Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Protocol
  • Published:

Quantitative prediction of charge mobilities of π-stacked systems by first-principles simulation

Nature Protocols volume 10, pages 632–642 (2015)Cite this article

Subjects

Abstract

This protocol is intended to provide chemists and physicists with a tool for predicting the charge carrier mobilities of π-stacked systems such as organic semiconductors and the DNA double helix. An experimentally determined crystal structure is required as a starting point. The simulation involves the following operations: (i) searching the crystal structure; (ii) selecting molecular monomers and dimers from the crystal structure; (iii) using density function theory (DFT) calculations to determine electronic coupling for dimers; (iv) using DFT calculations to determine self-reorganization energy of monomers; and (v) using a numerical calculation to determine the charge carrier mobility. For a single crystal structure consisting of medium-sized molecules, this protocol can be completed in ∼4 h. We have selected two case studies (a rubrene crystal and a DNA segment) as examples of how this procedure can be used.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Flowchart of the PROCEDURE (Steps 1–15).
Figure 2: Illustration of selecting molecular dimers in a rubrene crystal.
Figure 3: Comparisons of the predicted anisotropic hole mobility curve with experiments on a rubrene crystal.
Figure 4: Illustration of selecting molecular dimers in 4HW1 DNA.

Similar content being viewed by others

References

  1. Podzorov, V. Organic single crystals: addressing the fundamentals of organic electronics. MRS Bull. 38, 15–27 (2013).

    Article  Google Scholar 

  2. Li, Y. & Zou, Y. Conjugated polymer photovoltaic materials with broad absorption band and high charge carrier mobility. Adv. Mater. 20, 2952–2958 (2008).

    Article  CAS  Google Scholar 

  3. Sun, Y., Wu, Q. & Shi, G. Graphene based new energy materials. Energ. Environ. Sci. 4, 1113–1132 (2011).

    Article  CAS  Google Scholar 

  4. Hirakawa, T. & Kamat, P.V. Charge separation and catalytic activity of Ag@TiO2 core-shell composite clusters under UV-irradiation. J. Am. Chem. Soc. 127, 3928–3934 (2005).

    Article  CAS  PubMed  Google Scholar 

  5. Thompson, T.L. & Yates, J.T. Jr . TiO2-based photocatalysis: surface defects, oxygen and charge transfer. Top. Catal. 35, 197–210 (2005).

    Article  CAS  Google Scholar 

  6. Yoon, B. et al. Charging effects on bonding and catalyzed oxidation of CO on Au8 clusters on MgO. Science 307, 403–407 (2005).

    Article  CAS  PubMed  Google Scholar 

  7. Jortner, J., Bixon, M., Langenbacher, T. & Michel-Beyerle, M.E. Charge transfer and transport in DNA. Proc. Natl. Acad. Sci. 95, 12759–12765 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Lewis, F.D., Letsinger, R.L. & Wasielewski, M.R. Dynamics of photoinduced charge transfer and hole transport in synthetic DNA hairpins. Acc. Chem. Res. 34, 159–170 (2001).

    Article  CAS  PubMed  Google Scholar 

  9. Valis, L. et al. Base pair motions control the rates and distance dependencies of reductive and oxidative DNA charge transfer. Proc. Natl. Acad. Sci. 103, 10192–10195 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Orton, J.W. & Blood, P. The Electrical Characterization of Semiconductors: Measurement of Minority Carrier Properties. (Academic Press, London, 1990).

  11. Pernegger, H. et al. Charge-carrier properties in synthetic single-crystal diamond measured with the transient-current technique. J. Appl. Phys. 97, 073704 (2005).

    Article  CAS  Google Scholar 

  12. Schroder, D.K. Semiconductor Material and Device Characterization (John Wiley & Sons, 2006).

  13. Ling, M.M., Reese, C., Briseno, A.L. & Bao, Z. Non-destructive probing of the anisotropy of field-effect mobility in the rubrene single crystal. Synthetic Met. 157, 257–260 (2007).

    Article  CAS  Google Scholar 

  14. Lee, J.Y., Roth, S. & Park, Y.W. Anisotropic field effect mobility in single crystal pentacene. Appl. Phys. Lett. 88, 252106 (2006).

    Article  CAS  Google Scholar 

  15. Sundar, V.C. et al. Elastomeric transistor stamps: reversible probing of charge transport in organic crystals. Science 303, 1644–1646 (2004).

    Article  CAS  PubMed  Google Scholar 

  16. Grozema, F.C. & Siebbeles, L.D.A. Mechanism of charge transport in self-organizing organic materials. Int. Rev. Phys. Chem. 27, 87–138 (2008).

