CAREER: Turbo-Charging Hybrid Functional Electronic Structure Calculations via Adaptive Compression Methods

本项目旨在改进原子和分子电子结构模拟的数值方法。电子结构理论，特别是以Kohn-Sham密度泛函理论（KS-DFT）为代表的电子结构理论，已经发展成为在物理、化学、材料科学和生物学中有着广泛应用的主力工具。高保真电子结构仿真需要解决越来越大、越来越复杂的问题。高效、准确和可扩展的数值方法可以改变电子结构理论的适用范围，并使科学应用成为可能。该项目的教育部分侧重于向研究生，早期职业研究人员和具有数学背景的高级本科生介绍电子结构理论。应用数学界开发的高效技术，在适应特定的计算问题后，可以成为降低电子结构计算成本的有价值的工具。电子结构理论也可以为一般数学和数值技术的发展提供新的思路和应用领域。目前应用数学界和电子结构学界之间存在着很大的语言障碍。该项目将开发新的教育活动，如新主题课程和暑期学校活动，目的是减少语言障碍，弥合两个社区之间的差距。该项目的研究部分旨在通过高保真混合交换相关泛函显着降低KS-DFT计算的计算成本。在数学上，混合泛函涉及到Fock交换算子，而Fock交换算子一般是非局部的、全秩的，其处理在计算上非常具有挑战性。该项目将开发一种用于处理Fock交换算子的自适应压缩策略，并使用混合泛函加速两种重要类型的计算：从头算分子动力学和实时依赖时间的密度泛函理论。新方法将转移到化学家和材料科学家使用的社区电子结构软件包中，并通过真实材料的模拟验证。目标是改变混合功能电子结构计算在大型复杂系统中的执行方式。

This project aims to improve numerical methods for the simulation of electronic structure in atoms and molecules. Electronic structure theories, particularly represented by Kohn-Sham density functional theory (KS-DFT), have been developed into workhorse tools with a wide range of applications in physics, chemistry, materials science, and biology. High fidelity electronic structure simulation requires the solution of increasingly larger and more complex problems. Efficient, accurate, and scalable numerical methods can transform the range of applicability of electronic structure theories and enable scientific applications that are beyond reach today. The education component of this project focuses on introducing electronic structure theories to graduate students, early career researchers, and advanced undergraduate students with mathematical backgrounds. Efficient techniques developed in the applied mathematics community, after adapted to specific computational problems, can be valuable tools to reduce the cost of electronic structure calculations. Electronic structure theories can also offer new ideas and application areas for the development of general mathematical and numerical techniques. Currently there is a high language barrier between the applied mathematics community and the electronic structure community. This project will develop new education activities, such as new topic courses and summer school activities, with the goal of reducing the language barrier and bridging the gap between the two communities. The research component of this project aims at significantly reducing the computational cost for KS-DFT calculations with high fidelity hybrid exchange-correlation functionals. Mathematically, hybrid functionals involve the Fock exchange operator, which is generally nonlocal and full-rank, and its treatment is computationally very challenging. This project will develop an adaptive compression strategy for treating the Fock exchange operator, and accelerate two important types of calculations with hybrid functionals: ab initio molecular dynamics, and real-time time dependent density functional theory. The new methods will be transferred to community electronic structure software packages used by chemists and materials scientists, and be validated by simulation with real materials. The goal is to transform how hybrid functional electronic structure calculations are performed for large, complex systems.