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

在化学系化学理论、模型和计算方法项目的支持下，加州大学洛杉矶分校的丹尼尔诺伊豪泽教授正在开发用于确定超大分子系统光学性质的方法。这些性质在有机和无机能源材料的广泛应用中起着关键作用，包括半导体纳米颗粒，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非常大的系统的能力对于这些新材料和系统的操纵和控制以及未来系统的设计至关重要。为此，诺伊豪泽小组将开发一种随机形式来求解贝特-萨尔彼得方程（BSE），以表征非常大的化学系统的吸收光谱。已知BSE可以准确预测分子和固态系统的吸收特性。使用这些提出的随机方法，预计能够放大到非常大的系统，成千上万的原子与数万个电子。这项工作将被纳入一个新的基于代码的普通化学课程和推广活动，以服务不足的group. Generally BSE是太计算成本太大，考虑分子大于几百个原子，由于屏蔽库仑交换，W的产生和应用。诺伊豪泽研究小组将致力于为BSE开发三种具体的方法学进展：W作用的线性缩放生成，稀疏随机压缩和采样以存储巨大的W矩阵，BSE内W随机应用的实际二次缩放，具有基于W的交换内核的时间相关Hartree-Fock（TDHF），以及一阶动态校正的随机表示。具体地说，屏蔽库仑相互作用的作用将被分离成卷积交换类部分，该部分将被系统地改进以类似于真正的有效相互作用，以及小的剩余部分，该剩余部分应该容易被随机采样。总之，这些创新有望结合起来，产生一种模拟活性轨道中数千个电子的纳米级系统的方法。如果成功的话，这些对贝特-萨尔彼得方程的修改预计将产生深远的科学影响。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

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.