Critique of the foundations of timedependent densityfunctional theory
Abstract
The general expectation that, in principle, the timedependent densityfunctional theory (TDDFT) is an exact formulation of the time evolution of an interacting Nelectron system is critically reexamined. It is demonstrated that the previous TDDFT foundation, resting on four theorems by Runge and Gross (RG) [Phys. Rev. Lett. 52, 997 (1984)], is invalid because undefined phase factors corrupt the RG action integral functionals. Our finding confirms much of a previous analysis by van Leeuwen [Int. J. Mod. Phys. B 15, 1969 (2001)]. To analyze the RG theorems and other aspects of TDDFT, an utmost simplification of the KohnSham (KS) concept has been introduced, in which the groundstate density is obtained from a single KS equation for one spatial (spinless) orbital. The timedependent (TD) form of this radical KohnSham (rKS) scheme, which has the same validity status as the ordinary KS version, has proved to be a valuable tool for analysis. The rKS concept is used to clarify also the alternative nonvariational formulation of TD KS theory. We argue that it is just a formal theory, allowing one to reproduce but not predict the time development of the exact density of the interacting Nelectron system. Besides the issue of the formal exactnessmore »
 Authors:
 Theoretische Chemie, PhysikalischChemisches Institut, Universitaet Heidelberg, D69120 Heidelberg (Germany)
 (Germany)
 Publication Date:
 OSTI Identifier:
 20982112
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022513; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ACTION INTEGRAL; BORON 15; DENSITY; DENSITY FUNCTIONAL METHOD; ELECTRONS; FOUNDATIONS; FUNCTIONALS; GROUND STATES; LOSSES; MATRICES; MATRIX ELEMENTS; POTENTIALS; RADICALS; TIME DEPENDENCE
Citation Formats
Schirmer, J., Dreuw, A., and Institut fuer Physikalische und Theoretische Chemie, Universitaet Frankfurt, D60439 Frankfurt. Critique of the foundations of timedependent densityfunctional theory. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.022513.
Schirmer, J., Dreuw, A., & Institut fuer Physikalische und Theoretische Chemie, Universitaet Frankfurt, D60439 Frankfurt. Critique of the foundations of timedependent densityfunctional theory. United States. doi:10.1103/PHYSREVA.75.022513.
Schirmer, J., Dreuw, A., and Institut fuer Physikalische und Theoretische Chemie, Universitaet Frankfurt, D60439 Frankfurt. Thu .
"Critique of the foundations of timedependent densityfunctional theory". United States.
doi:10.1103/PHYSREVA.75.022513.
@article{osti_20982112,
title = {Critique of the foundations of timedependent densityfunctional theory},
author = {Schirmer, J. and Dreuw, A. and Institut fuer Physikalische und Theoretische Chemie, Universitaet Frankfurt, D60439 Frankfurt},
abstractNote = {The general expectation that, in principle, the timedependent densityfunctional theory (TDDFT) is an exact formulation of the time evolution of an interacting Nelectron system is critically reexamined. It is demonstrated that the previous TDDFT foundation, resting on four theorems by Runge and Gross (RG) [Phys. Rev. Lett. 52, 997 (1984)], is invalid because undefined phase factors corrupt the RG action integral functionals. Our finding confirms much of a previous analysis by van Leeuwen [Int. J. Mod. Phys. B 15, 1969 (2001)]. To analyze the RG theorems and other aspects of TDDFT, an utmost simplification of the KohnSham (KS) concept has been introduced, in which the groundstate density is obtained from a single KS equation for one spatial (spinless) orbital. The timedependent (TD) form of this radical KohnSham (rKS) scheme, which has the same validity status as the ordinary KS version, has proved to be a valuable tool for analysis. The rKS concept is used to clarify also the alternative nonvariational formulation of TD KS theory. We argue that it is just a formal theory, allowing one to reproduce but not predict the time development of the exact density of the interacting Nelectron system. Besides the issue of the formal exactness of TDDFT, it is shown that both the static and timedependent KS linear response equations neglect the particleparticle (pp) and holehole (hh) matrix elements of the perturbing operator. For a local (multiplicative) operator this does not lead to a loss of information due to a remarkable general property of local operators. Accordingly, no logical inconsistency arises with respect to DFT, because DFT requires any external potential to be local. For a general nonlocal operator the error resulting from the neglected matrix elements is of second order in the electronic repulsion.},
doi = {10.1103/PHYSREVA.75.022513},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}

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