Department of Mathematics , University of California , Berkeley , California 94720 , United States.
Materials Science Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States.
J Chem Theory Comput. 2018 Nov 13;14(11):5645-5652. doi: 10.1021/acs.jctc.8b00580. Epub 2018 Nov 2.
Real-time time-dependent density functional theory (RT-TDDFT) is known to be hindered by the very small time step (attosecond or smaller) needed in the numerical simulation, because of the fast oscillation of electron wave functions, which significantly limits its range of applicability for the study of ultrafast dynamics. In this paper, we demonstrate that such oscillation can be considerably reduced by optimizing the gauge choice using the parallel transport formalism. RT-TDDFT calculations can thus be significantly accelerated using a combination of the parallel transport gauge and implicit integrators, and the resulting scheme can be used to accelerate any electronic structure software that uses a Schrödinger representation. Using absorption spectrum, ultrashort laser pulse, and Ehrenfest dynamics calculations for example, we show that the new method can utilize a time step that is on the order of 10-100 attoseconds using a planewave basis set. Thanks to the significant increase of the size of the time step, we also demonstrate that the new method is more than 10 times faster, in terms of the wall clock time, when compared to the standard explicit fourth-order Runge-Kutta time integrator for silicon systems ranging from 32 to 1024 atoms.
实时含时密度泛函理论 (RT-TDDFT) 由于电子波函数的快速振荡，在数值模拟中需要非常小的时间步长（阿秒或更小），这极大地限制了其在超快动力学研究中的适用性。在本文中，我们证明通过使用平行传输形式优化规范选择，可以显著减少这种振荡。因此，通过结合平行传输规范和隐式积分器，可以显著加速 RT-TDDFT 计算，并且所得方案可用于加速使用薛定谔表示的任何电子结构软件。例如，通过吸收光谱、超短激光脉冲和 Ehrenfest 动力学计算，我们表明，使用平面波基组，新方法可以利用大约 10-100 阿秒的时间步长。由于时间步长的显著增加，我们还表明，与标准的显式四阶龙格-库塔时间积分器相比，新方法在处理从 32 到 1024 个原子的硅系统时，在墙钟时间方面快了 10 多倍。
