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

洛杉矶的加州大学的Daniel诺伊豪泽获得了化学系化学理论、模型和计算方法（CTMC）项目的一个奖项的支持，以探索纳米材料中电子运动对强激光照射的响应。 这是一个有趣而复杂的制度，新的现象正在出现，但它仍然在很大程度上未被探索，因为精确的理论和计算方法的描述激发态只能应用于小系统。 诺伊豪泽博士和同事们正在开发新的方法，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，凝聚态物理学和应用数学融合在一起。目前正在努力让本科生和高中生参与进来，该项目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，完全从头量子描述是必要的。 最合适的方法是采用真实的时间依赖于时间的密度泛函理论（TDDFT）与远程精确交换，近似准粒子的能量，并包括有吸引力的电子-空穴相互作用。 后者是必要的帐户激子效应和吸收截面中的光谱重量的重新分配。 然而，传统的实现方式严重限制了可以使用具有精确交换的TDDFT来处理的系统的最大大小。 该项目开发了一种随机TDDFT方法，该方法模拟了交换相互作用的随机性，即，对所有被占用状态的求和由被占用希尔伯特子空间的随机采样代替，而描述的其余部分可以传统地模拟。 这使得处理具有数千个原子的系统并计算以前无法处理的系统的非线性响应成为可能。 描述高度不均匀系统的光学响应，例如，缺陷状态，正在处理一个新的嵌入式随机TDDFT，它结合了随机和确定性TDDFT的不同区域的空间。通过这项工作，从高中到博士后的学生都可以得到指导，开发的软件正在向更广泛的社区提供。这个奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.