Sending report ...Overview of Computational Nanoscience: a UC Berkeley Course
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| Contributor(s) | Jeffrey Grossman, Elif Ertekin University of California, Berkeley |
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| Abstract | This course will provide students with the fundamentals of computational problem-solving techniques that are used to understand and predict properties of nanoscale systems. Emphasis will be placed on how to use simulations effectively, intelligently, and cohesively to predict properties that occur at the nanoscale for real systems. The course is designed to present a broad overview of computational nanoscience and is therefore suitable for both experimental and theoretical researchers.
While some aspects of the simulation methods such as numerical algorithms will be presented, there will be little if any programming required. Rather, we will emphasize the intelligent application (as opposed to “black box” use) of codes and methods, and the connection between the computer results and the physical properties of the problem. Course Syllabus |
| Credits | Nanoscale Science and Engineering C242/Physics C203 University of California, Berkeley |
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| Cite this work | If you reference this work in a publication, please cite as follows: |
| Date posted | 01 Feb, 2008 |
| Type | Courses |
| Tags |
| Lecture Number/Topic | Breeze | Video | Lecture Notes (PDF) | Supplemental Material | Suggested Exercises |
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| Computational Nanoscience, Lecture 1: Introduction to Computational Nanoscience In this lecture, we present a historical overview of computational science. We describe modeling and simulation as forms of "theoretical experiments" and "experimental theory". We also discuss nanoscience: "what makes nano nano?", as well as public perceptions of nanoscience and the "grey goo" phenomenon. Finally, we describe the process of setting up a computer experiment: choosing your model, making relevant assumptions, and interpreting your resutls.UC Berkeley |
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| Computational Nanoscience, Lecture 2: Introduction to Molecular Dynamics In this lecture, we present and introduction to classical molecular dynamics. Approaches to integrating the equations of motion (Verlet and other) are discussed, along with practical considerations such as choice of timestep. A brief discussion of interatomic potentials (the pair potential and Lennard-Jones) is provided. Finally, this lecture enables students to understand simulation results by computing physical averages and understanding systematic and statistical errors, error bars, ... |
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| Computational Nanoscience, Homework Assignment 1: Averages and Statistical Uncertainty The purpose of this assignment is to explore statistical errors and data correlation. This assignment is to be completed following lectures 1 and 2 using the "Average" program in the Berkeley Computational Nanoscience Toolkit.University of California, Berkeley |
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| Computational Nanoscience, Lecture 3: Computing Physical Properties In this lecture, we'll cover how to choose initial conditions, and how to compute a number of important physical observables from the MD simulation. For example, temperature, pressure, diffusion coefficient, and pair distribution function will be highlighted. We will also discuss briefly the use of periodic boundary conditions and its impact on the potential. This lecture enables students to conduct Lennard-Jones molecular dynamics simulations using the course toolkit for homework ... |
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| Computational Nanoscience, Lecture 4: Geometry Optimization and Seeing What You're Doing In this lecture, we discuss various methods for finding the ground state structure of a given system by minimizing its energy. Derivative and non-derivative methods are discussed, as well as the importance of the starting guess and how to find or generate good initial structures. We also briefly touch on the importance of visualizing your structures and the broad range of file formats for keeping structural data.Nanoscale Science and Engineering C242/Physics C203 University of California, ... |
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| Computational Nanoscience, Homework Assignment 2: Molecular Dynamics Simulation of a Lennard-Jones Liquid The purpose of this assignment is to perform a full molecular dynamics simulation based on the Verlet algorithm to calculate various properties of a simple liquid, modeled as an ensemble of identical classical particles interacting via the Lennard-Jones potential. This assignment is to be completed following lectures 3 and 4 using the "Lennard-Jones Molecular Dynamics" program in the Berkeley Computational Nanoscience Toolkit. University of California, Berkeley |
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| Computational Nanoscience, Lecture 5: A Day of In-Class Simulation: MD of Carbon Nanostructures In this lecture we carry out simulations in-class, with guidance from the instructors. We use the LAMMPS tool (within the nanoHUB simulation toolkit for this course). Examples include calculating the energy per atom of different fullerenes and nantubes, computing the Young's modulus of a nanotube with and without a Stone-Wales defect, and examining the effects of temperature.Nanoscale Science and Engineering C242/Physics C203 University of California, Berkeley |
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| Computational Nanoscience, Lecture 6: Pair Distribution Function and More on Potentials In this lecture we remind ourselves what a pair distribution function is, how to compute it, and why it is so important in simulations. Then, we revisit potentials and go into more detail including examples of typical functional forms, relative energy scales, and what to keep in mind when developing or using a potential.Nanoscale Science and Engineering C242/Physics C203 University of California, Berkeley |
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| Computational Nanoscience, Homework Assignment 3: Molecular Dynamics Simulation of Carbon Nanotubes The purpose of this assignment is to perform molecular dynamics simulations to calculate various properties of carbon nanotubes using LAMMPS and Tersoff potentials. This assignment is to be completed following lectures 5 and 6 using the "LAMMPS" program in the Berkeley Computational Nanoscience Toolkit.University of California, Berkeley |
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| Computational Nanoscience, Lecture 7: Monte Carlo Simulation Part I The purpose of this lecture is to introduce Monte Carlo methods as a form of stochastic simulation. Some introductory examples of Monte Carlo methods are given, and a basic introduction to relevant concepts in statistical mechanics is presented. Students will be introduced to the Metropolis approach to Monte Carlo simulation. Using Metropolis as an example, these lectures also introduce the comcepts of balance and detailed balance, and what "efficient sampling" means. |
