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Constrained Density Functional Theory of Molecular Dimers

  • J.-H. Franke
  • N. N. Nair
  • L. Chi
  • H. Fuchs

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.

Keywords

Reorganization Energy Intermolecular Distance Projection Scheme Charge Difference Ionic Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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 CrossRefGoogle Scholar
  2. 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 CrossRefGoogle Scholar
  3. 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 CrossRefGoogle Scholar
  4. 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 CrossRefGoogle Scholar
  5. 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 CrossRefGoogle Scholar
  6. 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 CrossRefGoogle Scholar
  7. 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 CrossRefGoogle Scholar
  8. 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. 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 CrossRefGoogle Scholar
  10. 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 CrossRefGoogle Scholar
  11. 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 CrossRefGoogle Scholar
  12. 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 CrossRefGoogle Scholar
  13. 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 CrossRefGoogle Scholar
  14. 14.
    Parr, R.G., Yang, W.: Density-Functional Theory of Atoms and Molecules. Oxford University Press (1988) Google Scholar
  15. 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 CrossRefGoogle Scholar
  16. 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 CrossRefGoogle Scholar
  17. 17.
    Szabo, A., Szabo, J., Ostlund, N.S.: Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover Publishing Inc. (1996) Google Scholar
  18. 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 CrossRefGoogle Scholar
  19. 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 CrossRefGoogle Scholar
  20. 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 CrossRefGoogle Scholar
  21. 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. 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 CrossRefGoogle Scholar
  23. 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 CrossRefGoogle Scholar
  24. 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 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Physikalisches InstitutWWU MünsterMünsterGermany
  2. 2.Department of ChemistryIIT KanpurUttar PradeshIndia

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