Skip to main content
Log in

Electronic excitation of benzene by low energy electron impact and the role of higher lying Rydberg states

  • Regular Article – Atomic and Molecular Collisions
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

Benzene is undoubtedly one of the most studied target molecules in electron scattering experiments and calculations. However, there is still a huge knowledge gap on the electronic excitation cross sections of this fundamental collision. Here, we report calculated differential and integral cross sections for elastic and electronic excitation, as well as total cross sections, for electron scattering by the benzene molecule, for impact energies in the 10–50 eV range. We have employed the Schwinger multichannel method, in two levels of approximation. By including extra diffuse functions in the second calculation, the role of higher lying Rydberg states in the multichannel coupling scheme was assessed. We found that such states have minor effects on the elastic and total cross sections. In contrast, the electronic excitation cross sections of the lower-lying bands decrease in magnitude when accounting for the higher Rydberg states, and this effect becomes more pronounced at lower impact energies. Our computed elastic cross sections are in quite good agreement with the available experimental data, whereas the comparison for the electronic excitation channels is still satisfactory. We also discuss the need for accurate excitation energies in order to properly compare theoretical and experimental electronic excitation cross sections.

Graphic Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: Our full set of cross sections is provided in the Zenodo repository, at https://doi.org/10.5281/zenodo.5567092].

References

  1. Z. Ates-Alagoz, N. Coleman, M. Martin, A. Wan, A. Adejare, Chem. Biol. Drug. Des. 80, 853 (2012)

    Article  Google Scholar 

  2. E. Alizadeh, T.M. Orlando, L. Sanche, Annu. Rev. Phys. Chem. 66, 379 (2015)

    Article  ADS  Google Scholar 

  3. J.D. Gorfinkiel, S. Ptasinska, J. Phys. B: At. Mol. Opt. Phys. 50, 182001 (2017)

    Article  ADS  Google Scholar 

  4. F.H. Read, G.L. Whiterod, Proc. Phys. Soc. 85, 71 (1965)

  5. E.N. Lassettre, A. Skerbele, M. Dillon, K. Ross, J. Chem. Phys. 48, 5066 (1968)

    Article  ADS  Google Scholar 

  6. R.N. Compton, R.H. Huebner, P.W. Reinhardt, L.G. Christophorou, J. Chem. Phys. 48, 901 (1968)

    Article  ADS  Google Scholar 

  7. J.P. Doering, J. Chem. Phys. 51, 2866 (1969)

    Article  ADS  Google Scholar 

  8. J.P. Doering, J. Chem. Phys. 67, 4065 (1977)

    Article  ADS  Google Scholar 

  9. D. Mathur, J.B. Hasted, J. Phys. B: Atom. Mol. Phys. 9, L31 (1976)

    Article  ADS  Google Scholar 

  10. J.S. Mahant Shetty, S.M. Bharathi, G. Basavaraju, Pramana. J. Phys. 39, 297 (1992)

    Article  ADS  Google Scholar 

  11. P. Mozejko, G. Karsperski, Cz. Szmytkowski, G.P. Karwasz, R.S. Brusa, A. Zecca, Chem. Phys. Lett. 257, 309 (1996)

    Article  ADS  Google Scholar 

  12. F.A. Gianturco, R.R. Lucchese, J. Chem. Phys. 108, 6144 (1998)

    Article  ADS  Google Scholar 

  13. R.J. Gulley, S.J. Buckman, J. Phys. B: At. Mol. Opt. Phys. 32, L405 (1999)

    Article  ADS  Google Scholar 

  14. M.H.F. Bettega, C. Winstead, V. McKoy, J. Chem. Phys. 112, 8806 (2000)

    Article  ADS  Google Scholar 

  15. Y. Jiang, J. Sun, L. Wan, Phys. Rev. A 62, 2473 (2000)

    Article  Google Scholar 

  16. H. Cho, R.J. Gulley, K. Sunohara, M. Kitajima, L.J. Uhlmann, H. Tanaka, S.J. Buckman, J. Phys. B: At. Mol. Opt. Phys. 34, 1019 (2001)

    Article  ADS  Google Scholar 

  17. H. Cho, R.J. Gulley, S.J. Buckman, J. Chin. Chem. Soc. 48, 381 (2001)

    Article  Google Scholar 

  18. D. Field, J.-P. Ziesel, S.L. Lunt, R. Parthasarathy, L. Suess, S.B. Hill, F.B. Dunning, R.R. Lucchese, F.A. Gianturco, J. Phys. B: At. Mol. Opt. Phys. 34, 4371 (2001)

