Computational Chemistry Theory
This series of courses covers quantum chemistry and density functional theory, molecular dynamics and machine-learning-based molecular dynamics, solid-state electronic structure, statistical thermodynamics, and free energy calculation methods. It systematically explores the core principles and cutting-edge applications of computational chemistry.
This course systematically explores key methods in quantum chemistry for addressing microscopic chemical problems. It covers the fundamental principles of Density Functional Theory (DFT), as well as the concepts and applications of pseudopotentials and basis sets in computational chemistry, aiming to provide a solid theoretical foundation for researchers entering the field.
The first part begins with the historical development of quantum mechanics, introducing fundamental concepts such as wave functions, operators, eigenvalue equations, the Schrödinger equation, and the Born–Oppenheimer approximation. It delves into the central role of approaches for handling many-electron problems in real chemical systems, introducing theories including the single-electron approximation, Pauli exclusion principle, and antisymmetric wave functions. Using the Hartree–Fock (HF) method as an example, the course illustrates how to treat many-electron wave functions and transitions into Density Functional Theory through the discussion of electron correlation.
The second part systematically presents the concepts of electron density and functionals, the Hohenberg–Kohn theorems (I & II), and the Kohn–Sham equations. Emphasis is placed on the physical significance of quantities in the Kohn–Sham framework and the methods for solving the equations. Finally, the course discusses the fundamental principles and characteristics of exchange–correlation functionals, including LDA, GGA, meta-GGA, and hybrid functionals.
The third part addresses the practical need for approximations in computational chemistry to treat complex problems, introducing the principles and applications of pseudopotentials and basis sets. Special focus is given to the physical significance of pseudopotentials and the representation of basis sets using the Linear Combination of Atomic Orbitals (LCAO), along with the concepts of polarization functions and diffuse functions.
- Molecular Dynamics/Machine Learning Molecular Dynamics
This course introduces the fundamental principles of Classical Molecular Dynamics (CMD) and Machine Learning Molecular Dynamics (MLMD). It covers how molecular dynamics simulations are used to investigate the physicochemical properties of molecules and materials, and how machine learning methods can be employed to construct potential energy functions that enhance the efficiency and accuracy of simulations. The classical molecular dynamics section includes the basic principles of MD, interatomic potentials and classical force fields, numerical solutions of Newton’s equations of motion, the concept of statistical ensembles, methods for temperature and pressure control, and the implementation of molecular dynamics simulations. The machine learning molecular dynamics section covers the relationship between machine-learning-based potentials, classical mechanics, and quantum mechanics; the theoretical foundations of MLMD; the concepts of atomic energy and deep potential energy surface models; as well as the architectures and optimization methods of machine learning models. This course is designed for students in materials science, chemistry, and related disciplines, as well as beginners interested in molecular simulations and machine learning. - Solid Electronic Structure
This course provides an overview of the historical development of solid-state physics, with a focus on crystal structures and band theory. By introducing the periodic arrangement of crystals and its significant influence on material properties, the course explains how Bloch’s theorem reveals the behavior of electrons in one-dimensional and three-dimensional periodic potentials. It also discusses the application of the tight-binding approximation for simplified band structure analysis and provides an in-depth explanation of the physical meaning of density of states and the Fermi surface, highlighting their critical roles in conductivity and semiconductor properties. This course is suitable for learners seeking to master the fundamentals of solid-state physics and understand their modern applications. - Statistical Thermodynamics
This course introduces the fundamental concepts of statistical thermodynamics commonly used in computational chemistry, with a particular focus on free energy calculation methods relevant to electrochemical simulations. - Free Energy Calculation Methods
This course presents the statistical foundations of free energy concepts, clarifying their relationship and distinction from potential energy surfaces. It introduces computational methods for evaluating reaction free energies in computational chemistry, with a focus on the principles and methodologies of enhanced sampling techniques, which are widely applied and frequently used in the research group. The discussion links back to the fundamental principles of free energy introduced earlier. Finally, the course includes a demonstration of a simple free energy calculation case study.