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/高瞻系列/中外物理学精品书系 fb2 pdf azw3 网盘 rtf 免费 下载 txt

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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

王恩哥，北京大学物理学院教授、 院士、第三世界科学院院士、美国物理学会Feilow、英国物理学会Fellow。主要研究领域为轻元素纳米新材料探索及其物理性质、原子尺度上的表面生长动力学、受限系统中水的微观行为与特性等。发表研究论文300余篇。曾获 自然科学二等奖、第三世界科学院物理奖、德国洪堡研究奖、世界华人物理学会“亚洲成就奖”、陈嘉庚数理科学奖、何梁何利科学与进步奖、周培源物理奖、北京市科学技术一等奖、 杰出科技成就奖、香港“求是”青年学者奖等奖励。

李新征，北京大学物理学院副教授，主要从事凝聚态物理中一些计算方法的发展与应用研究。2000年毕业于武汉大学物理系。毕业后分别在 半导体所夏建白院士的研究组（硕士阶段）、德国马普学会Fritz-Haber研究所Matthias Scheffter教授的研究组（博士阶段）、以及伦敦大学学院Angelos Michaelides教授的研究组（博士后阶段）接触到电子结构与分子动力学层面的多种计算方法。2012年进入北京大学物理学院，2014年获自然科学基金委 青年科学基金资助。现任J.Phys.：Condens Matter，Chemical Physics杂志编委。

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