Computational Materials Science

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August 1999



Powerful computers now enable scientists to model the physical and chemical properties and behavior of complex materials using first principles. This book introduces dramatically new computational techniques in materials research, specifically for understanding molecular dynamics.


1. Introduction.- 1.1 Computer Simulation as a Tool for Materials Science.- 1.2 Modeling of Natural Phenomena.- 2. Ab Initio Methods.- 2.1 Introduction.- 2.2 Electronic States of Many-Particle Systems.- 2.2.1 Quantum Mechanics of Identical Particles.- 2.2.2 The Hartree-Fock Approximation.- 2.2.3 Density Functional Theory.- 2.2.4 Periodic Systems.- 2.2.5 Group Theory.- 2.2.6 LCAO, OPW and Mixed-Basis Approaches.- 2.2.7 Pseudopotential Approach.- 2.2.8 APW Method.- 2.2.9 KKR, LMTO and ASW Methods.- 2.2.10 Some General Remarks.- 2.2.11 Ab Initio O(N) and Related Methods.- 2.3 Perturbation and Linear Response.- 2.3.1 Effective-Mass Tensor.- 2.3.2 Dielectric Response.- 2.3.3 Magnetic Susceptibility.- 2.3.4 Chemical Shift.- 2.3.5 Phonon Spectrum.- 2.3.6 Electrical Conductivity.- 2.4 Ab Initio Molecular Dynamics.- 2.4.1 Car-Parrinello Method.- 2.4.2 Steepest Descent and Conjugate Gradient Methods.- 2.4.3 Formulation with Plane Wave Basis.- 2.4.4 Formulation with Other Bases.- 2.5 Applications.- 2.5.1 Application to Fullerene Systems.- 2.5.2 Application to Point Defects in Crystals.- 2.5.3 Application to Other Systems.- 2.5.4 Coherent Potential Approximation.- 2.6 Beyond the Born-Oppenheimer Approximation.- 2.7 Electron Correlations Beyond the LDA.- 2.7.1 Generalized Gradient Approximation.- 2.7.2 Self-Interaction Correction.- 2.7.3 GW Approximation.- 2.7.4 Exchange and Coulomb Holes.- 2.7.5 Optimized Effective Potential Method.- 2.7.6 Time-Dependent Density Functional Theory.- 2.7.7 Inclusion of Ladder Diagrams.- 2.7.8 Further Remarks: Cusp Condition, etc.- References.- 3. Tight-Binding Methods.- 3.1 Introduction.- 3.2 Tight-Binding Formalism.- 3.2.1 Tight-Binding Parametrization.- 3.2.2 Calculation of the Matrix Elements.- 3.2.3 Total Energy.- 3.2.4 Forces.- 3.3 Methods to Solve the Schrödinger Equation for Large Systems.- 3.3.1 The Density Matrix O(N) Method.- 3.3.2 The Recursion Method.- 3.4 Self-Consistent Tight-Binding Formalism.- 3.4.1 Parametrization of the Coulomb Integral U.- 3.5 Applications to Fullerenes, Silicon and Transition-Metal Clusters.- 3.5.1 Fullerene Collisions.- 3.5.2 C240 Doughnuts and Their Vibrational Properties.- 3.5.3 IR Spectra of C60 and C60 Dimers.- 3.5.4 Simulated Annealing of Small Silicon Clusters.- 3.5.5 Titanium and Copper Clusters.- 3.6 Conclusions.- References.- 4. Empirical Methods and Coarse-Graining.- 4.1 Introduction.- 4.2 Reduction to Classical Potentials.- 4.2.1 Polar Systems.- 4.2.2 Van der Waals Potential.- 4.2.3 Potential for Covalent Bonds.- 4.2.4 Embedded-Atom Potential.- 4.3 The Connolly-Williams Approximation.- 4.3.1 Lattice Gas Model.- 4.3.2 The Connolly-Williams Approximation.- 4.4 Potential Renormalization.- 4.4.1 Basic Idea: Two-Step Renormalization Scheme.- 4.4.2 The First Step.- 4.4.3 The Second Step.- 4.4.4 Application to Si.- References.- 5. Monte Carlo Methods.- 5.1 Introduction.- 5.2 Basis of the Monte Carlo Method.- 5.2.1 Stochastic Processes.- 5.2.2 Markov Process.- 5.2.3 Ergodicity.- 5.3 Algorithms for Monte Carlo Simulation.- 5.3.1 Random Numbers.- 5.3.2 Simple Sampling Technique.- 5.3.3 Importance Sampling Technique.- 5.3.4 General Comments on Dynamic Models.- 5.4 Applications.- 5.4.1 Systems of Classical Particles.- 5.4.2 Modified Monte Carlo Techniques.- 5.4.3 Percolation.- 5.4.4 Polymer Systems.- 5.4.5 Classical Spin Systems.- 5.4.6 Nucleation.- 5.4.7 Crystal Growth.- 5.4.8 Fractal Systems.- References.- 6. Quantum Monte Carlo (QMC) Methods.- 6.1 Introduction.- 6.2 Variational Monte Carlo (VMC) Method.- 6.3 Diffusion Monte Carlo (DMC) Method.- 6.4 Path-Integral Monte Carlo (PIMC) Method.- 6.5 Quantum Spin Models.- 6.6 Other Quantum Monte Carlo Methods.- References.- A. Molecular Dynamics and Mechanical Properties.- A.l Time Evolution of Atomic Positions.- A.2 Acceleration of Force Calculations.- A.2.1 Particle-Mesh Method.- A.2.2 The Greengard-Rockhlin Method.- References.- B. Vibrational Properties.- References.- C. Calculation of the Ewald Sum.- References.- D. Optimization Methods Used in Materials Science.- D.l Conjugate-Gradient Minimization.- D.2 Broyden's Method.- D.3 SA and GA as Global Optimization Methods.- D.3.1 Simulated Annealing (SA).- D.3.2 Genetic Algorithm (GA).- References.


EAN: 9783540639619
ISBN: 3540639616
Untertitel: From Ab Initio to Monte Carlo Methods. 1999. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: August 1999
Seitenanzahl: 344 Seiten
Format: gebunden
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