    Article  CAS  Google Scholar 

  17. Yang, X.D., Wang, L.J., Wang, C.L., Long, W. & Shuai, Z.G. Influences of crystal structures and molecular sizes on the charge mobility of organic semiconductors: oligothiophenes. Chem. Mater. 20, 3205–3211 (2008).

    Article  CAS  Google Scholar 

  18. Yang, X.D., Li, Q.K. & Shuai, Z.G. Theoretical modelling of carrier transports in molecular semiconductors: molecular design of triphenylamine dimer systems. Nanotechnology 18, 424029 (2007).

    Article  PubMed  CAS  Google Scholar 

  19. Cornil, J., Brédas, J.L., Zaumseil, J. & Sirringhaus, H. Ambipolar transport in organic conjugated materials. Adv. Mater. 19, 1791–1799 (2007).

    Article  CAS  Google Scholar 

  20. Zhang, X.-Y. & Zhao, G.-J. Anisotropic charge transport in bisindenoanthrazoline-based n-type organic semiconductors. J. Phys. Chem. C 116, 13858–13864 (2012).

    Article  CAS  Google Scholar 

  21. Zhang, M.-X., Chai, S. & Zhao, G.-J. BODIPY derivatives as n-type organic semiconductors: isomer effect on carrier mobility. Organic Electronics 13, 215–221 (2012).

    Article  CAS  Google Scholar 

  22. Zhang, M.X. & Zhao, G.J. Modification of n-type organic semiconductor performance of perylene diimides by substitution in different positions: two-dimensional π-stacking and hydrogen bonding. ChemSusChem 5, 879–887 (2012).

    Article  CAS  PubMed  Google Scholar 

  23. Liu, D. et al. Anisotropic charge injection and transport in the cross stacking crystal of distyrylbenzene derivative and a possible new device structure. Chem. Phys. Lett. 514, 174–180 (2011).

    Article  CAS  Google Scholar 

  24. Jiang, L., Dong, H.L. & Hu, W.P. Organic single crystal field-effect transistors: advances and perspectives. J. Mater. Chem. 20, 4994–5007 (2010).

    Article  CAS  Google Scholar 

  25. Chai, S., Wen, S.H., Huang, J.D. & Han, K.L. Density functional theory study on electron and hole transport properties of organic pentacene derivatives with electronwithdrawing substituent. J. Comput. Chem. 32, 3218–3225 (2011).

    Article  CAS  PubMed  Google Scholar 

  26. Wen, S.-H. et al. First-principles investigation of anistropic hole mobilities in organic semiconductors. J. Phys. Chem. B 113, 8813–8819 (2009).

    Article  CAS  PubMed  Google Scholar 

  27. Wen, S.-H., Deng, W.-Q. & Han, K.-L. Ultra-low resistance at TTF–TCNQ organic interfaces. Chem. Commun. 46, 5133–5135 (2010).

    Article  CAS  Google Scholar 

  28. Brédas, J.-L., Norton, J.E., Cornil, J. & Coropceanu, V. Molecular understanding of organic solar cells: the challenges. Acc. Chem. Res. 42, 1691–1699 (2009).

    Article  PubMed  CAS  Google Scholar 

  29. Geng, H. et al. Toward quantitative prediction of charge mobility in organic semiconductors: tunneling enabled hopping model. Adv. Mater. 24, 3568–3572 (2012).

    Article  CAS  PubMed  Google Scholar 

  30. Ryno, S.M., Risko, C. & Bredas, J.L. Impact of molecular packing on electronic polarization in organic crystals: the case of pentacene vs TIPS-pentacene. J. Am. Chem. Soc. 136, 6421–6427 (2014).

    Article  CAS  PubMed  Google Scholar 

  31. Shuai, Z., Geng, H., Xu, W., Liao, Y. & André, J.-M. From charge transport parameters to charge mobility in organic semiconductors through multiscale simulation. Chem. Soc. Rev. 43, 2662–2679 (2014).

    Article  CAS  PubMed  Google Scholar 

  32. Shuai, Z., Wang, L. & Li, Q. Evaluation of charge mobility in organic materials: from localized to delocalized descriptions at a first-principles level. Adv. Mater. 23, 1145–1153 (2011).

    Article  CAS  PubMed  Google Scholar 

  33. Wang, L. et al. Computational methods for design of organic materials with high charge mobility. Chem. Soc. Rev. 39, 423–434 (2010).

