## Abstract

Time-dependent density-functional theory is a rather accurate and efficient way to compute electronic excitations for finite systems. However, in the macroscopic limit (systems of increasing size), for the usual adiabatic random-phase, local-density, or generalized-gradient approximations, one recovers the Kohn-Sham independent-particle picture, and thus the incorrect band gap. To clarify this trend, we investigate the macroscopic limit of the exchange-correlation kernel in such approximations by means of an algebraical analysis complemented with numerical studies of a one-dimensional tight-binding model. We link the failure to shift the Kohn-Sham spectrum of these approximate kernels to the fact that the corresponding operators in the transition space act only on a finite subspace.

Original language | English |
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Article number | 035126 |

Pages (from-to) | - |

Number of pages | 6 |

Journal | Physical Review B (Condensed Matter) |

Volume | 76 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 2007 |