Jian Liu Group @PKU
Theoretical Chemistry / Chemical Dynamics
Course #: 01004672 (Credit: 2)
Lecture Time: 13:00-15:00 Tuesday; 8:00-10:00 Friday (Week 1-8, Fall 2025).
2025秋评估分：96.43 (out of 100)
'Quantum Mechanics in Chemistry' by Schatz and Ratner
'Understanding Molecular Simulation: From Algorithms to Applications' by Frenkel and Smit
'Statistical Mechanics: Theory and Molecular Simulation' by Tuckerman
'Quantum Mechanics: A Modern Development' by Ballentine
'Nonequilibrium Statistical Mechanics' by Zwanzig
'Introduction to Modern Statistical Mechanics' by Chandler
'Principles of Nonlinear Optical Spectroscopy' by Mukamel
'Introduction to Quantum Mechanics: A Time-Dependent Perspective' by Tanor
'Classical Mechanics' by Goldstein
黎乐民、方维海、高加力、高毅勤、蒋鸿、刘剑、刘文剑、邵久书、帅志刚、吴云东、杨金龙、杨伟涛、张增辉，《中国学科发展战略•理论与计算化学》，科学出版社，2016，ISBN 978-7-03-048919-7
课程号：01035240 （4学分，研本）；01035260（2学分，本科）
上课时间: 周二18:40-22:30；周四8:00-10:00（2024年春季学期，4学分）.
2019秋评估分：95.50 (out of 100)
2018春评估分：89.63 (out of 100)
这门课程面向已经学过《高等数学》和《线性代数》这两门课程并有初步编程经验的学生，帮助他们补充一些数学知识并结合现代计算平台来实践解决一些简单的化学问题。
在学校理学院的支持下，这门课程配有20万高性能计算平台的机时。选修人数计划在20人以内，使得真正有兴趣的学生能得到足够的计算资源。
往年日程，仅供参考。
| 日期 | 内容 | 备注 |
|---|---|---|
| 2月26日（周一） | 线性代数和量子力学 | 课程内容简介 |
| 3月1日（周四） | 线性代数回顾 | |
| 3月5日（周一） | 线性代数回顾 | 课堂小测试 |
| 3月8日（周四） | 量子力学基本概念1 | |
| 3月12日（周一） | 量子力学基本概念2 | 课堂小测试 |
| 3月15日（周四） | 量子力学基本概念3 | |
| 3月19日（周一） | 分子的简正模分析(1) | 课堂小测试 |
| 3月22日（周四） | 分子的简正模分析(2) | |
| 3月26日（周一） | Franck-Condon Principle
上机实习实例1：分子结构的比较，简正模分析 上机实习实例2.1：一维非解析体系的量子本征态的数值求解 |
课堂小测试, 高性能计算校级公共平台的使用； LAPACK程序使用 |
| 3月29日（周四） | 上机实习实例1：分子结构的比较，简正模分析
上机实习实例2.1：一维非解析体系的量子本征态的数值求解 |
高性能计算校级公共平台的使用； LAPACK程序使用 |
| 4月2日（周一） | 上机实习实例2.2：一维非解析体系的热力学涨落和量子涨落的数值求解 | 高性能计算校级公共平台的使用； LAPACK程序使用 |
| 4月5日（周四） | 清明节 | 学校停课 |
| 4月9日（周一） | 上机实习实例2.2：一维非解析体系的热力学涨落和量子涨落的数值求解 | 高性能计算校级公共平台的使用； LAPACK程序使用 |
| 4月12日（周四） | 傅立叶变换 | |
| 4月16日（周一） | 解析函数1 | |
| 4月19日（周四） | 解析函数2 | 课堂小测试 |
| 4月23日（周一） | 留数定理1 | |
| 4月26日（周四） | 留数定理2 | 课堂小测试 |
| 4月30日（周一） | 稳相近似 | |
| 5月3日（周四） | 量子与经典的对应1， Wigner变换 | 课堂小测试 |
| 5月7日（周一） | 量子与经典的对应2， Wigner变换 | |
| 5月10日（周四） | 上机实习实例4.1：零温或有限温度条件下双原子分子的振动：量子与经典情况 | 高性能计算校级公共平台的使用 |
| 5月14日（周一） | 上机实习实例4.2：双原子分子的振动配分函数的数值计算 | 高性能计算校级公共平台的使用 |
| 5月17日（周四） | 量子与经典的对应3， 拉格郎日量和哈密顿量 | 期中考试部分解答 |
| 5月21日（周一） | 量子与经典的对应4， 路径积分简介 | 课堂小测试 |
| 5月24日（周四） | 量子与经典的对应5， 量子轨迹 | |
| 5月28日（周一） | 量子与经典的对应6， 量子轨迹 | 课堂小测试 |
| 5月31日（周四） | 反应过渡态理论简介 | |
| 6月4日（周一） | Monte Carlo方法简介 | |
| 6月7日（周四） | 郎之万方程简介 | 课堂小测试 |
| 6月11日（周一） | 上机实习实例5：双原子分子的振动光谱的数值计算 | 高性能计算校级公共平台的使用 |
| 6月14日（周四） | 上机实习实例6：恒温体系的分子动力学模拟 | 高性能计算校级公共平台的使用 |
| 6月25日（周一晚上） | 期末考试 |
'Quantum Mechanics: A Modern Development' by Ballentine
'Nonequilibrium Statistical Mechanics' by Zwanzig
'Introduction to Modern Statistical Mechanics' by Chandler
'Principles of Nonlinear Optical Spectroscopy' by Mukamel
'Introduction to Quantum Mechanics: A Time-Dependent Perspective' by Tanor
'Mathematics of Classical and Quantum Physics' by Byron and Fuller
'Quantum Mechanics in Chemistry' by Schatz and Ratner
'Modern Quantum Mechanics' by Sakurai
'Modern Quantum Chemistry' by Szabo and Ostlund
'Understanding Molecular Simulation: From Algorithms to Applications' by Frenkel and Smit
'Statistical Mechanics: Theory and Molecular Simulation' by Tuckerman
'Classical Mechanics' by Goldstein
'Methematical Methods of Classical Mechanics' by Arnold
'Linear Operators for Quantum Mechanics' (Dover Publications, 2006) by Thomas F. Jordan
《高等量子力学》，倪光炯，陈苏卿 著
Course #：01002904 (Credit: 3)
Lecture Time: 15:10-18:00 Thursday (Fall Semester)
Lecturers: Prof. Jian Liu (Theory) / Prof. Junrong Zheng (Experiment)
'Quantum Mechanics: A Modern Development' by Ballentine
'Quantum Mechanics in Chemistry' by Schatz and Ratner
'Modern Quantum Mechanics' by Sakurai
'Introduction to Modern Statistical Mechanics' by Chandler
'Statistical Mechanics: Theory and Molecular Simulation' by Tuckerman
'Elements of quantum mechanics' by Fayer
'Classical Electrodynamics' by Jackson