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| Computational Nanoscience, Lecture 8: Monte Carlo Simulation Part II In this lecture, we continue our discussion of Monte Carlo simulation. Examples from Hard Sphere Monte Carlo simulations based on the Metropolis algorithm and from Grand Canonical Monte Carlo simulations of fullerene growth on spherical surfaces are presented. A discussion of meaningful statistics, result interpretation, and error analysis is presented as well.University of California, Berkeley. |
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| Computational Nanoscience, Lecture 9: Hard-Sphere Monte Carlo In-Class Simulation In this lecture we carry out simulations in-class, with guidance from the instructors. We use the HSMC tool (within the nanoHUB simulation toolkit for this course). The hard sphere system is one of the simplest systems which exhibits an order-disorder phase transition, which we will explore with Monte Carlo simulations.Nanoscale Science and Engineering C242/Physics C203 University of California, Berkeley |
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| Computational Nanoscience, Lecture 10: Brief Review, Kinetic Monte Carlo, and Random Numbers We conclude our discussion of Monte Carlo methods with a brief review of the concepts covered in the three previous lectures. Then, the Kinetic Monte Carlo method is introduced, including discussions of Transition State Theory and basic KMC algorithms. A simulation of vacancy-mediated diffusion is provided as an example of KMC. Finally, a brief primer on random number generation is presented.University of California, Berkeley |
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| Computational Nanoscience, Lecture 11: Phase Transitions and the Ising Model In this lecture, we present an introduction to simulations of phase transitions in materials. The use of Monte Carlo methods to model phase transitions is described, and the Ising Model is given as an example for modeling the ferromagnetic-paramagnetic transition. Some of the subtleties of simulating phase transitions are also discussed, including finite size effects and critical slowing down. The concept of linear response is introduced as well.University of California, Berkeley |
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| Computational Nanoscience, Lecture 12: In-Class Simulation of Ising Model This is a two part lecture in which we discuss the spin-spin correlation function for the the Ising model, correlation lengths, and critical slowing down. An in-class simulation of the 2D Ising Model is performed using the tool "Berkeley Computational Nanoscience Class Tools". We look at domain wall formation at low temperature, and the phase transition for the anti-ferromagnetic and ferromagnetic system. University of California, Berkeley |
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| Computational Nanoscience, Homework Assignment 4: Hard-Sphere Monte Carlo and Ising Model In this assignment, you will explore the use of Monte Carlo techniques to look at (1) hard-sphere systems and (2) Ising model of the ferromagnetic-paramagnetic phase transition in two-dimensions. This assignment is to be completed following lecture 12 and using the "Hard Sphere Monte Carlo" and the "Ising Model" program in the Berkeley Computational Nanoscience Toolkit.University of California, Berkeley |
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| Computational Nanoscience, Lecture 13: Introduction to Computational Quantum Mechanics In this lecture we introduce the basic concepts that will be needed as we explore simulation approaches that describe the electronic structure of a system. |
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| Computational Nanoscience, Lecture 14: Hartree-Fock Calculations A description of the Hartree-Fock method and practical overview of its application. This lecture is to be used in conjunction with the course toolkit, with the Hartree-Fock simulation module. |
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| Computational Nanoscience, Lecture 15: In-Class Simulations: Hartree-Fock Using a range of examples, we study the effect of basis set on convergence, the Hartree-Fock accuracy compared to experiment, and explore a little bit of molecular chemistry. |
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| Computational Nanoscience, Lecture 16: More and Less than Hartree-Fock In the lecture we discuss both techniques for going "beyond" Hartree-Fock in order to include correlation energy as well as techniques for capturing electronic structure effects while not having to solve the full Hartree-Fock equations (ie, semi-empirical methods). We also very briefly touch upon the pseudopotential approximation. |
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| Computational Nanoscience, Lecture 17: Tight-Binding, and Moving Towards Density Functional Theory The purpose of this lecture is to illustrate the application of the Tight-Binding method to a simple system and then to introduce the concept of Density Functional Theory. The motivation to mapping from a wavefunction to a density-based description of atomic systems is provided, and the necessary ingredients to do so (two Hohenberg-Kohn Theorems and the Kohn-Sham formalism) is presented.University of California, Berkeley |
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| Computational Nanoscience, Lecture 18: Density Functional Theory and some Solid Modeling We continue our discussion of Density Functional Theory, and describe the most-often used approaches to describing the exchange-correlation in the system (LDA, GGA, and hybrid functionals). We discuss as well the strengths and weaknesses of the LDA and present some examples of its use. Finally, a short introduction to modeling band structures in solids is presented.University of California, Berkeley |
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| Computational Nanoscience, Lecture 18.5: A Little More, and Lots of Repetition, on Solids Here we go over again some of the basics that one needs to know and understand in order to carry out electronic structure, atomic-scale calculations of solids. |
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| Computational Nanoscience, Lecture 19: Band Structure and Some In-Class Simulation: DFT for Solids In this class we briefly review band structures and then spend most of our class on in-class simulations. Here we use the DFT for molecules and solids (Siesta) course toolkit. We cover a variety of solids, optimizing structures, testing k-point convergence, computing cohesive energies, and computing band structures and density of states. |
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