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

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

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.