    Article  ADS  Google Scholar 

  19. P. Carsky, R. Curik, F.A. Gianturco, R.R. Lucchese, M. Polasek, Phys. Rev. A 65, 052713 (2002)

    Article  ADS  Google Scholar 

  20. J. Sun, C. Du, Y. Liu, Phys. Lett. A 314, 150 (2003)

    Article  ADS  Google Scholar 

  21. C. Makochekanwa, O. Sueoka, M. Kimura, Phys. Rev. A 68, 032707 (2003)

    Article  ADS  Google Scholar 

  22. M. Kimura, C. Makochekanwa, O. Sueoka, J. Phys. B: At. Mol. Opt. Phys. 37, 1461 (2004)

    Article  ADS  Google Scholar 

  23. H.M. Boechat-Roberty, M.L.M. Rocco, C.A. Lucas, G.G.B. de Souza, J. Phys. B: At. Mol. Opt. Phys. 37, 1467 (2004)

    Article  ADS  Google Scholar 

  24. S. De-Heng, S. Jin-Feng, Z. Zun-Lue, L. Yu-Fang, Y. Chiang-Dong, Chin. Phys. 15, 1278 (2006)

    Article  Google Scholar 

  25. F. Blanco, G. García, Phys. Lett. A 360, 707 (2007)

    Article  ADS  Google Scholar 

  26. I. Iga, I.P. Sanches, E. de Almeida, R.T. Sugohara, L. Rosani, M.-T. Lee, J. Electron Spectrosc. Rel. Phenom. 155, 14 (2007)

    Article  Google Scholar 

  27. M.A. Er-Jun, M.A. Yu-Gang, C. Xiang-Zhou, F. De-Qing, S. Wen-Quing, T. Wen-Dong, Chin. Phys. Lett. 25, 97 (2008)

    Article  ADS  Google Scholar 

  28. I.P. Sanches, R.T. Sugohara, L. Rosani, M.-T. Lee, I. Iga, J. Phys. B: At. Mol. Opt. Phys. 41, 185202 (2008)

    Article  ADS  Google Scholar 

  29. H. Kato, M.C. Garcia, T. Asahina, M. Hoshino, C. Makochekanwa, H. Tanaka, Phys. Rev. A 79, 62703 (2009)

    Article  ADS  Google Scholar 

  30. H. Kato, M. Hoshino, H. Tanaka, P. Limão-Vieira, O. Ingólfsson, L. Campbell, M.J. Brunger, J. Chem. Phys. 134, 134308 (2011)

    Article  ADS  Google Scholar 

  31. G.L.C. de Souza, A.S. dos Santos, R.R. Lucchese, L.E. Machado, L.M. Brescansin, H.V. Manini, I. Iga, M.-T. Lee, Chem. Phys. 393, 19 (2012)

    Article  Google Scholar 

  32. S. Singh, R. Naghma, J. Kaur, B. Antony, J. Chem. Phys. 145, 034309 (2016)

    Article  ADS  Google Scholar 

  33. A.S. Barbosa, M.H.F. Bettega, J. Chem. Phys. 146, 154302 (2017)

  34. D. Prajapati, H. Yadav, P.C. Vinodkumar, C. Limbachiya, A. Dora, M. Vinodkumar, Eur. Phys. J. D 72, 210 (2018)

  35. M. Allan, R. Curik, P. Carsky, J. Chem. Phys. 151, 064119 (2019)

    Article  ADS  Google Scholar 

  36. F. Costa, L. Álvarez, A.I. Lozano, F. Blanco, J.C. Oller, M.H.F. Bettega, F. Ferreira da Silva, P. Limão-Vieira, G. García, J. Chem. Phys. 151, 084310 (2019)

    Article  ADS  Google Scholar 

  37. A.I. Lozano, F. Costa, X. Ren, A. Dorn, L. Álvarez, F. Blanco, P. Limão-Vieira, G. García, Int. J. Mol. Sci. 22(9), 4601 (2021)

