Time-dependent Density-Functional Approaches for Excitons: Linear Response Versus Real Time

非技术性总结材料研究部和化学部共同资助基础研究和教育奖，以开发半导体和绝缘材料中光物质相互作用研究的理论和计算方法。光与物质的相互作用在科学和技术中具有根本的重要性：它通过光谱学确定材料的特性，并构成光化学作为可再生能源的基础。这项研究的目标是开发比现有方法更准确和有效的光-物质相互作用的理论和计算方法。当光被材料吸收时，带负电荷的电子被激发到更高的状态，留下一个带正电荷的空隙，称为“空穴”状态。电子和空穴可以组合形成成对的激子，激子会产生特有的光谱特征，并且通常主导材料的光学性质。激子效应的理论和计算描述是具有挑战性的，因为电子-空穴对是在原始材料中形成的，并且受到其中所有其他电子的影响。本项目将利用称为时间依赖密度泛函理论（TDDFT）的量子力学方法，该方法在物理，化学，和材料科学。在这个理论框架内，PI将开发新的方法来解释多电子系统的量子行为，特别是专注于在光谱学中精确描述激子所必需的特性。另一个研究目标将是调整一种名为Qb@ll的计算机代码，该代码能够描述复杂电子系统的实时动态，以解释激子特性，并使用它来研究具有缺陷和界面的材料的光学特性。研究活动将与教育工作齐头并进，包括在理论和计算凝聚态研究方面对研究生进行培训和指导，以及在本科生和研究生阶段开发密度泛函理论在线课程。本科生将参与课程材料和动手计算练习的设计和开发。材料研究部和化学部共同资助该基础研究和教育奖，以开发半导体和绝缘体激子性质研究的理论和计算方法。激子在吸收边附近的光谱区域中主导许多材料的光学性质;它们来自于在光学激发期间产生的电子和空穴的吸引屏蔽相互作用。目前，Bethe-Salpeter方程是计算固体中激子性质的标准方法，但计算成本很高。PI将开发和实施基于含时密度泛函理论（TDDFT）的激子替代方法。TDDFT的关键挑战是通过适当的近似来解释交换和相关（XC）效应;激子性质的准确描述需要具有适当长程行为和适当筛选的XC泛函。在这个项目中的第一个目标是开发更准确的激子XC泛函的线性响应TDDFT，使用三个关键的想法：简单的参数化的矩阵形式的远程校正XC内核，来自多体理论的近似，和非局部交换屏蔽模型介电函数。这些模型将通过比较计算的激子结合能和光谱强度与实验数据进行评估。第二个目标是使激子动力学的Qb@ll计算机代码与固体的随时间变化的Kohn-Sham方程相适应。Qb@ll能够与包含许多原子的单位单元进行大规模并行计算，这使得它适合于处理复杂系统。将应用于缺陷处的束缚激子复合物和分子晶体中的电荷转移激子。此外，Qb@ll代码允许电子和离子自由度的耦合，这是从第一原理描述光伏过程中的弛豫和电荷分离的关键。研究活动将与教育工作齐头并进，包括对理论和计算凝聚态研究的研究生进行培训和指导，以及在本科生和研究生阶段开发密度泛函理论在线课程。本科生将参与课程材料和动手计算练习的设计和开发。该奖项反映了NSF的法定使命，并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，被认为值得支持。

NONTECHNICAL SUMMARYThe Division of Materials Research and the Chemistry Division jointly fund this award on fundamental research and education to develop theoretical and computational methodology for the study of light-matter interactions in semiconducting and insulating materials. The interaction of light and matter is of fundamental importance in science and technology: it determines the characterization of materials through optical spectroscopy and forms the basis of photovoltaics as a renewable energy resource. The goal of this research is to develop theoretical and computational methods for light-matter interactions that are more accurate and efficient than existing approaches.When light gets absorbed in a material, negatively charged electrons are excited into higher states, leaving behind them a positively charged void that is called a "hole" state. Electrons and holes can team up to form pairs, called excitons, which give rise to characteristic spectroscopic features and often dominate the optical properties of materials. The theoretical and computational description of excitonic effects is challenging, since the electron-hole pairs are formed within the original material and are subject to the influence of all other electrons therein.This project will utilize a quantum-mechanical method called time-dependent density-functional theory (TDDFT), which has been very successful in describing the dynamics of interacting electronic systems in many areas in physics, chemistry, and materials science. Within this theoretical framework, the PI will develop new ways of accounting for the quantum behavior of many-electron systems, specifically focusing on properties that are necessary for the accurate description of excitons in optical spectroscopy. Another research goal will be to adapt a computer code called Qb@ll that is capable of describing the real-time dynamics of complex electronic systems, to account for excitonic properties, and use it to study the optical properties of materials with defects and interfaces.The research activities will go hand-in-hand with educational efforts, consisting of training and mentoring of graduate students in theoretical and computational condensed-matter research, and the development of an online course in density-functional theory at the undergraduate and beginning-graduate level. Undergraduate students will be involved in the design and development of course materials and of hands-on computational exercises. TECHNICAL SUMMARYThe Division of Materials Research and the Chemistry Division jointly fund this award on fundamental research and education to develop theoretical and computational methodology for the study of excitonic properties in semiconductors and insulators. Excitons dominate the optical properties of many materials in the spectral region around the absorption edge; they arise from the attractive screened interaction of electrons and holes created during optical excitations. At present, the Bethe-Salpeter equation is the standard method for calculating excitonic properties in solids, but at significant computational cost. The PI will develop and implement alternative approaches for excitons based on time-dependent density-functional theory (TDDFT).The key challenge for TDDFT is to account for exchange and correlation (XC) effects via suitable approximations; the accurate description of excitonic properties requires XC functionals with the proper long-range behavior and with proper screening. The first goal in this project is to develop more accurate excitonic XC functionals for linear-response TDDFT, using three key ideas: simple parametrizations of the matrix form of long-range-corrected XC kernels, approximations derived from many-body theory, and nonlocal exchange screened with model dielectric functions. These models will be assessed by comparing calculated exciton binding energies and spectral strengths with experimental data.The second goal is to adapt the Qb@ll computer code for exciton dynamics with the time-dependent Kohn-Sham equation for solids. Qb@ll is capable of massively parallel calculations with unit cells containing many atoms, which makes it suitable to treat complex systems. Applications to bound exciton complexes at defects and charge-transfer excitons in molecular crystals will be carried out. In addition, the Qb@ll code allows coupling of electronic and ionic degrees of freedom, which is key for describing relaxation and charge separation in photovoltaic processes from first principles.The research activities will go hand-in-hand with educational efforts, consisting of training and mentoring of graduate students in theoretical and computational condensed-matter research, and the development of an online course in density-functional theory at the undergraduate and beginning-graduate level. Undergraduate students will be involved in the design and development of course materials and of hands-on computational exercises.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.