What is Time-Dependent Density Functional Theory? Successes and Challenges

  • Neepa T. Maitra
  • Adam Wasserman
  • Kieron Burke


We discuss ongoing projects in ground-state density functional theory (DFT) before introducing some basic concepts in time-dependent DFT (TDDFT). The accuracy of simple approximations to transition frequencies and oscillator strengths is analyzed, developing scattering theory within TDDFT is discussed, and the importance of memory in fully time-dependent calculations is emphasized.


Density Functional Theory Oscillator Strength Linear Response Regime Singlet Excitation Approximate Functional 
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  1. A. I. Al-Sharif, R. Resta, C.J. Umrigar, Evidence of physical reality in the Kohn-Sham potential: The case of atomic Ne, Phys. Rev. A 57, 2466 (1998).ADSCrossRefGoogle Scholar
  2. Y. Andersson, D.C. Langreth, and B.I. Lunqvist, van der Waals Interactions in Density-Functional Theory, Phys. Rev. Lett. 76, 102 (1996).ADSCrossRefGoogle Scholar
  3. T. Ando, Inter-subband optical absorption in space-charge layers on semiconductor surfaces?, Z. Phys. B. 26, 263 (1977).ADSCrossRefGoogle Scholar
  4. H. Appel, K. Burke, and E.K.U. Gross, Oscillator strengths in density functional theory,in preparation.Google Scholar
  5. A.D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A 38, 3098 (1988).ADSCrossRefGoogle Scholar
  6. A.D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98, 5648 (1993).ADSCrossRefGoogle Scholar
  7. G.F. Bertsch, J.-I. Iwata, A. Rubio, and K. Yabana, Real-space, real-time method for the dielectric function, Phys. Rev. B 61, 7998 (2000).ADSCrossRefGoogle Scholar
  8. P. L. de Boeij, F. Kootstra, J. A. Berger, R. van Leeuwen, and J. G. Snijders, Current density functional theory for optical spectra: A polarization functional, J. Chem. Phys. 115, 1995 (2001).ADSCrossRefGoogle Scholar
  9. K. Burke, F.G. Cruz, and K.C. Lam, Unambiguous exchange-correlation energy density, J. Chem. Phys. 109, 8161 (1998).ADSCrossRefGoogle Scholar
  10. K. Burke and E.K.U. Gross, A guided tour of time-dependent density functional theory, in Density functionals: Theory and applications, ed. D. Joubert ( Springer, Berlin, 1998 ).Google Scholar
  11. K. Burke, M. Petersilka, and E.K.U. Gross, A hybrid functional for the exchange-correlation kernel in time-dependent density functional theory, in Recent advances in density functional methods, vol. III, ed. P. Fantucci and A. Bencini (World Scientific Press, 2000 ).Google Scholar
  12. M.E. Casida, Time-dependent density functional response theory of molecular systems: Theory, computational methods, and functionals, in Recent developments and applications in density functional theory, ed. J.M. Seminario ( Elsevier, Amsterdam, 1996 ).Google Scholar
  13. J.F. Dobson, M. Bünner, and E.K.U. Gross, Time-dependent density functional theory beyond linear response: An exchange-correlation potential with memory, Phys. Rev. Lett. 79, 1905 (1997).ADSCrossRefGoogle Scholar
  14. C. Filippi, C.J. Umrigar, and X. Gonze, Excitation energies from density functional perturbation theory, J. Chem. Phys., 107, 9994 (1997).ADSCrossRefGoogle Scholar
  15. P. Hessler, N.T. Maitra, and K. Burke, Dynamic effects in time-dependent density functional theory submitted (2001).Google Scholar
  16. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B 864 (1964).Google Scholar
  17. J. Katriel, F. Zahariev, and K. Burke, Symmetry and degeneracy in density functional theory to appear in Int. J. Quantum Chem. (2001).Google Scholar
