Skip to main content

Constrained Density Functional Theory of Molecular Dimers

  • Conference paper
High Performance Computing in Science and Engineering '11
  • 2120 Accesses

Abstract

For charge transport in organic semiconductors the geometrical response to the presence of the charge plays a crucial role. Often, charge transport in these materials can be considered as the hopping of a localized polaron. Unfortunately, the description of localized charge carriers within semilocal Density Functional Theory (DFT) is prevented by the self-interaction error that artificially delocalizes the charge. Here, we present a computational scheme for the description of localized charges in an organic semiconductor. Constrained DFT is used to localize the charge on one of the molecules of a molecular dimer. The availability of the forces from this constraint enables ab initio molecular dynamics calculations and gives access to the geometrical response of neighboring molecules to the presence of a charged neighbor. This is demonstrated for a pentacene dimer. The reorganization energy is found to increase from 91 meV to 108 meV when decreasing the distance between two Pentacene molecules from 7 Å to 4 Å.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Becke, A.D.: A multicenter numerical integration scheme for polyatomic molecules. The Journal of Chemical Physics 88, 2547–2553 (1988). DOI 10.1063/1.454033. http://link.aip.org/link/?JCP/88/2547/1

    Article  Google Scholar 

  2. Behler, J., Delley, B., Reuter, K., Scheffler, M.: Nonadiabatic potential-energy surfaces by constrained density-functional theory. Physical Review B 75, 115,409 (2007). http://link.aps.org/doi/10.1103/PhysRevB.75.115409

    Article  Google Scholar 

  3. Cohen, A.J., Mori-Sanchez, P., Yang, W.: Insights into current limitations of density functional theory. Science 321, 792–794 (2008). DOI 10.1126/science.1158722. http://www.sciencemag.org/cgi/content/abstract/321/5890/792

    Article  Google Scholar 

  4. Dederichs, P.H., Blügel, S., Zeller, R., Akai, H.: Ground states of constrained systems: Application to cerium impurities. Physical Review Letters 53, 2512–2515 (1984). http://link.aps.org/doi/10.1103/PhysRevLett.53.2512

    Article  Google Scholar 

  5. Deng, W.Q., Goddard III, W.A.: Predictions of hole mobilities in oligoacene organic semiconductors from quantum mechanical calculations. The Journal of Physical Chemistry B 108, 8614–8621 (2004). http://dx.doi.org/10.1021/jp0495848

    Article  Google Scholar 

  6. Gruhn, N.E., da Silva Filho, D.A., Bill, T.G., Malagoli, M., Coropceanu, V., Kahn, A., Bredas, J.L.: The vibrational reorganization energy in pentacene: Molecular influences on charge transport. Journal of the American Chemical Society 124, 7918–7919 (2002). http://dx.doi.org/10.1021/ja0175892

    Article  Google Scholar 

  7. Han, M.J., Ozaki, T., Yu, J.: O (N) LDA+U electronic structure calculation method based on the nonorthogonal pseudoatomic orbital basis. Physical Review B 73, 045110 (2006). http://link.aps.org/doi/10.1103/PhysRevB.73.045110

    Article  Google Scholar 

  8. Hirshfeld, F.L.: Bonded-atom fragments for describing molecular charge densities. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 44, 129–138 (1977). http://dx.doi.org/10.1007/BF00549096

    Google Scholar 

  9. Jorgensen, P., Simons, J.: Ab initio analytical molecular gradients and Hessians. The Journal of Chemical Physics 79, 334–357 (1983). DOI 10.1063/1.445528. http://link.aip.org/link/?JCP/79/334/1

    Article  Google Scholar 

  10. Mantz, Y.A., Gervasio, F.L., Laino, T., Parrinello, M.: Charge localization in stacked radical cation DNA base pairs and the benzene dimer studied by self-interaction corrected density-functional theory. The Journal of Physical Chemistry A 111, 105–112 (2007). http://dx.doi.org/10.1021/jp063080n

