Institute for Biocomputation and Physics of Complex Systems , University of Zaragoza , Calle Mariano Esquillor , 50018 Zaragoza , Spain.
Institut für Physik , Martin-Luther-Universität Halle-Wittenberg , 06120 Halle (Saale) , Germany.
J Chem Theory Comput. 2018 Jun 12;14(6):3040-3052. doi: 10.1021/acs.jctc.8b00197. Epub 2018 May 9.
We examine various integration schemes for the time-dependent 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 time-dependent 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 fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.
我们研究了时变 Kohn-Sham 方程的各种积分方案。与时间相关的薛定谔方程不同，由于哈密顿量依赖于电子密度，这套方程是非线性的。我们讨论了它们的一些精确性质，特别是它们的辛结构。考虑了四种不同的传播子族，即线性多步、龙格-库塔、指数龙格-库塔和无伴随马克斯算子方案。之所以选择这些方案，是因为过去在进行时间相关电子结构计算时，它们在很大程度上被忽略了。根据成本与精度的关系来分析性能。在鲁棒性、简单性和效率方面，明显的赢家是简化版的四阶无伴随马克斯算子积分器。然而，在某些特定情况下，其他的传播子，如多步方法的一些隐式版本，可能会有用。
