Advertisement

Symmetry Considerations in the Modelling of Light–Matter Interactions in Nanoelectrochemistry

  • Chitra Rangan
Chapter
Part of the Modern Aspects of Electrochemistry book series (MAOE, volume 44)

Summary

The modelling of light–matter interactions at nanometre length scales is becoming increasingly important in modern nanoelectrochemistry. The ability to fabricate extremely sophisticated nanostructures in the laboratory that cannot be described analytically has driven the need for modelling. Advances in scientific computation techniques, and the availability of computing resources have also led to cost savings in several industries, such as the automotive industry. One of the most important considerations for choosing the optimal numerical technique for a problem is symmetry. This rather old-fashioned consideration has tremendous effects on both the accuracy and the efficiency of numerical methods. We show how symmetry considerations play a major role in modern scientific computation. Examples of supported and unsupported quantum dots and quantum dot clusters are presented.

Keywords

Collocation Point Effective Electron Mass Laguerre Function Radial Grid Coulomb Singularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I would like to gratefully acknowledge help from and discussions with Silvia Mittler, Bulent Mutus, Mordechay Schlesinger, Mohammed Hashemi, Jeffrey Rau and Daniel Trojand. Research support by the Natural Sciences and Engineering Research Council of Canada, and Canada Foundation for Innovation is gratefully appreciated. Part of the computations were done on the SharcNet supercomputing network.

References

  1. 1.
    G.A. Somorjai and J.Y. Park, Physics Today, p. 48, Oct. (2007).Google Scholar
  2. 2.
    C.F. Bohren and D.R. Huffman, “Absorption and scattering of light by small particles”, Wiley, New York, (1983).Google Scholar
  3. 3.
    J.C. Maxwell-Garnett, Philos. Trans. R. Soc. Lond. 203, 385 (1904).CrossRefGoogle Scholar
  4. 4.
    J.C. Maxwell-Garnett, Philos. Trans. R. Soc. Lond. Ser. A 205, 237 (1906).CrossRefGoogle Scholar
  5. 5.
    U. Kreibig and M. Vollmer, “Optical properties of metal clusters”, Springer, Berlin, (1995).Google Scholar
  6. 6.
    A.P. Alivisatos, Science 271, 933 (1996).CrossRefGoogle Scholar
  7. 7.
    V.V. Klimov and D.V. Guzatov, Phys. Rev. B 75, 024303 (2007).CrossRefGoogle Scholar
  8. 8.
    B.T. Draine and P.J. Flatau, J. Opt. Soc. Am. A 11, 1491 (1973).CrossRefGoogle Scholar
  9. 9.
    B.T. Draine and J.J. Goodman, Ap. J. 485, 685 (1993).CrossRefGoogle Scholar
  10. 10.
    J.P. Marton and M. Schlesinger, J. Electrochem. Soc. 115, 16 (1968).CrossRefGoogle Scholar
  11. 11.
    D. Bedeaux and J. Vlieger, “Optical properties of surfaces”, 2nd Edn., World Scientific, Singapore, (2004).Google Scholar
  12. 12.
    R. Lazzari, I. Simonsen, D. Bedeaux, J. Vlieger and J. Jupille, Eur. Phys. J. B 24, 267 (2001).CrossRefGoogle Scholar
  13. 13.
    P. Rooney, S. Xu, A. Rezaee, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Boehmer, C. Rangan and S. Mittler, Phys. Rev. B 77, 235446 (2008).CrossRefGoogle Scholar
  14. 14.
    S.M. Hashemi Rafsanjani, C. Rangan and S. Mittler, “A novel measure of refractive index sensitivity in gold nanoparticle biosensors”, (submitted for publication).Google Scholar
  15. 15.
    S. Durocher, A. Rezaee, C. Hamm, C. Rangan, S. Mittler and B. Mutus, 1: J. Am. Chem. Soc. 131, 2475 (2009).CrossRefGoogle Scholar
  16. 16.
    M.A. Kastner, Ann. Phys. 9, 885 (2000).CrossRefGoogle Scholar
  17. 17.
    H.A. Bethe and E.E. Salpeter, “Quantum mechanics of one- and two-electron atoms”, Springer, New York, (1957).Google Scholar
  18. 18.
    H. Friedrich, “Theoretical atomic physics”, Springer, New York, (1990).Google Scholar
  19. 19.
    L.I. Schiff, “Quantum mechanics”, McGraw-Hill, Singapore, (1968).Google Scholar
  20. 20.
    U. Fano and A.R.P. Rau, “Symmetries in quantum physics”, Academic, New York, (1996).Google Scholar
  21. 21.
    A.R.P. Rau and M. Inokuti, Am. J. Phys. 65, 221 (1997).CrossRefGoogle Scholar
  22. 22.
    P. Hawrylak, Phys. Rev. Lett. 71, 3347 (1993).CrossRefGoogle Scholar
  23. 23.
    U. Woggon, “Optical properties of semiconductor quantum dots,” Springer, Berlin, (1997).Google Scholar
  24. 24.
    T.F. Gallagher, “Rydberg atoms”, Cambridge University Press, Cambridge, (1994).CrossRefGoogle Scholar
  25. 25.
    J.P. Boyd, “Chebyshev and Fourier spectral methods”, 2nd Edn., Dover, Mineola, New York, (2001).Google Scholar
  26. 26.
    J.P. Boyd, C. Rangan and P.H. Bucksbaum, J. Comp. Phys., 188, 56 (2003).CrossRefGoogle Scholar
  27. 27.
    S.E. Koonin, “Computational physics”, Benjamin-Cummings, San Fransisco, USA, (1985).Google Scholar
  28. 28.
    J.L. Krause and K.J. Schafer, J. Phys. Chem. A 103, 10118 (1999).CrossRefGoogle Scholar
  29. 29.
    C. Rangan, K.J. Schafer and A.R.P. Rau, Phys. Rev. A 61, 053410 (2000).CrossRefGoogle Scholar
  30. 30.
    R. Varga, “Matrix iterative analysis”, Prentice-Hall, Englewood Cliffs, NJ (1963).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of WindsorWindsorCanada

Personalised recommendations