Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.
Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.
复制标题
具有短时轨迹和最小自适应基集的量子动力学。
DOI：
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发表时间：
2017
影响因子：
5.5
通讯作者：
S. Habershon
中科院分区：
文献类型：
--
作者：
Maximilian A C Saller;S. Habershon
通过波函数的基组展开求解瞬态薛定谔方程的方法通常可分为静态（瞬态）或动态（瞬态）基函数。我们最近引入了一种替代模拟方法，它代表了这两个极端之间的中间道路，采用动态（类似经典）轨迹在与波函数的未来传播相关的相空间区域中创建高斯波包的静态基组[J.化学。理论计算, 11, 8 (2015)].在这里，我们提出并测试了对我们的方法的修改，其目的是减少我们原始方案中生成的基组的大小。特别是，我们利用短时经典轨迹不断生成新的基函数，用于波函数的短时量子传播；为了避免描述瞬态波函数的基组持续增长，我们采用匹配追踪来定期最小化准确描述波函数所需的基函数的数量。总的来说，这种方法生成了一个适应波函数演化的基础集，同时也尽可能小。在应用具有挑战性的基准问题（即光激发吡嗪的 4 维模型和三个不同的双井隧道问题）时，我们发现我们的新方案能够实现精确的波函数传播，其基组比我们原来的轨迹引导基组方法小一个数量级，突出了波函数传播自适应策略的好处。
Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation.
DOI：
10.1063/1.4929478
发表时间：
2015-08
期刊：
The Journal of chemical physics
影响因子：
--
作者：
I. Polyak;Charlotte S. M. Allan;G. Worth
通讯作者：
I. Polyak;Charlotte S. M. Allan;G. Worth
DOI：
10.1063/1.4939205
发表时间：
2016
期刊：
The Journal of chemical physics
影响因子：
--
作者：
Green JA
通讯作者：
Green JA
影响因子：
4.4
作者：
Burghardt, I.;Giri, K.;Worth, G. A.
通讯作者：
Worth, G. A.