# Excitons and Localized States in Nanosized Molecular Aggregates with Impurities

- 12 Downloads

### Abstract

The eigenvalues and eigenfunctions of excitons and localized states making up the spectrum of nanosized (number of sites <100) molecular chains with one and two impurity sites have been found from the solution of secular equations at an energy *V* of excited impurity states and their interaction energy *W* with neighboring sites (in a homogeneous chain, *V* = 0, *W* = 1). A method is proposed for determining the universal relations of energies, density of states, amplitude distributions, and localization lengths to *V* and *W*. It has been shown that the rates of tunneling and hopping between impurities located at different relative distances depend on band reorganization in the initial and transition states.

## Keywords:

one-dimensional molecular models band and localized states density of states localization length## Notes

### ACKNOWLEDGMENTS

This work was supported by the Presidium of the Russian Academy of Sciences under the Fundamental Research Program PFI 1.8 P and in the framework of project no. 0007-2014-FANO.

## REFERENCES

- 1.Van Amerongen, H., Valcunas, L., and Grondelle, R.,
*Photo-Synthetic Excitons*, Singapore: World Scientific, 2000.CrossRefGoogle Scholar - 2.Blakenship, R.E.,
*Molecular Mechanisms of Photosynthesis*, Oxford: Blackwell Science, 2002.CrossRefGoogle Scholar - 3.Ishizaki, A. and Fleming, G.R.,
*J. Chem. Phys*., 2009, vol. 130, p. 234111.CrossRefGoogle Scholar - 4.Di Ventra, M. and Zwolak, M.,
*Encyclopedia of Nanoscience and Nanotechnology*, Singh-Nalwa, H. Ed., Stevenson Ranch, CA: American Scientific, 2004, vol. 2, p. 475.Google Scholar - 5.Chen, M.C., Liaw, D.J., Huang, Y.C., Wu, H.Y., and Tai, Y.,
*Sol. Energy Mater. Sol. Cells*, no. (2011), p. 2621.Google Scholar - 6.
*Organic Solar Cells: Materials and Device Physics*, Choy, W.C.H., Ed., London: Springer, 2013.Google Scholar - 7.You, J., Dou, L., Hong, Z., Li, G., and Yang, Y.,
*Prog. Polym. Sci*., 2013, vol. 38, p. 1909.CrossRefGoogle Scholar - 8.Reineke, S., Thomschke, M., Lussem, B., and Leo, K.,
*Rev. Mod. Phys*., 2013, vol. 85, p. 1246.CrossRefGoogle Scholar - 9.Benderskii, V.A. and Kats, E.I.,
*JETP Lett*., 2015, vol. 101, p. 17.CrossRefGoogle Scholar - 10.Benderskii, V.A. and Kats, E.I.,
*J. Exp. Theor. Phys*., 2018. (in press).Google Scholar - 11.Benderskii, V.A. and Kats, E.I.,
*High Energy Chem*., 2018, vol. 52, no. 5, p. 390.CrossRefGoogle Scholar - 12.Benderskii, V.A. and Kats, E.I.,
*High Energy Chem*., 2018, vol. 52, no. 5, p. 400.CrossRefGoogle Scholar - 13.Touless, D.J.,
*Phys. Rep*., 1974, vol. 13, p. 93.CrossRefGoogle Scholar - 14.Datta, S.,
*Electronic Transport in Mesoscopic Systems*, Cambridge: Cambridge Univ. Press, 1995.CrossRefGoogle Scholar - 15.Sokoulis, C.M. and Economou, E.N.,
*Waves Random Media*, 1999, vol. 9, p. 255.CrossRefGoogle Scholar - 16.Oguri, A.,
*Phys. Rev. B: Condens. Matter*, 2001, vol. 63, p. 115305.CrossRefGoogle Scholar - 17.Cheragchi, H., Fazeli, S.M., and Esfariani, K.,
*Phys. Rev. B: Condens. Matter*, 2005, vol. 72, p. P. 174207.Google Scholar - 18.Carter, J.M. and Mackinnon,
*Phys. Rev. B: Condens. Matter*, 2005, vol. 72, p. 024208.CrossRefGoogle Scholar - 19.Ruiz, J., Jodar, E., and Gasparian, V.,
*Phys. Rev. B: Condens. Matter*, 2007, vol. 75, p. 235123.CrossRefGoogle Scholar - 20.Wu, J., Liu, F., Shen, Y., Cao, J., and Silbey, R.J.,
*New J. Phys*., 2010, vol. 12, p. 105012.CrossRefGoogle Scholar - 21.Zhong, X., Zhao, Y., and Cao, J.,
*J. Chem. Phys*., 2013, vol. 139, p. 224112.CrossRefGoogle Scholar - 22.Szegö, G.,
*Orthogonal Polynomials*, Providence, Rhode Island: American Mathematical Society, 1958, 2nd ed.Google Scholar - 23.Zaslavskii, G.M.,
*Stokhastichnost’ dinamicheskikh sistem*(Stochasticity of Dynamic Systems), Moscow: Nauka, 1984.Google Scholar - 24.Benderskii, V.A., Fal’kovsky, L.A., and Kats, E.I.,
*JETP Lett*., 2007, vol. 86, p. 221.CrossRefGoogle Scholar - 25.Benderskii, V.A. and Kats, E.I.,
*J. Exp. Theor. Phys*., 2011, vol. 140, p. 562.CrossRefGoogle Scholar - 26.Benderskii, V.A., Kotkin, A.S., and Kats, E.I.,
*Phys. Lett. A*, 2013, vol. 377, p. 737.CrossRefGoogle Scholar