Developing Methods for Efficient Electronic Structure Calculations and Analyses

Abstract

This thesis presents a collection of my PhD-stage research on computational quantum chemistry, including development of quantum chemistry methods as well as case studies on organic reaction mechanisms. It is divided into seven chapters.

The first chapter reviews literature on fundamental knowledge of density-functional theory (DFT), orbital-based wavefunction analysis and manifold optimization applied to quantum chemistry problems, on the basis of which the following chapters are built.

Chapter 2 and Chapter 3 discuss my work on grand-canonical (GC) DFT. GC-DFT is suitable for simulation of electrochemical systems featuring variable numbers of electrons and finite (non-zero) temperatures. In Chapter 2, I propose methods to obtain the derivatives of grand potential (analogous to energy in conventional DFT in the micro-canonical ensemble) with respect to the nuclear coordinates. Chapter 3 showcases my ongoing work on accelerating GC self-consistent field (SCF) with Fock-matrix-based second-order optimization.

Chapter 4 is devoted to the natural fragment bond orbital method I developed for inter-fragment bonding study, as an orbital-based wavefunction analysis method reviewed in Section 1.2.

My project on augmented direct inversion in the iterative subspace, a technique to ensure SCF convergence, enabled by optimization on the simplex manifold, is summarized in Chapter 5, as an example where a quantum chemistry problem boil down to numerical optimization subject to a certain constraint, for which manifold optimization is designed in the first place, as reviewed in Section 1.3.

Chapter 6 displays my computational studies on reaction mechanism of CPA-catalyzed synthesis of a stable vinyl sulfoxonium ylide with DFT calculation, concentration evolution simulation and reduced density gradient.

In the end, Chapter 7 concludes the thesis with my ideal on my research output.

Date of Award	2025
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Yong HUANG (Supervisor) & Haibin SU (Supervisor)