Propagators for the Time-Dependent Kohn–Sham Equations: Multistep, Runge–Kutta, Exponential Runge–Kutta, and Commutator Free Magnus Methods
Journal Of Chemical Theory And Computation 14,6, 3040 - 3052 (2018)
Propagators for the Time-Dependent Kohn–Sham Equations: Multistep, Runge–Kutta, Exponential Runge–Kutta, and Commutator Free Magnus Methods
We examine various integration schemes for the timedependent Kohn−Sham equations. Contrary to the time-dependent Schrödinger’s equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered,specifically the linear multistep, Runge−Kutta, exponential Runge−Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for timedependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourthorder commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.
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- http://dx.doi.org/10.1021/acs.jctc.8b00197
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- http://arxiv.org/abs/1803.02113
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- We acknowledge support from Ministerio de Economiá y Competitividad (MINECO) grants FIS2013-46159-C3-2-P,FIS2014-61301-EXP, and FIS2017-82426-P, from the European Research Council (ERC-2015- dG-694097), from Grupos Consolidados (IT578-13), from the European Union Horizon 2020 program under Grant Agreement 676580 (NOMAD), from the Salvador de Madariaga mobility grant PRX16/00436, and from the DFG Project B09 of TRR 227.
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- Center for Computational Quantum Physics (CCQ), The Flatiron Institute, New York
- MPSD-Max-Planck Hamburg