Improving the theoretical description of charge transport in organic crystals

  • Wiliam F. da CunhaEmail author
  • Sara S. de Brito
  • Leonardo E. de Sousa
  • Bernhard G. Enders
  • Pedro H. de Oliveira Neto
Original Paper
Part of the following topical collections:
  1. VII Symposium on Electronic Structure and Molecular Dynamics – VII SeedMol


Charge hopping based on Marcus theory is often used to predict charge carrier mobilities in organic crystals, although it is known to systematically underestimate the values. Here we show that this deficiency may lie on a fundamental aspect of quantum statistical averages, rather than on the approximation itself. Under adequate Boltzmann weighing procedure used to evaluate electron and hole transfer integrals, a kinetic Monte Carlo model is employed to describe mobilities in an azacene derivative. The values are in good agreement with experimental data suggesting that the evaluation of transfer integrals may be the weak link in hopping transport models.


Charge carrier mobility Transfer rate Marcus theory Monte Carlo method Hopping transport 



The authors gratefully acknowledge the financial support from CAPES, CNPq and FAP-DF. P.H.O.N. and W.F.C. also acknowledge the financial support from FAP-DF grants 0193.001662/2017, and 0193.001694/2017, respectively.


  1. 1.
    Hou J, Inganäs O, Friend RH, Gao F (2018) Organic solar cells based on non-fullerene acceptors. Nat Mater 17:119CrossRefGoogle Scholar
  2. 2.
    Yang F, Cheng S, Zhang X, Ren X, Li R, Dong H, Hu W (2018) 2D organic materials for optoelectronic applications. Adv Mater 30(170):2415Google Scholar
  3. 3.
    Shuai Z, Geng H, Xu W, Liao Y, André J-M (2014) From charge transport parameters to charge mobility in organic semiconductors through multiscale simulation. Chem Soc Rev 43:2662–2679CrossRefGoogle Scholar
  4. 4.
    Zarate X, Schott E, Alvarado-Soto L, Sutherland TC (2013) A molecular study of tetrakis (p-methoxyphenyl) porphyrin and its Zn (II) complex as discotic liquid crystals. Int J Quantum Chem 113:2287–2294CrossRefGoogle Scholar
  5. 5.
    Lee N-E, Zhou J-J, Agapito LA, Bernardi M (2018) Charge transport in organic molecular semiconductors from first principles: the bandlike hole mobility in a naphthalene crystal. Phys Rev B 97:115203CrossRefGoogle Scholar
  6. 6.
    Parashchuk OD, Mannanov AA, Konstantinov VG, Dominskiy DI, Surin NM, Borshchev OV, Ponomarenko SA, Pshenichnikov MS, Paraschuk DY (2018) Molecular self-doping controls luminescence of pure organic single crystals. Adv Funct Mater, 1800116Google Scholar
  7. 7.
    Yao Y, Zhang L, Leydecker T, Samorì P (2018) Direct photolithography on molecular crystals for high performance organic optoelectronic devices. J Am Chem SocGoogle Scholar
  8. 8.
    Lemaur V, et al. (2004) Charge transport properties in discotic liquid crystals: a quantum-chemical insight into structure– property relationships. J Am Chem Soc 126:3271–3279CrossRefGoogle Scholar
  9. 9.
    Coropceanu V, Cornil J, da Silva Filho D, Olivier Y, Silbey R, Brédas J-L (2007) Charge transport in organic semiconductors. Chem Rev 107:926–952CrossRefGoogle Scholar
  10. 10.
    Deng W-Q, Sun L, Huang J-D, Chai S, Wen S-H, Han K-L (2015) Quantitative prediction of charge mobilities of π-stacked systems by first-principles simulation. Nat Protoc 10:632CrossRefGoogle Scholar
  11. 11.
    Oberhofer H, Reuter K, Blumberger J (2017) Charge transport in molecular materials: an assessment of computational methods. Chem Rev 117:10319–10357CrossRefGoogle Scholar
  12. 12.
    Yavuz I (2017) Dichotomy between the band and hopping transport in organic crystals: insights from experiments. Phys Chem Chem Phys 19:25819–25828CrossRefGoogle Scholar
  13. 13.
    Meneau AY, Olivier Y, Backlund T, James M, Breiby DW, Andreasen JW, Sirringhaus H (2016) Temperature dependence of charge localization in high-mobility, solution-crystallized small molecule semiconductors studied by charge modulation spectroscopy. Adv Funct Mater 26:2326–2333CrossRefGoogle Scholar
  14. 14.
