Quantitative nonlinear time-dependent density functional theory (TDDFT) for large systems

摘要加州大学洛杉矶分校的daniel Neuhauser获得化学学部化学理论、模型和计算方法（CTMC）项目的奖励，研究了纳米材料在强激光照射下的电子运动。这是一个有趣而复杂的领域，新现象不断出现，但由于描述激发态的精确理论和计算方法只能应用于小系统，因此它在很大程度上仍未被探索。Neuhauser博士及其同事正在开发新的方法，以适度的计算成本将必要的量子力学效应结合起来。一种新的计算框架正在开发中，它通过概率方法将量子化学、凝聚态物理和应用数学结合起来。该项目特别致力于让本科生和高中生参与其中，并强调研究生和博士后的领导机会。为了获得复杂系统的基本物理特性，一个完全从头算的量子描述是必要的。最合适的方法是采用实时时变密度泛函理论（TDDFT），它具有近似准粒子能量的远程精确交换，并包含吸引电子-空穴相互作用。后者对于解释激子效应和吸收截面中光谱重分布是必要的。然而，传统的实现严重限制了可以使用精确交换的TDDFT处理的系统的最大大小。该项目开发了一种随机TDDFT方法，该方法随机模拟交换相互作用，即将所有被占用状态的求和替换为被占用希尔伯特子空间的随机采样，而其余部分的描述可以传统地模拟。这使得处理具有数千个原子的系统和计算以前无法处理的系统的非线性响应成为可能。高度非均匀系统的光学响应描述，例如缺陷状态，正在用一种新的嵌入式随机TDDFT来处理，它结合了不同空间区域的随机和确定性TDDFT。通过这项工作，为从高中到博士后的学生提供指导，开发的软件正在向更广泛的社区提供。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

AbstractDaniel Neuhauser at the University of California, Los Angeles, is supported by an award from the Chemical Theory, Models and Computational Methods (CTMC) Program in the Chemistry Division to explore electron motion in nanomaterials in response to intense laser irradiation. This is an interesting and complex regime where new phenomena are emerging but it remains largely unexplored since accurate theoretical and computational methods for the description of excited states can only be applied to small systems. Dr. Neuhauser and coworkers are developing new methods which incorporate the necessary quantum mechanical effects at moderate computational costs. A novel computational framework is being developed that merges quantum chemistry, condensed matter physics and applied mathematics through a probabilistic approach to the problem. Specific efforts are being made to involve undergraduate and high school students, and the project emphasizes leadership opportunities for graduate students and postdocs.To obtain the fundamental physical characteristics of complex systems, a fully ab-initio quantum description is necessary. The most suitable approach is to employ real time Time-Dependent Density Functional Theory (TDDFT) with long-range exact exchange which approximates quasiparticle energies and includes attractive electron-hole interactions. The latter are necessary to account for excitonic effects and the redistribution of spectral weight in absorption cross sections. However, conventional implementations severely limit the maximum size of the system that can be treated using TDDFT with exact exchange. The project develops a stochastic TDDFT method which simulates the exchange interaction stochastically, i.e., summations over all occupied states are replaced by random sampling of the occupied Hilbert subspace, while the remaining parts of the description can be simulated traditionally. This makes it possible to treat systems with thousands of atoms and calculate the nonlinear response for systems that could not be handled previously. Description of the optical response of highly inhomogeneous systems, e.g., defect states, is being treated with a new Embedded Stochastic TDDFT, which combines stochastic and deterministic TDDFT for different regions of space. Mentoring of students ranging from high school to postdoctoral status is provided through this work, and the software developed is being made available to the wider community.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.