Abstract
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.
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References
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).
Y. Andersson, D.C. Langreth, and B.I. Lunqvist, van der Waals Interactions in Density-Functional Theory, Phys. Rev. Lett. 76, 102 (1996).
T. Ando, Inter-subband optical absorption in space-charge layers on semiconductor surfaces?, Z. Phys. B. 26, 263 (1977).
H. Appel, K. Burke, and E.K.U. Gross, Oscillator strengths in density functional theory,in preparation.
A.D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A 38, 3098 (1988).
A.D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98, 5648 (1993).
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).
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).
K. Burke, F.G. Cruz, and K.C. Lam, Unambiguous exchange-correlation energy density, J. Chem. Phys. 109, 8161 (1998).
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 ).
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 ).
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 ).
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).
C. Filippi, C.J. Umrigar, and X. Gonze, Excitation energies from density functional perturbation theory, J. Chem. Phys., 107, 9994 (1997).
P. Hessler, N.T. Maitra, and K. Burke, Dynamic effects in time-dependent density functional theory submitted (2001).
P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B 864 (1964).
J. Katriel, F. Zahariev, and K. Burke, Symmetry and degeneracy in density functional theory to appear in Int. J. Quantum Chem. (2001).
W. Kohn, Nobel Lecture: Electronic structure of matter - wave functions and density functionals, Rev. Mod. Phys. 71, 1253 (1999).
W. Kohn and L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A 1133 (1965).
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).
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).
J. Larkin, C. Bock, N.T. Maitra, and K. Burke, A new tool for studying the kinetic energy density functional, in prep., Fall 2001.
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).
R. van Leeuwen, Mapping from Densities to Potentials in Time-Dependent DensityFunctional Theory,Phys. Rev. Lett. 82, 3863, (1999).
R. Magyar,B. Terilla, and K. Burke, Extrapolating the adiabatic connection, in preparation for Chem. Phys. Letts., Fall 2001.
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).
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 ).
N.T. Maitra, K. Burke, and C. Woodward, Memory in time-dependent density functional theory, submitted (2001).
J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple,Phys. Rev. Lett. ‘77, 3865 (1996); 78, 1396 (1997) (E).
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).
M. Petersilka, U.J. Gossmann, and E.K.U. Gross, Excitation energies from time-dependent density-functional theory, Phys. Rev. Lett. 76, 1212 (1996).
E. Runge and E.K.U. Gross, Density-functional theory for time-dependent systems, Phys. Rev. Lett. 52, 997 (1984).
D. Sundholm, Density functional theory calculations of the visible spectrum of chlorophyll a, Chem. Phys. Lett., 302, 480 (1999).
G. Vignale and W. Kohn, Current-Dependent Exchange-Correlation Potential for Dynamical Linear Response Theory, Phys. Rev. Lett. 77, 2037 (1996).
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).
T. Whittingham, R.J. Magyar, and K. Burke, Scaling one spin density at a time, in prep, Fall 2001.
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).
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Maitra, N.T., Wasserman, A., Burke, K. (2002). What is Time-Dependent Density Functional Theory? Successes and Challenges. In: Gonis, A., Kioussis, N., Ciftan, M. (eds) Electron Correlations and Materials Properties 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3760-8_16
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DOI: https://doi.org/10.1007/978-1-4757-3760-8_16
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