Propagators for the time-dependent Kohn-Sham equations

被引:470
作者
Castro, A [1 ]
Marques, MAL
Rubio, A
机构
[1] Univ Valladolid, Dept Fis Teor, E-47011 Valladolid, Spain
[2] DIPC, San Sebastian 20018, Spain
[3] Free Univ Berlin, Inst Theoret Phys, D-14195 Berlin, Germany
[4] Univ Basque Country, Fac Quim, Dept Fis Mat, San Sebastian 20018, Spain
[5] Ctr Mixto CSIC Univ Basque Country, San Sebastian 20018, Spain
关键词
D O I
10.1063/1.1774980
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
In this paper we address the problem of the numerical integration of the time-dependent Schrodinger equation ipartial derivative(t)Phi=(H) over cap Phi. In particular, we are concerned with the important case where (H) over cap 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, (H) over cap 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 approximate exp((A) over cap), where (A) over cap is a time-independent operator [e.g., A=-iDeltatH(tau) for some given time tau]. 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. (C) 2004 American Institute of Physics.
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页码:3425 / 3433
页数:9
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