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##### Propagators for the time-dependent Kohn-Sham equations

**Authors**: Alberto Castro, and M.A.L. Marques

**Ref.**: in *Time-dependent density functional theory*, ed. by M.A.L. Marques, C. Ullrich, F. Nogueira, A. Rubio, K. Burke, and E.K.U. Gross, Lecture Notes in Physics, Vol. 706, Springer, Berlin, 197-210 (2006)

**Abstract**: The main practical result of the Runge-Gross theorem are the
time-dependent Kohn-Sham (TDKS) equations: a set of coupled one-particle
Schroedinger-like equations.

During the last years, most applications of TDDFT were performed within linear
response theory, where the response properties of the system are usually
obtained in frequency domain. One may, however, work directly in the
time-domain, propagating Eqs.~(1). This has the advantage of
allowing the inclusion of intense external perturbations, beyond the linear
response regime. Of course, this "real-time" formulation of TDDFT requires
the use of an algorithm to propagate Schroedinger-like equations.

Not surprisingly, the study of efficacious algorithms for this purpose has a
long history, and multiple answers. We are concerned with a very general
problem, yet we must beware of general purpose solutions: one expects
that the efficiency depends strongly on the characteristics of the
time-independent part of the Hamiltonian, on the time-dependent perturbation,
and also on the initial state. From all possible approaches, we focus in this
chapter on the ones most relevant to the propagation of the TDKS equations.

**Citations**: 15 (Google scholar)

**Bibtex**:

@incollection{Castro_2006, doi = {10.1007/3-540-35426-3_12}, url = {https://doi.org/10.1007%2F3-540-35426-3_12}, year = 2006, publisher = {Springer Berlin Heidelberg}, pages = {197--210}, author = {A. Castro and M.A.L. Marques}, title = {Propagators for the Time-Dependent Kohn-Sham Equations}, booktitle = {Time-Dependent Density Functional Theory} }