Reply to “Comment on ‘Critique of the foundations of time-dependent density-functional theory’ ”

In the preceding Comment, Maitra, van Leeuwen, and Burke (MLB) [Phys. Rev. A 78, 056501 (2008) attempt to refute our criticism of the foundations of time-dependent density functional theory [see J. Schirmer and A. Dreuw, Phys. Rev. A 75, 022513 (2007)]. However, their arguments miss the essence of our position. This is partly due to an ambiguity concerning the present status of the time-dependent (TD) Kohn-Sham (KS) equations. Based on the first Runge-Gross (mapping) theorem, the TD KS equations have to be established as a fixed-point iteration scheme for potential functionals (PF-FPI). Here, however, the convergence of the FPI is not assured. On the other hand, time propagation of the TD KS equations in their PF-FPI form fails because these equations do not represent physical equations of motion. MLB present a construction of the exact exchange-correlation potential, apparently contradicting one of our findings. We explain that their construction is explicitly based on the solution of the TD Schrödinger equation and, for this reason, does not address our objections, let alone refute them.