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Propagators for the time-dependent Kohn-Sham equations

AutorCastro, Alberto; Marques, Miguel A. L.; Rubio, Angel
Fecha de publicación2004
EditorAmerican Institute of Physics
CitaciónJournal of Chemical Physics 121(8): 3425-3433 (2004)
ResumenIn this paper we address the problem of the numerical integration of the time-dependent Schrödinger equationi∂ t φ=Ĥφ. In particular, we are concerned with the important case whereĤ is the self-consistent Kohn–Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn–Sham potential depends parametrically on the time-dependent density,Ĥ is in general time dependent, even in the absence of an external time-dependent field. The present analysis also holds for the description of the excited state dynamics of a many-electron system under the influence of arbitrary external time-dependent electromagnetic fields. Our discussion is separated in two parts: (i) First, we look at several algorithms to approximateexp(Â), where is a time-independent operator [e.g.,Â=−iΔtĤ(τ) for some given time τ]. In particular, polynomial expansions, projection in Krylov subspaces, and split-operator methods are investigated. (ii) We then discuss different approximations for the time-evolution operator, such as the midpoint and implicit rules, and Magnus expansions. Split-operator techniques can also be modified to approximate the full time-dependent propagator. As the Hamiltonian is time dependent, problem (ii) is not equivalent to (i). All these techniques have been implemented and tested in our computer code OCTOPUS, but can be of general use in other frameworks and implementations.
Versión del editorhttp://dx.doi.org/10.1063/1.1774980
Identificadoresdoi: 10.1063/1.1774980
issn: 0021-9606
e-issn: 1089-7690
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