    Article  CAS  PubMed  Google Scholar 

  34. Marcus, R.A. On the theory of oxidation–reduction reactions involving electron transfer. I. J. Chem. Phys. 24, 966–978 (1956).

    Article  CAS  Google Scholar 

  35. Hush, N.S. Adiabatic rate processes at electrodes. I. energy–charge relationships. J. Chem. Phys. 28, 962–972 (1958).

    Article  CAS  Google Scholar 

  36. Valeev, E.F., Coropceanu, V., da Silva Filho, D.A., Salman, S. & Brédas, J.-L. Effect of electronic polarization on charge-transport parameters in molecular organic semiconductors. J. Am. Chem. Soc. 128, 9882–9886 (2006).

    Article  CAS  PubMed  Google Scholar 

  37. Yu, G. et al. Structures, electronic states, photoluminescence, and carrier transport properties of 1,1-disubstituted 2,3,4,5-tetraphenylsiloles. J. Am. Chem. Soc. 127, 6335–6346 (2005).

    Article  CAS  PubMed  Google Scholar 

  38. Senthilkumar, K., Grozema, F.C., Bickelhaupt, F.M. & Siebbeles, L.D.A. Charge transport in columnar stacked triphenylenes: effects of conformational fluctuations on charge transfer integrals and site energies. J. Chem. Phys. 119, 9809–9817 (2003).

    Article  CAS  Google Scholar 

  39. Chu, T.-S., Zhang, Y. & Han, K.-L. The time-dependent quantum wave packet approach to the electronically nonadiabatic processes in chemical reactions. Int. Rev. Phys. Chem. 25, 201–235 (2006).

    Article  CAS  Google Scholar 

  40. Coropceanu, V. et al. Charge transport in organic semiconductors. Chem. Rev. 107, 926–952 (2007).

    Article  CAS  PubMed  Google Scholar 

  41. Deng, W.-Q. & Goddard, W.A. Predictions of hole mobilities in oligoacene organic semiconductors from quantum mechanical calculations. J. Phys. Chem. B 108, 8614–8621 (2004).

    Article  CAS  Google Scholar 

  42. Demiralp, E. & Goddard, W.A. Conduction properties of the organic superconductor based on Hubbard–unrestricted-Hartree-Fock band calculations. Phys. Rev. B 56, 11907–11919 (1997).

    Article  CAS  Google Scholar 

  43. Wang, C., Wang, F., Yang, X., Li, Q. & Shuai, Z. Theoretical comparative studies of charge mobilities for molecular materials: Pet versus bnpery. Organic Electronics 9, 635–640 (2008).

    Article  CAS  Google Scholar 

  44. te Velde, G. et al. Chemistry with ADF. J. Comput. Chem. 22, 931–967 (2001).

    Article  CAS  Google Scholar 

  45. Frisch, M.J. et al. Gaussian 09, Revision C01. (Gaussian, Inc., 2009).

  46. Burke, K., Perdew, J.P. & Wang, Y. in Electronic Density Functional Theory 81–111 (Springer, 1998).

  47. Becke, A.D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648–5652 (1993).

    Article  CAS  Google Scholar 

  48. Lewis, F.D. et al. Crossover from superexchange to hopping as the mechanism for photoinduced charge transfer in DNA hairpin conjugates. J. Am. Chem. Soc. 128, 791–800 (2006).

    Article  CAS  PubMed  Google Scholar 

  49. Renaud, N., Berlin, Y.A. & Ratner, M.A. Impact of a single base pair substitution on the charge transfer rate along short DNA hairpins. Proc. Natl. Acad. Sci. 110, 14867–14871 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Messer, A. et al. Electron spin resonance study of electron transfer rates in DNA: determination of the tunneling constant β for single-step excess electron transfer. J. Phys. Chem. B 104, 1128–1136 (2000).

    Article  CAS  Google Scholar 

  51. Cai, Z., Gu, Z. & Sevilla, M.D. Electron spin resonance study of the temperature dependence of electron transfer in DNA: competitive processes of tunneling, protonation at carbon, and hopping. J. Phys. Chem. B 104, 10406–10411 (2000).

    Article  CAS  Google Scholar 

  52. Elias, B., Genereux, J.C. & Barton, J.K. Ping-pong electron transfer through DNA. Angew. Chem. Int. Edit. 47, 9067–9070 (2008).

    Article  CAS  Google Scholar 

  53. Renaud, N., Berlin, Y.A., Lewis, F.D. & Ratner, M.A. Between superexchange and hopping: an intermediate charge-transfer mechanism in poly(A)-poly(T) dna hairpins. J. Am. Chem. Soc. 135, 3953–3963 (2013).

