A linear‐scaling time‐dependent density functional theory is developed. The equation of motion is solved for the reduced single‐electron density matrix in the real time domain. Chebyshev expansion is used for integration in time domain. Filter diagonalization is implemented to determine the excited state energies. The locality of the reduced single‐electron density matrix is utilized to ensure computational time scales linearly with system size. We summarize these methods in this brief review.A linear‐scaling time‐dependent density functional theory is developed. The equation of motion is solved for the reduced single‐electron density matrix in the real time domain. Chebyshev expansion is used for integration in time domain. Filter diagonalization is implemented to determine the excited state energies. The locality of the reduced single‐electron density matrix is utilized to ensure computational time scales linearly with system size. We summarize these methods in this brief review.

AIP conference proceedingsJan 1, 20090 citations

Time-Dependent Density-Functional Theory: Conceptual and Practical Aspects

H. Köhl, R. M. Dreizler

We sketch the proof of an existence theorem for a time-dependent density-functional theory on the set of $N$ -representable densities, extending the constrained-search formulation of Levy into the time-dependent domain, and add a brief comment on practical issues.We sketch the proof of an existence theorem for a time-dependent density-functional theory on the set of $N$-representable densities, extending the constrained-search formulation of Levy into the time-dependent domain, and add a brief comment on practical issues.

Physical Review LettersMay 12, 198639 citations

We sketch the proof of an existence theorem for a time-dependent density-functional theory on the set of

N

-representable densities, extending the constrained-search formulation of Levy into the time-dependent domain, and add a brief comment on practical issues.