Abstract
Generalized Kohn–Sham (GKS) theory extends the realm of density functional theory (DFT) by providing a rigorous basis for non-multiplicative potentials, the use of which is outside original Kohn–Sham theory. GKS theory is of increasing importance as it underlies commonly used approximations, notably (conventional or range-separated) hybrid functionals and meta-generalized-gradient-approximation (meta-GGA) functionals. While this approach is often extended in practice to time-dependent DFT (TDDFT), the theoretical foundation for this extension has been lacking, because the Runge–Gross theorem and the van Leeuwen theorem that serve as the basis of TDDFT have not been generalized to non-multiplicative potentials. Here, we provide the necessary generalization. Specifically, we show that with one simple but non-trivial additional caveat – upholding the continuity equation in the GKS electron gas – the Runge–Gross and van Leeuwen theorems apply to time-dependent GKS theory. We also discuss how this is manifested in common GKS-based approximations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R.G. Parr, W. Yang, Density functional theory of atoms and molecules (Oxford University Press, New York, 1989)
E.K.U. Gross, R.M. Dreizler, Density functional theory (Plenum Press, New York, 1990)
W. Koch, M.C. Holthausen, A Chemist’s Guide to Density Functional Theory (Wiley-VCH, Weinheim, 2001)
C. Fiolhais, F. Nogueira, M.A.L. Marques (Eds.), Density functionals for Non-relativistic Coulomb systems in the new century (Springer, Berlin, 2003)
D. Sholl, J.A. Steckel (Eds.), Density functional theory: a practical introduction (Wiley-VCH, Weinheim, 2009)
T. Tsuneda, Density functional theory in quantum chemistry (Springer, Berlin, 2014)
P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)
C. Ullrich, Time-dependent density functional theory: concepts and applications (Oxford University Press, Oxford, 2012)
M. Marques, N.T. Maitra, F.M. Nogueira, E.K.U. Gross, A. Rubio (Eds.), Fundamentals of time-dependent density functional theory (Springer, Berlin, 2012)
E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)
S. Kümmel, L. Kronik, Rev. Mod. Phys. 80, 3 (2008)
T. Grabo, T. Kreibich, E.K.U. Gross, Mol. Eng. 7, 27 (1997)
E. Engel, in A Primer in density functional theory, edited by C. Fiolhais, F. Nogueira, M.A.L. Marques (Springer, Berlin, 2003), p. 56
A.D. Becke, J. Chem. Phys. 98, 1372 (1993)
R. Neumann, R.H. Nobes, N.C. Handy, Mol. Phys. 87, 1 (1996)
A. Seidl, A. Görling, P. Vogl, J.A. Majewski, M. Levy, Phys. Rev. B 53, 3764 (1996)
L. Kronik, T. Stein, S. Refaely-Abramson, R. Baer, J. Chem. Theory Comput. 8, 1515 (2012)
N.T. Maitra, K. Burke, Phys. Rev. A 63, 042501 (2001)
R. van Leeuwen Phys. Rev. Lett. 82, 3863 (1999)
C.A. Ullrich, U.J. Gossmann, E.K.U. Gross, Phys. Rev. Lett. 74, 872 (1995)
S.-L. Liao, T.-S. Ho, H. Rabitz, S.-I Chu, Phys. Rev. Lett. 118, 243001 (2017)
C. Adamo, G.E. Scuseria, V. Barone, J. Chem. Phys. 111, 2889 (1999)
S. Tretiak, V. Chernyak, J. Chem. Phys. 119, 8809 (2003)
Y. Tawada, T. Tsuneda, S. Yanagisawa, T. Yanai, K. Hirao, J. Chem. Phys. 120, 8245 (2004)
V.U. Nazarov, G. Vignale, Phys. Rev. Lett. 107, 216402 (2011)
C. Adamo, D. Jacquemin, Chem. Soc. Rev. 42, 845 (2013)
D. Jacquemin, B. Moore, A. Planchat, C. Adamo, J. Autschbach, J. Chem. Theory Comput. 10, 1677 (2014)
N.T. Maitra, J. Chem. Phys. 144, 220901 (2016)
L. Kronik, J.B. Neaton, Annu. Rev. Phys. Chem. 67, 587 (2016)
S. Kümmel, Adv. Energy Mater. 7, 1700440 (2017)
A. Görling, M. Levy, J. Chem. Phys. 106, 2675 (1997)
T. Yanai, D.P. Tew, N.C. Handy, Chem. Phys. Lett. 393, 51 (2004)
A.D. Becke, J. Chem. Phys. 104, 1040 (1996)
V.N. Staroverov, G.E. Scuseria, J. Tao, J.P. Perdew, J. Chem. Phys. 119, 12129 (2003)
J. Tao, Phys. Rev. B 71, 205107 (2005)
J.E. Bates, F. Furche, J. Chem. Phys. 137, 164105 (2012)
G. Vignale, Phys. Rev. B 70, 201102 (2004)
J.F. Dobson, J. Chem. Phys. 98, 8870 (1993)
A.D. Becke, J. Chem. Phys. 117, 6935 (2002)
T. Burnus, M.A.L. Marques, E.K.U. Gross, Phys. Rev. A 71, 010501 (2005)
Author information
Authors and Affiliations
Corresponding authors
Additional information
Contribution to the Topical Issue “Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.
Rights and permissions
About this article
Cite this article
Baer, R., Kronik, L. Time-dependent generalized Kohn–Sham theory. Eur. Phys. J. B 91, 170 (2018). https://doi.org/10.1140/epjb/e2018-90103-0
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2018-90103-0