  18. W. Kohn, Nobel Lecture: Electronic structure of matter - wave functions and density functionals, Rev. Mod. Phys. 71, 1253 (1999).ADSCrossRefGoogle Scholar
  19. W. Kohn and L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A 1133 (1965).Google Scholar
  20. F. Kootstra, P.L. de Boeij, and J.G. Snijders, Efficient real-space approach to time-dependent density functional theory for the dielectric response of nonmetallic crystals, J. Chem. Phys. 112, 6517 (2000).ADSCrossRefGoogle Scholar
  21. S. Kurth and J.P. Perdew, Density-functional correction of random-phase-approximation correlation with results for jellium surface energies, Phys. Rev. B 59, 10461 (1999).ADSCrossRefGoogle Scholar
  22. J. Larkin, C. Bock, N.T. Maitra, and K. Burke, A new tool for studying the kinetic energy density functional, in prep., Fall 2001.Google Scholar
  23. C. Lee, W. Yang, and R.G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37, 785 (1988).ADSCrossRefGoogle Scholar
  24. R. van Leeuwen, Mapping from Densities to Potentials in Time-Dependent DensityFunctional Theory,Phys. Rev. Lett. 82, 3863, (1999).Google Scholar
  25. R. Magyar,B. Terilla, and K. Burke, Extrapolating the adiabatic connection, in preparation for Chem. Phys. Letts., Fall 2001.Google Scholar
  26. N.T. Maitra and K. Burke, Demonstration of initial-state dependence in time-dependent density functional theory, Phys. Rev. A 63, 042501 (2001); (E) 64, 039901 (2001).Google Scholar
  27. N.T. Maitra, K. Burke, H. Appel, E.K.U. Gross, and R. van Leeuwen, Ten topical questions in time-dependent density functional theory, to appear in Reviews in Modern Quantum Chemistry: A Celebration of the Contributions of R.G. Parr, ed. K.D. Sen (World Scientific, 2001 ).Google Scholar
  28. N.T. Maitra, K. Burke, and C. Woodward, Memory in time-dependent density functional theory, submitted (2001).Google Scholar
  29. J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple,Phys. Rev. Lett. ‘77, 3865 (1996); 78, 1396 (1997) (E).Google Scholar
  30. M. Petersilka, E.K.U. Gross, and K. Burke, Excitation energies from time-dependent density functional theory using exact and approximate functionals, Int. J. Quantum Chem. 80, 534 (2000).CrossRefGoogle Scholar
  31. M. Petersilka, U.J. Gossmann, and E.K.U. Gross, Excitation energies from time-dependent density-functional theory, Phys. Rev. Lett. 76, 1212 (1996).ADSCrossRefGoogle Scholar
  32. E. Runge and E.K.U. Gross, Density-functional theory for time-dependent systems, Phys. Rev. Lett. 52, 997 (1984).ADSCrossRefGoogle Scholar
  33. D. Sundholm, Density functional theory calculations of the visible spectrum of chlorophyll a, Chem. Phys. Lett., 302, 480 (1999).ADSCrossRefGoogle Scholar
  34. G. Vignale and W. Kohn, Current-Dependent Exchange-Correlation Potential for Dynamical Linear Response Theory, Phys. Rev. Lett. 77, 2037 (1996).ADSCrossRefGoogle Scholar
  35. G. Vignale, C.A. Ullrich, and S. Conti, Time-dependent density functional theory beyond the adiabatic local density approximation, Phys. Rev. Lett. 79, 4878 (1997).ADSCrossRefGoogle Scholar
  36. T. Whittingham, R.J. Magyar, and K. Burke, Scaling one spin density at a time, in prep, Fall 2001.Google Scholar
  37. A. Zangwill and P Soven, Density-functional approach to local-field effects in finite systems: Photoabsorption in the rare gases, Phys. Rev. A 21, 1561 (1980).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Neepa T. Maitra
    • 1
  • Adam Wasserman
    • 1
  • Kieron Burke
    • 1
  1. 1.Departments of Chemistry and PhysicsRutgers UniversityUSA

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