    Geng H, Peng Q, Wang L, Li H, Liao Y, Ma Z, Shuai Z (2012) Toward quantitative prediction of charge mobility in organic semiconductors: tunneling enabled hopping model. Adv Mater 24:3568–3572CrossRefGoogle Scholar
  15. 15.
    Stehr V, Fink RF, Tafipolski M, Engels B (2012) Comparison of different rate constant expressions for the prediction of charge and energy transport in oligoacenes. Adv Rev 6:1–27Google Scholar
  16. 16.
    Fratini S, Mayou D, Ciuchi S (2016) The transient localization scenario for charge transport in crystalline organic materials. Adv Funct Mater 26:2292–2315CrossRefGoogle Scholar
  17. 17.
    Troisi A (2011) Charge transport in high-mobility molecular semiconductors: classical models and new theories. Chem Soc Rev 40:2347–2358CrossRefGoogle Scholar
  18. 18.
    Ortmann F, Bechstedt F, Hannewald K (2011) Charge transport in organic crystals: theory and modelling. Phys Status Solidi B 248:511–525CrossRefGoogle Scholar
  19. 19.
    Shuai Z, Wang L, Li Q (2011) Evaluation of charge mobility in organic materials: from localized to delocalized descriptions at a first-principles level. Adv Mater 23:1145–1153CrossRefGoogle Scholar
  20. 20.
    da Silva Filho D, Kim E-G, Brédas J-L (2005) Transport properties in the rubrene crystal: electronic coupling and vibrational reorganization energy. Adv Mater 17:1072–1076CrossRefGoogle Scholar
  21. 21.
    Wang L, Nan G, Yang X, Peng Q, Li Q, Shuai Z (2010) Computational methods for design of organic materials with high charge mobility. Chem Soc Rev 39:423–434CrossRefGoogle Scholar
  22. 22.
    Liang Z, Tang Q, Xu J, Miao Q (2011) Soluble and stable N-heteropentacenes with high field-effect mobility. Adv Mater 23:1535–1539CrossRefGoogle Scholar
  23. 23.
    Landsberg PT (1981) Einstein and statistical thermodynamics. III. The diffusion-mobility relation in semiconductors. Eur J Phys 2:213CrossRefGoogle Scholar
  24. 24.
    Li L, Lu N, Liu M, Bässler H (2014) General Einstein relation model in disordered organic semiconductors under quasiequilibrium. Phys Rev B 90:214107CrossRefGoogle Scholar
  25. 25.
    Richert R, Pautmeier L, Bässler H (1989) drift of charge carriers in a random potential diffusion deviation from Einstein’s law. Phys Rev Lett 63:547CrossRefGoogle Scholar
  26. 26.
    Marcus RA, Sutin N (1985) Electron transfer in chemistry and biology. Biochim Biophys Acta 811:265–322CrossRefGoogle Scholar
  27. 27.
    López-Estrada O, Laguna HG, Barrueta-Flores C, Amador-Bedolla C (2018) Reassessment of the four-point approach to the electron-transfer Marcus–Hush theory. ACS Omega 3:2130–2140CrossRefGoogle Scholar
  28. 28.
    Nelsen SF, Blackstock SC, Kim Y (1987) Estimation of inner shell Marcus terms for amino nitrogen compounds by molecular orbital calculations. J Am Chem Soc 109:677–682CrossRefGoogle Scholar
  29. 29.
    Nan G, Wang L, Yang X, Shuai Z, Zhao Y (2009) Charge transfer rates in organic semiconductors beyond first-order perturbation: from weak to strong coupling regimes. J Chem Phys 024704:130Google Scholar
  30. 30.
    Gunther F, Gemming S, Seifert G (2016) Hopping-based charge transfer in diketopyrrolopyrrole-based donor–acceptor polymers: a theoretical study. J Phys Chem C 120:9581–9587CrossRefGoogle Scholar
  31. 31.
    Frisch MJ, et al. (2009) Gaussian 09 Revision E.01. Gaussian Inc Wallingford CTGoogle Scholar
  32. 32.
    Evaristo de Sousa L, Ferreira da Cunha W, Antônio da Silva Filho D, de Oliveira Neto P H (2018) Biexciton cascade emission in multilayered organic nanofibers. Appl Phys Lett 112 :143301CrossRefGoogle Scholar
  33. 33.
    Volpi R, Kottravel S, Nørby MS, Stafstrom S, Linares M (2016) Effect of polarization on the mobility of C60: a kinetic Monte Carlo study. J Chem Theory Comput 12:812–824CrossRefGoogle Scholar
  34. 34.
    Sousa L, Volpi R, da Silva Filho D, Linares M (2017) Mobility temperature dependence in PC61BM mobility field. A kinetic Monte-Carlo study. Chem Phys Lett 689:74–81CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of BrasíliaBrasíliaBrazil

Personalised recommendations