    Article  Google Scholar 

  11. Mori-Sanchez, P., Cohen, A.J., Yang, W.: Many-electron self-interaction error in approximate density functionals. The Journal of Chemical Physics 125, 201102 (2006). DOI 10.1063/1.2403848. http://link.aip.org/link/?JCP/125/201102/1

    Article  Google Scholar 

  12. Mori-Sanchez, P., Cohen, A.J., Yang, W.: Localization and delocalization errors in density functional theory and implications for band-gap prediction. Physical Review Letters 100, 146,401 (2008). http://link.aps.org/doi/10.1103/PhysRevLett.100.146401

    Article  Google Scholar 

  13. Oberhofer, H., Blumberger, J.: Charge constrained density functional molecular dynamics for simulation of condensed phase electron transfer reactions. The Journal of Chemical Physics 131, 064101 (2009). DOI 10.1063/1.3190169. http://link.aip.org/link/?JCP/131/064101/1

    Article  Google Scholar 

  14. Parr, R.G., Yang, W.: Density-Functional Theory of Atoms and Molecules. Oxford University Press (1988)

    Google Scholar 

  15. Perdew, J.P., Parr, R.G., Levy, M., Balduz, J.L.: Density-functional theory for fractional particle number: Derivative discontinuities of the energy. Physical Review Letters 49, 1691–1694 (1982). http://link.aps.org/doi/10.1103/PhysRevLett.49.1691

    Article  Google Scholar 

  16. Perdew, J.P., Zunger, A.: Self-interaction correction to density-functional approximations for many-electron systems. Physical Review B 23, 5048–5079 (1981). http://link.aps.org/abstract/PRB/v23/p5048

    Article  Google Scholar 

  17. Szabo, A., Szabo, J., Ostlund, N.S.: Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover Publishing Inc. (1996)

    Google Scholar 

  18. Wang, L., Nan, G., Yang, X., Peng, Q., Li, Q., Shuai, Z.: Computational methods for design of organic materials with high charge mobility. Chemical Society Reviews 39, 423–434 (2010). http://dx.doi.org/10.1039/b816406c

    Article  Google Scholar 

  19. Wu, Q., Cheng, C.L., Van Voorhis, T.: Configuration interaction based on constrained density functional theory: A multireference method. The Journal of Chemical Physics 127, 164119 (2007). DOI 10.1063/1.2800022. http://link.aip.org/link/?JCP/127/164119/1

    Article  Google Scholar 

  20. Wu, Q., Kaduk, B., Van Voorhis, T.: Constrained density functional theory based configuration interaction improves the prediction of reaction barrier heights. The Journal of Chemical Physics 130, 034109 (2009). DOI 10.1063/1.3059784. http://link.aip.org/link/?JCP/130/034109/1

    Article  Google Scholar 

  21. Wu, Q., Van Voorhis, T.: Direct optimization method to study constrained systems within density-functional theory. Physical Review A 72, 024,502 (2005). http://link.aps.org/doi/10.1103/PhysRevA.72.024502

    Google Scholar 

  22. Wu, Q., Van Voorhis, T.: Constrained density functional theory and its application in long-range electron transfer. Journal of Chemical Theory and Computation 2, 765–774 (2006). http://dx.doi.org/10.1021/ct0503163

    Article  Google Scholar 

  23. Wu, Q., Van Voorhis, T.: Extracting electron transfer coupling elements from constrained density functional theory. The Journal of Chemical Physics 125, 164105 (2006). DOI 10.1063/1.2360263. http://link.aip.org/link/?JCP/125/164105/1

    Article  Google Scholar 

  24. Zhang, Y., Yang, W.: Comment on “generalized gradient approximation made simple”. Physical Review Letters 80, 890–890 (1998). http://link.aps.org/abstract/PRL/v80/p890

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J.-H. Franke .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Franke, JH., Nair, N.N., Chi, L., Fuchs, H. (2012). Constrained Density Functional Theory of Molecular Dimers. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering '11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23869-7_14

Download citation

Publish with us

Policies and ethics