    Article  CAS  PubMed  Google Scholar 

  54. Novoa, J.J. & Sosa, C. luation of the density functional approximation on the computation of hydrogen bond interactions. J. Phys. Chem. 99, 15837–15845 (1995).

    Article  CAS  Google Scholar 

  55. Stephens, P.J., Devlin, F.J., Chabalowski, C.F. & Frisch, M.J. Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J. Phys. Chem. 98, 11623–11627 (1994).

    Article  CAS  Google Scholar 

  56. Nan, G.J., Yang, X.D., Wang, L.J., Shuai, Z.G. & Zhao, Y. Nuclear tunneling effects of charge transport in rubrene, tetracene, and pentacene. Phys. Rev. B 79 (2009).

  57. Zeis, R. et al. Field effect studies on rubrene and impurities of rubrene. Chem. Mater. 18, 244–248 (2006).

    Article  CAS  Google Scholar 

  58. Ling, M.-M., Reese, C., Briseno, A.L. & Bao, Z. Non-destructive probing of the anisotropy of field-effect mobility in the rubrene single crystal. Synthetic. Met. 157, 257–260 (2007).

    Article  CAS  Google Scholar 

  59. Park, M.J., Fujitsuka, M., Kawai, K. & Majima, T. Direct measurement of the dynamics of excess electron transfer through consecutive thymine sequence in DNA. J. Am. Chem. Soc. 133, 15320–15323 (2011).

    Article  CAS  PubMed  Google Scholar 

  60. Briseno, A.L. et al. Patterning organic single-crystal transistor arrays. Nature 444, 913–917 (2006).

    Article  CAS  PubMed  Google Scholar 

  61. Podzorov, V., Sysoev, S.E., Loginova, E., Pudalov, V.M. & Gershenson, M.E. Single-crystal organic field effect transistors with the hole mobility ∼8cm2/Vs. Appl. Phys. Lett. 83, 3504–3506 (2003).

    Article  CAS  Google Scholar 

  62. da Silva Filho, D.A., Kim, E.G. & Brédas, J.L. Transport properties in the rubrene crystal: electronic coupling and vibrational reorganization energy. Adv. Mater. 17, 1072–1076 (2005).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge support from the National Basic Research Program of China (2013CB834604) and National Natural Science Foundation of China (91333116 and 21321091).

Author information

Author notes

  1. Wei-Qiao Deng and Lei Sun: These authors contributed equally to this work.

Authors and Affiliations

  1. State Key Laboratory of Molecular Reaction Dynamics, Dalian National Laboratory for Clean Energy, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China

    Wei-Qiao Deng, Lei Sun, Jin-Dou Huang, Shuo Chai, Shu-Hao Wen & Ke-Li Han

Authors
  1. Wei-Qiao Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jin-Dou Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shuo Chai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shu-Hao Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ke-Li Han
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

W.-Q.D. and L.S. contributed equally to this work and performed the research; J.-D.H., S.C. and S.-H.W. performed the calculations; K.-L.H. conceived and supervised the work; all authors co-wrote the manuscript.

Corresponding author

Correspondence to Ke-Li Han.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Note (PDF 188 kb)

Supplementary Data 1

A zip file containing the crystal files download from the online database (“DNA-4HW1.ent” and “Rubrene.cif”) A zip file containing the matlab code (“mobility.m”), the corresponding parameters file (“input. txt”) and the help information (example-input.txt). (ZIP 127 kb)

Supplementary Data 2

A zip file containing the matlab code (“mobility.m”), the corresponding parameters file (“input. txt”) and the help information (example-input.txt). (ZIP 2 kb)

Supplementary Data 3

A zip file containing four types of the molecular dimers chosen from rubrene crystal (“rubrene-L.mol”, “rubrene-P.mol”, “rubrene-T1.mol” and “rubrene-T2.mol”) and four types of the molecular dimers chosen from DNA-4HW1 (“adenine-dimer-1.mol”, “adenine-dimer-2.mol”, “thymine-dimer-1.mol” and “thymine -dimer-2.mol”). (ZIP 11 kb)

Supplementary Data 4

A zip file containing the ADF-output files for each of the molecular dimers. (ZIP 596 kb)

Supplementary Data 5

Gaussian-output files for each molecular monomer. (ZIP 724 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, WQ., Sun, L., Huang, JD. et al. Quantitative prediction of charge mobilities of π-stacked systems by first-principles simulation. Nat Protoc 10, 632–642 (2015). https://doi.org/10.1038/nprot.2015.038

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nprot.2015.038

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing