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Visualizing electronic excitations with the particle-hole map: orbital localization and metric space analysis

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Abstract

The particle-hole map (PHM) is a computational tool to visualize electronic excitations–calculated using time-dependent density-functional theory–based on representations in canonical molecular orbital transition space. Beyond the standard canonical representation, transformation to localized orbitals is a common technique in electronic structure theory. We analyze the PHM as a visualization tool for both canonical and localized orbital representations and give numerical examples for simple one-dimensional model systems. We show that the localized PHMs can be used to construct simple descriptors of the charge-transfer character of an excitation through metric space analysis, and that it can improve the clarity of the visualization provided by the canonical PHM.

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References

  1. C. Deibel, T. Strobel, V. Dyakonov, Adv. Mater. 22, 4097 (2010)

    Article  Google Scholar 

  2. E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)

    Article  ADS  Google Scholar 

  3. E.K.U. Gross, J.F. Dobson, M. Petersilka, Density functional theory of time-dependent phenomena, in Density-Functional Theory II. Topics in Current Chemistry, edited by R.F. Nalewajski (Springer, Berlin, 1996), Vol. 181, pp. 81–172

  4. C.A. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications (Oxford University Press, Oxford, 2012)

  5. M.A.L. Marques, N.T. Maitra, F.M.S. Nogueira, E.K.U. Gross, A. Rubio (Eds.), Fundamentals of Time-Dependent Density-Functional Theory (Springer, Berlin, 2012)

  6. T. Burnus, M.A.L. Marques, E.K.U. Gross, Phys. Rev. A 71, 010501 (2005)

    Article  ADS  Google Scholar 

  7. S. Tretiak, S. Mukamel, Chem. Rev. 102, 3171 (2002)

    Article  Google Scholar 

  8. F. Furche, J. Chem. Phys. 114, 5982 (2001)

    Article  ADS  Google Scholar 

  9. F. Plasser, M. Wormit, A. Dreuw, J. Chem. Phys. 141, 024106 (2014)

    Article  ADS  Google Scholar 

  10. T. Etienne, J. Chem. Phys. 142, 244103 (2015)

    Article  ADS  Google Scholar 

  11. K.M. Coakley, M.D. McGehee, Chem. Mater. 16, 4533 (2004)

    Article  Google Scholar 

  12. Jerzy Cioslowski, (Ed.), Many-electron densities and reduced density matrices (Kluwer Academic/Plenum Publishers, New York, 2000)

  13. P.-O. Löwdin, Phys. Rev. 97, 1474 (1955)

    Article  MathSciNet  ADS  Google Scholar 

  14. R. McWeeny, Rev. Mod. Phys. 32, 335 (1960)

    Article  MathSciNet  ADS  Google Scholar 

  15. S. Bäppler, F. Plasser, M. Wormit, A. Dreuw, Phys. Rev. A 90, 052521 (2014)

    Article  ADS  Google Scholar 

  16. R.L. Martin, J. Chem. Phys. 118, 4775 (2003)

    Article  ADS  Google Scholar 

  17. Y. Li, C.A. Ullrich, Chem. Phys. 391, 157 (2011)

    Article  ADS  Google Scholar 

  18. Y. Li, C.A. Ullrich, J. Chem. Theor. Comput. 11, 5838 (2015)

    Article  Google Scholar 

  19. Y. Li, D. Moghe, S. Patil, S. Guha, C.A. Ullrich, Mol. Phys. 114, 1365 (2016)

    Article  ADS  Google Scholar 

  20. Y. Li, C.A. Ullrich, J. Chem. Phys. 145, 164107 (2016)

  21. J.M. Foster, S.F. Boys, Rev. Mod. Phys. 32, 300 (1960)

    Article  MathSciNet  ADS  Google Scholar 

  22. C. Edmiston, K. Ruedenberg, Rev. Mod. Phys. 35, 457 (1963)

    Article  ADS  Google Scholar 

  23. E.Ö. Jónsson, S. Lehtola, M. Puska, H. Jónsson, J. Chem. Theory Comput. 13, 460 (2017)

    Article  Google Scholar 

  24. G.H. Wannier, Phys. Rev. 52, 191 (1937)

    Article  ADS  Google Scholar 

  25. G.H. Wannier, Rev. Mod. Phys. 34, 645 (1962)

    Article  MathSciNet  ADS  Google Scholar 

  26. N. Marzari, A.A. Mostofi, R.Y. Yates, I. Souza, D. Vanderbilt, Rev. Mod. Phys. 84, 1419 (2012)

    Article  ADS  Google Scholar 

  27. X. Ge, D. Lu, Phys. Rev. B 92, 241107 (2015)

    Article  ADS  Google Scholar 

  28. X. Ge, D. Lu, Phys. Rev. B 96, 075114 (2017)

    Article  ADS  Google Scholar 

  29. R. Iftimie, J.W. Thomas, M.E. Tuckerman, J. Chem. Phys. 120, 2169 (2003)

    Article  ADS  Google Scholar 

  30. O.B. Oña, D.R. Alcoba, W. Tiznado, A. Torre, L. Lain, Int. J. Quant. Chem. 113, 1401 (2013)

    Article  Google Scholar 

  31. J.P. Perdew, A. Zunger, Phys. Rev. B 23, 5048 (1981)

    Article  ADS  Google Scholar 

  32. R.A. Heaton, J.G. Harrison, C.C. Lin, Phys. Rev. B 28, 5992 (1983)

    Article  ADS  Google Scholar 

  33. M.R. Pederson, A. Ruzsinszky, J.P. Perdew, J. Chem. Phys. 140, 121103 (2014)

    Article  ADS  Google Scholar 

  34. M.E. Casida, Time-dependent density functional response theory for molecules, in Recent Advances in Density Functional Methods, Recent Advances in Computational Chemistry, edited by D.E. Chong (World Scientific, Singapore, 1995), Vol. 1, pp. 155–192

  35. M. Petersilka, U.J. Gossmann, E.K.U. Gross, Phys. Rev. Lett. 76, 1212 (1996)

    Article  ADS  Google Scholar 

  36. I. D’Amico, J.P. Coe, V.V. França, K. Capelle, Phys. Rev. Lett. 106, 050401 (2011)

    Article  MathSciNet  Google Scholar 

  37. P.M. Sharp, I. D’Amico, Phys. Rev. B 89, 115137 (2014)

    Article  ADS  Google Scholar 

  38. P.M. Sharp, I. D’Amico, Phys. Rev. A 94, 062509 (2016)

    Article  ADS  Google Scholar 

  39. S. Marocchi, S. Pittalis, I. D’Amico, Phys. Rev. Mat. 1, 043801 (2017)

    Google Scholar 

  40. J. Neugebauer, J. Chem. Phys. 126, 134116 (2007)

    Article  ADS  Google Scholar 

  41. M. Pavanello, J. Chem. Phys. 138, 204118 (2013)

    Article  ADS  Google Scholar 

  42. A. Krishtal, D. Sinha, A. Genova, M. Pavanello, J. Phys.: Condens. Matter 27, 183202 (2015)

    ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Missouri, Columbia, Missouri, 65211, USA

    Edward A. Pluhar III & Carsten A. Ullrich

Authors
  1. Edward A. Pluhar III
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  2. Carsten A. Ullrich
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Correspondence to Carsten A. Ullrich.

Additional information

Contribution to the Topical Issue “Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.

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Pluhar, E.A., Ullrich, C.A. Visualizing electronic excitations with the particle-hole map: orbital localization and metric space analysis. Eur. Phys. J. B 91, 137 (2018). https://doi.org/10.1140/epjb/e2018-90200-0

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