    Article  Google Scholar 

  38. K. Takatsuka, V. McKoy, Phys. Rev. A 24, 2473 (1981)

    Article  ADS  Google Scholar 

  39. K. Takatsuka, V. McKoy, Phys. Rev. A 30, 1734 (1984)

    Article  ADS  Google Scholar 

  40. J. S. dos Santos, R. F. da Costa, M. T. do N. Varella, J. Chem. Phys 136, 084307 (2012)

    Article  ADS  Google Scholar 

  41. M.H.F. Bettega, L.G. Ferreira, M.A.P. Lima, Phys. Rev. A 47, 1111 (1993)

    Article  ADS  Google Scholar 

  42. R.F. da Costa, F.J. da Paixão, M.A.P. Lima, J. Phys. B: At. Mol. Opt. Phys. 38, 4363 (2005)

    Article  ADS  Google Scholar 

  43. A.G. Falkowski, M.A.P. Lima, F. Kossoski, J. Chem. Phys. 152, 244302 (2020)

    Article  ADS  Google Scholar 

  44. G.B. Bachelet, D.R. Hamann, M. Schlüter, Phys. Rev. B 26, 4199 (1982)

    Article  ADS  Google Scholar 

  45. R. F. da Costa, M. T. do N. Varella, M. H. F. Bettega, M. A. P. Lima, Eur. Phys. J. D 69, 159 (2015)

    Article  ADS  Google Scholar 

  46. G.M. Barca et al., J. Chem. Phys. 152, 154102 (2020)

    Article  ADS  Google Scholar 

  47. M.H.F. Bettega, Phys. Rev. A 81, 062717 (2010)

    Article  ADS  Google Scholar 

  48. T.H. Dunning Jr., J. Chem. Phys. 53, 2823 (1970)

    Article  ADS  Google Scholar 

  49. B.M. Bode, M.S. Gordon, J. Mol. Graph. Model. 16, 133 (1998)

    Article  Google Scholar 

  50. William J. Hunt, W.A. Goddard, Chem. Phys. Lett. 3, 414 (1969)

    Article  ADS  Google Scholar 

  51. J.F. Stanton, R.J. Bartlett, J. Chem. Phys. 98, 7029 (1993)

    Article  ADS  Google Scholar 

  52. O. Christiansen, H. Koch, P. Jørgensen, J. Chem. Phys. 103, 7429 (1995)

    Article  ADS  Google Scholar 

  53. H. Koch, O. Christiansen, P. Jørgensen, A.M. Sanchez de Merás, T. Helgaker, J. Chem. Phys. 106, 1808 (1997)

    Article  ADS  Google Scholar 

  54. D.G.A. Smith, L.A. Burns, A.C. Simmonett, R.M. Parrish, M.C. Schieber, R. Galvelis, P. Kraus, H. Kruse, R. Di Remigio, A. Alenaizan, A.M. James, S. Lehtola, J.P. Misiewicz, M. Scheurer, R.A. Shaw, J.B. Schriber, Y. Xie, Z.L. Glick, D.A. Sirianni, J.S. O’Brien, J.M. Waldrop, A. Kumar, E.G. Hohenstein, B.P. Pritchard, B.R. Brooks, H.F. Schaefer, AYu. Sokolov, K. Patkowski, A.E. DePrince, U. Bozkaya, R.A. King, F.A. Evangelista, J.M. Turney, T.D. Crawford, C.D. Sherrill, J. Chem. Phys. 152, 184108 (2020)

  55. CFOUR, a quantum chemical program package written by J.F. Stanton, J. Gauss, L. Cheng, M.E. Harding, D.A. Matthews, P.G. Szalay with contributions from A.A. Auer, R.J. Bartlett, U. Benedikt, C. Berger, D.E. Bernholdt, Y.J. Bomble, O. Christiansen, F. Engel, R. Faber, M. Heckert, O. Heun, C. Huber, T.-C. Jagau, D. Jonsson, J. Jusélius, K. Klein, W.J. Lauderdale, F. Lipparini, T. Metzroth, L.A. Mück, D.P. O’Neill, D.R. Price, E. Prochnow, C. Puzzarini, K. Ruud, F. Schiffmann, W. Schwalbach, C. Simmons, S. Stopkowicz, A. Tajti, J. Vázquez, F. Wang, J.D. Watts and the integral packages MOLECULE (J. Almlóf and P.R. Taylor), PROPS (P.R. Taylor), ABACUS (T. Helgaker, H.J. Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A. V. Mitin and C. van Wüllen. For the current version, see http://www.cfour.de

  56. D.A. Matthews, L. Cheng, M.E. Harding, F. Lipparini, S. Stopkowicz, T.-C. Jagau, P.G. Szalay, J. Gauss, J.F. Stanton, J. Chem. Phys. 152, 214108 (2020)

    Article  ADS  Google Scholar 

  57. T.N. Rescigno, B.I. Schneider, Phys. Rev. A 45, 2894 (1992)

    Article  ADS  Google Scholar 

  58. R.F. da Costa, M.H.F. Bettega, M.A.P. Lima, M.C.A. Lopes, L.R. Hargreaves, G. Serna, M.A. Khakoo, Phys. Rev. A 85, 062706 (2012)

    Article  ADS  Google Scholar 

  59. R. F. da Costa, M. H. F. Bettega, M. T. do N. Varella, E. M. de Oliveira, M. A. P. Lima, Phys. Rev. A 90, 052707 (2014)

    Article  ADS  Google Scholar 

  60. R. F. da Costa, E. M. de Oliveira, M.H. F. Bettega, M. T. do N. Varella, D.B. Jones, M.J. Brunger, F. Blanco, R. Colmenares, P. Limão-Vieira, G. García, M.A.P. Lima, J. Chem. Phys 142, 104304 (2015)

