李新征、王恩哥编著的《分子及凝聚态系统物性的计算模拟：从电子结构到分子动力学》为“中外物理学精品书系”高瞻系列中的一本。主要讲述总电子结构到分子动力学的分子及凝聚态系统物理的计算模拟。属于我国近年来物理学方面前沿的科研成果。可供相关领域研究生作为教材使用。

1 Introduction to Computer Simulations of Molecules and Condensed Matter

 1.1 Born-Oppenheimer Approximation and the Born-Oppenheimer Potential Energy Surface

 1.2 Categorization of the Tasks in Computer Simulations of Molecules and Condensed Matters

1.2.1 Electronic Structure Calculations

1.2.2 Geometry Optimization, Stationary Points on PES, Local Minimum, and Transition State

1.2.3 Meta-Stable State and Transition State Searching

1.2.4 Molecular Dynamics for the Thermal Effects

1.2.5 Extensions of MD: Enhanced Sampling and Free-Energy Calculations

1.2.6 Path Integral Simulations for the Quantum Nuclear Effects

 1.3 Layout of the Book

2 Quantum Chemistry Methods and Density-Functional Theory

 2.1 Wave-Function Based Method

2.1.1 The Hartree and Hartree-Fock Approximations

2.1.2 Beyond the Hartree-Foek Approximation

 2.2 Density-Functional Theory

2.2.1 Thomas-Fermi Theory

2.2.2 Density-Functional Theory

2.2.3 Exchange-Correlation Energy

2.2.4 Interpretation of the Kohn-Sham Energies

3 Pseudopotentials, Full Potential, and Basis Sets

 3.1 Pseudopotential Method

3.1.1 Generation of the Pseudcpotential

3.1.2 Implicit Approximations

 3.1.2.1 Frozen Core

 3.1.2.2 Core-Valence Linearization

 3.1.2.3 Pseudoization

 3.2 FP-（L）APW+lo Method

3.2.1 LAPW Basis Functions

3.2.2 APW+lo Basis Functions

3.2.3 Core States

3.2.4 Potential and Density

4 Many-Body Green Function Theory and the GW Approximation

 4.1 Green Function Method

4.1.1 The Green Fhncticn

4.1.2 The Dyson Equation

4.1.3 Self-Energy: Hedin Equations

4.1.4 The Quasiparticle Concept

 4.2 GW Approximation

 4.3 GoWo Al:proximation

 4.4 Numerical Implementation of an All-Elctron GoWo Code: FHI-gap

4.4.1 Summary of the GoWo Equations

4.4.2 The Mixed Basis

4.4.3 Matrix Form of the GoWo Equations

4.4.4 Brillouin-Zone Integration of the Polarization

4.4.5 The Frequency Integration

4.4.6 Flowchart

5 Molecular Dynamics

 5.1 Introduction to Molecular Dynamics

5.1.1 The Verlet Algorithm

5.1.2 The Velocity Verlet Algorithm

5.1.3 The Leap Frog Algorithm

 5.2 Other Ensembles

5.2.1 Andersen Thermostat

5.2.2 Nose-Hoover Thermostat

5.2.3 Nose-Hoover Chain

5.2.4 Langevin Thermostat

5.2.5 Andersen and Parrinello-Rahman Barostats

 5.3 Examples for Practical Simulations in Real Poly-Atomic Systems

6 Extension of Molecular Dynamics, Enhanced Sampling and the Free-Energy Calculations

 6.1 Umbrella Sampling and Adaptive Umbrella Sampling Methods

 6.2 Metadynamics

 6.3 Integrated Tempering Sampling

 6.4 Thermodynamic Integration

7 Quantum Nuclear Effects

 7.1 Path-Integral Molecular Simulations

7.1.1 Path-Integral Representation of the Propagator

7.1.2 Path-Integral Representation of the Density Matrix

7.1.3 Statistical Mechanics: Path-Integral Molecular Simulations

7.1.4 Staging and Normal-Mode Transformations

7.1.5 Evaluation of the Zero-Point Energy

 7.2 Extensions Beyond the Statistical Studies

7.2.1 Different Semiclassical Dynamical Methods

7.2.2 Centroid Molecular Dynamics and Ring-Polymer Molecular Dynamics

 7.3 Free-Energy with Anharmonic QNEs

 7.4 Examples

7.4.1 Impact of QNEs on Structures of the Water-Hydroxyl Overlayers on Transition Metal Surfaces

7.4.2 Impact of Quantum Nuclear Effects on the Strength of Hydrogen Bonds

7.4.3 Quantum Simulation of the Low-Temperature Metallic Liquid Hydrogen

 7.5 Summary

Appendix A Useful Mathematical Relations

 A.1 Spherical Harmonics

 A.2 Plane Waves

 A.3 Fourier Transform

 A.4 Spherical Coordinates

 A.5 The Step（Heaviside） Function

Appendix B Expansion of a Non-Local Function

Appendix C The BrillouinoZone Integration

 C.1 The Linear Tetrahedron Method

C.1.1 The Isoparametric Transfromation

C.1.2 Integrals in One Tetrahedron

C.1.3 The Integration Weights

 C.2 Tetrahedron Method for q-Dependent Brillouin-Zone Integration

C.2.1 Isoparametric Transformation

C.2.2 The Integration Region

C.2.3 Polarizability

 C.2.3.1 Polarisability on the Real Frequency Axis

 C.2.3.2 Polarisability on the Imaginary Frequency Axis

Appendix D The Frequency Integration

References

Acknowledgements