2006/02/28 by J. Schirmer, A. Dreuw
Chemical Engineering · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Catalysis and Oxidation Reactions #Density functional theory #Ground state #Mathematical analysis #Mathematical physics #Mathematics #Multiplicative function #Operator (biology) #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Time-dependent density functional theory #cond-mat.other
paper · pdf · doi:10.1103/physreva.75.022513
published as Phys. Rev. A 75, 022513 (2007) · Reason for replacement: Change of content essentially in subsection 5.C, plus minor adaptions in the Appendix, Sec. 1, and Sec. 6
arxiv created 2006/04/03 · openalex publication_date 2007/02/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The general expectation that, in principle, the time-dependent density-functional theory (TDDFT) is an exact formulation of the time evolution of an interacting N-electron 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 Kohn-Sham (KS) concept has been introduced, in which the ground-state density is obtained from a single KS equation for one spatial (spinless) orbital. The time-dependent (TD) form of this radical Kohn-Sham (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 N-electron system. Besides the issue of the formal exactness of TDDFT, it is shown that both the static and time-dependent KS linear response equations neglect the particle-particle (p-p) and hole-hole (h-h) 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.