Bethe Salpeter Equation Spectra for Very Large Systems with Thousands of Electrons or More

在化学系化学理论、模型和计算方法计划的支持下，加州大学洛杉矶分校的Daniel Neuhauser教授正在开发确定超大分子体系光学性质的方法。这些性质在有机和无机能源材料的广泛应用中起着至关重要的作用，包括半导体纳米粒子、有机超分子结构和有机光伏纳米结构。通过计算表征具有数千个原子的超大型系统的能力，对于操纵和控制这些新材料和系统，以及未来系统的设计是至关重要的。为此，Neuhauser小组将发展一种随机形式来求解Bethe-Salpeter方程(BSE)，以表征超大型化学体系的吸收光谱。众所周知，BSE能够准确预测分子和固态体系的吸收特性。这些拟议的随机方法的使用有望扩大到由数千个原子和数万个电子组成的非常大的系统。这项工作将被纳入一门新的基于代码的普通化学课程和面向服务不足的群体的推广活动。典型的情况是，由于屏蔽库仑交换的产生和应用，对于大于数百个原子的分子，BSE的计算成本太高而无法考虑。Neuhauser研究小组将致力于开发BSE的三个具体方法进展：W作用的线性标度生成，用于存储巨大W矩阵的稀疏随机压缩和采样，W在BSE中随机应用的实际二次标度，具有W基交换核的含时Hartree-Fock(TDHF)，以及一阶动态修正的随机表示。具体地说，屏蔽的库仑相互作用的作用将被分成卷积交换部分和一小部分，该部分将被系统地改进以类似于真正的有效相互作用，以及一小部分应该容易地随机抽样。总而言之，这些创新有望结合在一起，产生一种模拟活跃轨道上数千个电子的纳米级系统的方法。如果成功，这些对Bethe-Salpeter方程的修改预计将产生深远的科学影响。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

With support from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry, Professor Daniel Neuhauser of UCLA is developing methods for determining the optical properties of very large molecular systems. These properties play a critical role in broad applications of organic and inorganic energy materials, including semiconducting nanoparticles, organic supramolecular structures, and organic photovoltaic nanostructures. The ability to characterize very large systems with thousands of atoms computationally is critical for the manipulation and control of these new materials and systems, and for the design of future systems. Toward this end, the Neuhauser group will develop a stochastic formalism to solve the Bethe-Salpeter Equation (BSE) for characterizing the absorption spectrum of very large chemical systems. BSE is known to predict accurately the absorption properties of molecular and solid-state systems. The use of these proposed stochastic methods is expected to enable scaling up to very large systems of thousands of atoms with tens of thousands of electrons. This work will be incorporated into a new code-based General Chemistry course and outreach activities to underserved groups.Typically the BSE is too computationally costly to consider for molecules larger than few hundred atoms due to the generation and application of the screened Coulomb exchange, W. The Neuhauser research group will undertake to develoop three specific methodology advances to the BSE: linear scaling generation of the action of W, sparse stochastic compression and sampling for storage of huge W matrices, practically quadratic scaling of the stochastic application of W within the BSE, a time-dependent Hartree-Fock (TDHF) with W-based exchange kernels, and stochastic representation of first-order dynamic corrections. Specifically, the action of the screened Coulomb interaction will be separated into a convolutional exchange-like portion that is to be systematically improved to resemble the true effective interaction, and a small remainder that should easily be stochastically sampled. Together, these innovations are expected to couple to yield a method for simulating nanoscale systems of thousands of electrons in active orbitals. If successful, these modification of the Bethe-Salpeter Equation are expected to have far-reaching scientific impact.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.