Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA.
J Chem Phys. 2012 Dec 14;137(22):22A546. doi: 10.1063/1.4758792.
Explicit integrators for real-time propagation of time-dependent Kohn-Sham equations are compared regarding their suitability for performing large-scale simulations. Four algorithms are implemented and assessed for both stability and accuracy within a plane-wave pseudopotential framework, employing the adiabatic approximation to the exchange-correlation functional. Simulation results for a single sodium atom and a sodium atom embedded in bulk magnesium oxide are discussed. While the first-order Euler scheme and the second-order finite-difference scheme are unstable, the fourth-order Runge-Kutta scheme is found to be conditionally stable and accurate within this framework. Excellent parallel scalability of the algorithm up to more than a thousand processors is demonstrated for a system containing hundreds of electrons, evidencing the suitability for large-scale simulations based on real-time propagation of time-dependent Kohn-Sham equations.
针对实时传播时变 Kohn-Sham 方程的显式积分器，比较了它们在进行大规模模拟方面的适用性。在平面波赝势框架内，采用交换关联泛函的绝热近似，实现并评估了四种算法在稳定性和准确性方面的性能。讨论了单个钠原子和嵌入体心立方镁氧化物中的钠原子的模拟结果。虽然一阶 Euler 方案和二阶有限差分方案是不稳定的，但发现四阶龙格-库塔方案在该框架内是条件稳定且准确的。对于包含数百个电子的系统，该算法的并行可扩展性高达一千多个处理器，证明了其基于实时传播时变 Kohn-Sham 方程的大规模模拟的适用性。