    Article  ADS  Google Scholar 

  61. R.F. da Costa, M. T. do N. Varella, M.H.F. Bettega, R.F.C. Neves, M.C.A. Lopes, F. Blanco, G. García, D.B. Jones, M.J. Brunger, M.A.P. Lima, J. Chem. Phys. 144, 124310 (2016)

    Article  ADS  Google Scholar 

  62. D.B. Jones, R.F.C. Neves, M.C.A. Lopes, R.F. da Costa, M. T. do N. Varella, M.H.F. Bettega, M.A.P. Lima, G. García, P. Limão-Vieira, M.J. Brunger, J. Chem. Phys 144, 124309 (2016)

    Article  ADS  Google Scholar 

  63. D.B. Jones, F. Blanco, G. García, R.F. da Costa, F. Kossoski, M. T. do N. Varella, M.H.F. Bettega, M.A.P. Lima, R.D. White, J. Brunger, J. Chem. Phys 147, 244304 (2017)

    Article  ADS  Google Scholar 

  64. D.B. Jones, R.F. da Costa, F. Kossoski, M.TDo.N. Varella, M.H.F. Bettega, F.F. da Silva, P. Limão-Vieira, G. García, M.A.P. Lima, R.D. White, M.J. Brunger, J. Chem. Phys. 148, 124312 (2018)

    Article  ADS  Google Scholar 

  65. R.F. da Costa, J.C. Ruivo, F. Kossoski, MTdoN. Varella, M.H.F. Bettega, D.B. Jones, M.J. Brunger, M.A.P. Lima, J. Chem. Phys. 149, 174308 (2018)

    Article  ADS  Google Scholar 

  66. G.M. Moreira, F. Kossoski, M.H.F. Bettega, RFd. Costa, J. Phys. B: At., Mol. Opt. Phys. 53, 085002 (2020)

    Article  ADS  Google Scholar 

  67. G.M. Moreira, M.H.F. Bettega, RFd. Costa, J. Appl. Phys. 129, 203301 (2021)

    Article  ADS  Google Scholar 

  68. P.-F. Loos, F. Lipparini, M. Boggio-Pasqua, A. Scemama, D. Jacquemin, J. Chem. Theory Comput. 16, 1711 (2020)

    Article  Google Scholar 

  69. N. Nakashima, M. Sumitani, I. Ohmine, K. Yoshihara, J. Chem. Phys. 72, 2226 (1980)

    Article  ADS  Google Scholar 

  70. N. Nakashima, K. Yoshihara, J. Chem. Phys. 77, 6040 (1982)

    Article  ADS  Google Scholar 

  71. Y. Li, J. Wan, X. Xu, J. Comput. Chem. 28, 1658 (2007)

    Article  Google Scholar 

  72. Y.-K. Kim, M.E. Rudd, Phys. Rev. A 50, 3954 (1994)

    Article  ADS  Google Scholar 

  73. H. Tanaka, M.J. Brunger, L. Campbell, H. Kato, M. Hoshino, A.R.P. Rau, Rev. Mod. Phys. 88, 025004 (2016)

    Article  ADS  Google Scholar 

  74. Y.-K. Kim, K. K. Irikura, M. E. Rudd, M. A. Ali, P. M. Stone, J. Chang, J. S. Coursey, R. Dragoset, A. R. Kishore, K. J. Olsen, A. Sansonetti, G. Wiersma, D. Zucker, M. Zucker, Electron-impact ionization cross section for ionization and excitation database (version 3.0), [Online]. Available: http://physics.nist.gov/ionxsec [2021, September 1]. National Institute of Standards and Technology, Gaithersburg, MD. (2004)

  75. O. Sueoka, J. Phys. B: At. Mol. Opt. Phys. 21, L631 (1988)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

A.G.F. acknowledges support from Coordenaão de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES) —Finance Code 001, and M.A.P.L. and R.F.C. acknowledge the Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). This research used the computing resour- ces and assistance of the John David Rogers Computing Center (CCJDR) in the Institute of Physics “Gleb Wataghin,” University of Campinas. M.J.B. acknowledges funding from the Australian Research Council through Grant # DP180101655.

Author information

Authors and Affiliations

Authors

Contributions

AGF performed the calculations. All authors analyzed and discussed the results and contributed to the outline of the manuscript. AGF, RFC, and FK wrote the first version of the manuscript. MJB and MAPL contributed to the final version of the manuscript.

Corresponding author

Correspondence to Fábris Kossoski.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Falkowski, A.G., da Costa, R.F., Kossoski, F. et al. Electronic excitation of benzene by low energy electron impact and the role of higher lying Rydberg states. Eur. Phys. J. D 75, 310 (2021). https://doi.org/10.1140/epjd/s10053-021-00326-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-021-00326-x

Navigation