Reply to "Comment on 'Critique of the foundations of time-dependent density functional theory'"

TL;DR

This paper clarifies misconceptions in a recent critique of time-dependent density functional theory (TDDFT), emphasizing the importance of precise definitions and convergence issues in the foundational mapping derivation.

Contribution

It distinguishes two conceptions of the TDDFT mapping derivation and argues that one is not a density-functional method while the other lacks guaranteed convergence.

Findings

DKSP scheme is not a density-functional method

PF-FPI scheme's convergence is not assured

Clarifies the conceptual foundations of TDDFT

Abstract

In a recent Comment (arXiv:0710.0018), Maitra, Burke, and van Leeuwen (MBL) attempt to refute our criticism of the foundations of TDDFT (see Phys. Rev. A 75, 022513 (2007)). However, their arguments miss the essence of our position. This is mainly due to an ambiguity concerning the meaning of the so-called mapping derivation of time-dependent Kohn-Sham equations. We distinguish two different conceptions, referred to as potential-functional based fixed-point iteration (PF-FPI) and direct Kohn-Sham potential (DKSP) scheme, respectively. We argue that the DKSP scheme, apparently adopted by MBL, is not a density-functional method at all. The PF-FPI concept, on the other hand, while legitimately predicated on the Runge-Gross mapping theorem, is invalid because the convergence of the fixed-point iteration is not assured.