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分子及凝聚态系统物性的计算模拟：从电子机构到分子动力学=Computer sim-ulations of molecules and condensed matters:from electronicPDF|Epub|txt|kindle电子书版本下载
- 饶静著 著
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- 出版时间：2014
- 标注页数：0页
- 文件大小：37MB
- 文件页数：287页
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分子及凝聚态系统物性的计算模拟：从电子机构到分子动力学=Computer sim-ulations of molecules and condensed matters:from electronicPDF格式电子书版下载
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图书目录
1 Introduction to Computer Simulations of Molecules and Condensed Matter1
1.1 Born-Oppenheimer Approximation and the Born-Oppenheimer Potential Energy Surface2
1.2 Categorization of the Tasks in Computer Simulations of Molecules and Condensed Matters6
1.2.1 Electronic Structure Calculations6
1.2.2 Geometry Optimization,Stationary Points on PES,Local Minimum,and Transition State7
1.2.3 Meta-Stable State and Transition State Searching10
1.2.4 Molecular Dynamics for the Thermal Effects12
1.2.5 Extensions of MD:Enhanced Sampling and Free-Energy Calculations13
1.2.6 Path Integral Simulations for the Quantum Nuclear Effects15
1.3 Layout of the Book16
2 Quantum Chemistry Methods and Density-Functional Theory18
2.1 Wave-Function Based Method18
2.1.1 The Hartree and Hartree-Fock Approximations19
2.1.2 Beyond the Hartree-Fock Approximation22
2.2 Density-Functional Theory23
2.2.1 Thomas-Fermi Theory23
2.2.2 Density-Functional Theory25
2.2.3 Exchange-Correlation Energy27
2.2.4 Interpretation of the Kohn-Sham Energies29
3 Pseudopotentials,Full Potential,and Basis Sets31
3.1 Pseudopotential Method32
3.1.1 Generation of the Pseudopotential33
3.1.2 Implicit Approximations38
3.1.2.1 Frozen Core38
3.1.2.2 Core-Valence Linearization39
3.1.2.3 Pseudoization39
3.2 FP-(L)APW+lo Method40
3.2.1 LAPW Basis Functions43
3.2.2 APW+lo Basis Functions44
3.2.3 Core States45
3.2.4 Potential and Density46
4 Many-Body Green Function Theory and the GW Approximation47
4.1 Green Function Method49
4.1.1 The Green Function49
4.1.2 The Dyson Equation52
4.1.3 Self-Energy:Hedin Equations54
4.1.4 The Quasiparticle Concept57
4.2 GW Approximation58
4.3 G0W0 Approximation61
4.4 Numerical Implementation of an All-Elctron G0W0 Code:FHI-gap67
4.4.1 Summary of the G0W0 Equations68
4.4.2 The Mixed Basis70
4.4.3 Matrix Form of the G0W0 Equations72
4.4.4 Brillouin-Zone Integration of the Polarization74
4.4.5 The Frequency Integration78
4.4.6 Flowchart80
5 Molecular Dynamics82
5.1 Introduction to Molecular Dynamics84
5.1.1 The Verlet Algorithm85
5.1.2 The Velocity Verlet Algorithm87
5.1.3 The Leap Frog Algorithm89
5.2 Other Ensembles90
5.2.1 Andersen Thermostat92
5.2.2 Nosé-Hoover Thermostat93
5.2.3 Nosé-Hoover Chain102
5.2.4 Langevin Thermostat104
5.2.5 Andersen and Parrinello-Rahman Barostats106
5.3 Examples for Practical Simulations in Real Poly-Atomic Systems109
6 Extension of Molecular Dynamics,Enhanced Sampling and the Free-Energy Calculations116
6.1 Umbrella Sampling and Adaptive Umbrella Sampling Methods118
6.2 Metadynamics128
6.3 Integrated Tempering Sampling131
6.4 Thermodynamic Integration134
7 Quantum Nuclear Effects141
7.1 Path-Integral Molecular Simulations145
7.1.1 Path-Integral Representation of the Propagator145
7.1.2 Path-Integral Representation of the Density Matrix149
7.1.3 Statistical Mechanics:Path-Integral Molecular Simulations153
7.1.4 Staging and Normal-Mode Transformations161
7.1.5 Evaluation of the Zero-Point Energy171
7.2 Extensions Beyond the Statistical Studies180
7.2.1 Different Semiclassical Dynamical Methods181
7.2.2 Centroid Molecular Dynamics and Ring-Polymer Molecular Dynamics184
7.3 Free-Energy with Anharmonic QNEs191
7.4 Examples194
7.4.1 Impact of QNEs on Structures of the Water-Hydroxyl Overlayers on Transition Metal Surfaces194
7.4.2 Impact of Quantum Nuclear Effects on the Strength of Hydrogen Bonds203
7.4.3 Quantum Simulation of the Low-Temperature Metallic Liquid Hydrogen212
7.5 Summary226
Appendix A Useful Mathematical Relations228
A.1 Spherical Harmonics228
A.2 Plane Waves229
A.3 Fourier Transform229
A.4 Spherical Coordinates229
A.5 The Step(Heaviside) Function230
Appendix B Expansion ofa Non-Local Function231
Appendix C The Brillouin-Zone Integration234
C.1 The Linear Tetrahedron Method234
C.1.1 The Isoparametric Transfromation236
C.1.2 Integrals in One Tetrahedron238
C.1.3 The Integration Weights239
C.2 Tetrahedron Method for q-Dependent Brillouin-Zone Integration240
C.2.1 Isoparametric Transformation241
C.2.2 The Integration Region242
C.2.3 Polarizability244
C.2.3.1 Polarisability on the Real Frequency Axis244
C.2.3.2 Polarisability on the Imaginary Frequency Axis246
Appendix D The Frequency Integration248
References251
Acknowledgements271