'Principles of Nonlinear Optical Spectroscopy' by Mukamel
'Introduction to Quantum Mechanics: A Time-Dependent Perspective' by Tanor
Atkins' Physical Chemistry (7th edition)
《今日化学》理论化学部分
上课时间: 周三15：10-17：00 (秋季学期)
Time: Jul 25-29, 2026
Place: College of Chemistry and Molecular Engineering, Peking University
Website: [Event Page] [Registration Page] [CECAM Page]
Reliable simulations or predictions of dynamic, spectroscopic, and thermodynamic properties of real systems that contain light atoms, where nuclear quantum effects are important at low or room temperatures, present challenging frontiers in both quantum molecular dynamics and electronic structure theory.
State-of-the-art wavefunction-based approaches, and DFT with accurate functionals faithfully and efficiently help yield the single (ground) electronic state potential energy surface or force field. Recent advances in excited-state electronic structure theory can reliably describe multiple electronic states and nonadiabatic couplings/spin–orbit couplings between different states. When the time scales of electronic and nuclear dynamics are separable, modern semiclassical dynamics, phase space quantum dynamics, path integral-based methods, or time-dependent basis set methods provide practical tools for studying the vibrational spectrum, thermal reaction rate, vibrational energy relaxation rate, thermal conductivity, isobaric heat capacity, thermal expansion coefficient, isothermal compressibility, and so forth. On the other hand, in many light-driven, intersystem crossing, or electron/charge/spin transfer processes in chemical, biological, or materials systems, electronic motion and nuclear motion can be strongly coupled, and nonadiabatic transitions play an important role. Significant progress has been made in the field of nonadiabatic dynamics, including quantum phase-space methods, symmetrical quasi-classical dynamics with the mapping Hamiltonian model, surface hopping, exact factorization, real-time path-integral methods (e.g. SMatPI), and multiconfiguration-based dynamics approaches (multiple spawning, multiple cloning, multi-configuration Ehrenfest, MCTDH, etc.) for studying the electronic population and coherence, time-resolved spectroscopy, carrier mobility, nonadiabatic reaction rate, and other properties in large systems in gas phase and condensed phase.
Despite the aforementioned advances in the context of ab initio quantum molecular dynamics, it remains challenging to economically generate the accurate description of conical intersections, spin-orbit couplings, and long time nonequilibrium dynamics in complex systems with multiple scales in space and time. The efficient integration of electronic structure and quantum dynamics for larger systems involves scalable strategies, such as automatically adaptive time-step, quantum embedding, fragmentation-based techniques, enhanced sampling approaches for consistent initial condition sampling as well as for faithful observable evaluation, and robust artificial intelligence (AI) methods with rational design.
The summer school will bring together experts in electronic structure theory/force field, (quantum) molecular dynamics, spectroscopy, AI for science, and CPU/GPU-based software development in order to promote the synergy between these frontiers of theoretical chemistry. If successful, it may open a new avenue for collaborative research for the next generation of ab initio quantum molecular dynamics.
The summer school is also a CECAM Flagship School in the Beijing node. Please check the CECAM webpage of this summer school: https://www.cecam.org/workshop-details/frontiers-in-ab-initio-quantum-molecular-dynamics-1503
Special topics on "Relativistic Effects and Strong Correlation" and their influence on dynamics and thermodynamics will be covered.
A welcome reception will be held on the evening of July 24. The summer school will take place from July 25 to 29. We look forward to seeing you in Beijing!