[18] Yaghobi M., Adabinezhad A. R., (2016),Structural and optical properties of the M@C59X cages (X=N, B and M=Li, Na). Pramana  J. Phys. 86: 109–116.
[19] Juárez R., Salazar Villanueva M., Cortés-Arriagada D., Chigo Anota E., (2019), Fullerene-like boron nitride cages BxNy (x+y=28): Stabilities and electronic properties from density functional theory computation. J. Mol. Model. 25:21-27.
[20] Fu W., Zhang J., Fuhrer T., Champion H., Furukawa K., Kato T., Mahaney J. E., Burke B. G., Williams K. A., Walker K., Dixon C., Ge J., Shu C., Harich K., Dorn H. C., (2011), Gd2@C79N: Isolation, characterization, and mono adduct formation of a very stable hetero fullerene with a magnetic spin state of S = 15/2. Am. Chem. Soc. 133: 9741-9750.
[21] Frisch M. J., Trucks G. W.,  Schlegel H. B., Scuseria G. E.,  Robb M. A.,  Cheeseman J. R.,  Zakrzewski V. G.,  Montgomery J. A., Stratmann R. E., Burant J. C., Dapprich S.,  Millam J. M., Daniels A. D., Kudin K. N., Strain M. C., Farkas O., Tomasi J., Barone V., Cossi M.,  Cammi R., Mennucci B., Pomelli C., Adamo C.,  Clifford S., Ochterski J., Petersson G. A., Ayala P. Y., Cui Q.,  Morokuma K., Malick D. K.,  Rabuck A. D., Raghavachari K. , Foresman J. B., Cioslowski J., Ortiz J. V., Baboul A. G., Stefanov B. B., Liu G., Liashenko A., Piskorz  P., Komaromi I., Gomperts R. , Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Andres J.  L., Gonzalez C., Head-Gordon M., Replogle E. S., Pople J. A., Gaussian 98, Revision A., Gaussian, Inc , ittsburgh PA( 1998).
[22] Karamanis P., Pouchan C., (2011), On the shape dependence of cluster (hyper) polarizabilities. A combined ab initio and DFT study on large fullerene–like gallium arsenide semiconductor clusters. Int. J. Quantum Chem.111: 788-796.
[23] Hehre W. J., Ditchfield R., Pople J. A., (1972), 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. 56: 2257-2262.
[24] Mattuck R. D., (1967), A Guide to Feynman Diagrams in the Many-Body Problem, New York, McGraw-Hill.
[25] Orr B. J., Ward J. F., (1971), Perturbation theory of the non-linear optical polarization of an isolated system. Moll. Phys. 20: 513-526.
[26] Guan W., Liu C. G., Song P., Yang G. C., Su Z. M., (2009), Quantum chemical study of redox-switchable second-order optical nonlinearity in Keggin-type organoimido derivative [PW11O39(ReNC6H5)]n (n = 2–4). Theor. Chem. Account. 122: 265-273.
[27] Campbell E. E. B., Fanti M., Hertel I. V., Mitzner R., Zerbetto F., (1998), The hyperpolarisability of an endohedral fullerene: Li@C60. Chem. Phys. Lett. 288: 131-137.
[28] Campbell E. E. B., Couris S., Fanti M., Koudoumas E., Krawez N., Zerbetto F., (1999), Third‐order susceptibility of Li@C60.Adv. Mater. 11: 405-408.
[29] Xie R. H., (1999), Doping effect on the third-order optical nonlinearities of C70. Phys. Lett. A. 12: 51-58.
[30] Liu T., Iwata S., Gu B. J., (1994), Structural properties of the endohedral complex Na+@C60. Phys. Condens. Matter. 6: L253-L258.
[31] Guo T., Jin C., Smalley R. E., (1991), Doping bucky: Formation and properties of boron-doped buckminsterfullerene. J. Phys. Chem. 95: 4948-4950.