Computational Nanoscience, Lecture 7: Monte Carlo Simulation Part I

15 Feb 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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 …

Computational Nanoscience, Lecture 12: In-Class Simulation of Ising Model

28 Feb 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

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 …

Computational Nanoscience, Lecture 1: Introduction to Computational Nanoscience

13 Feb 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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" …

Computational Nanoscience, Lecture 19: Band Structure and Some In-Class Simulation: DFT for Solids

30 Apr 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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 …

Computational Nanoscience, Lecture 11: Phase Transitions and the Ising Model

27 Feb 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

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 …

Computational Nanoscience, Lecture 5: A Day of In-Class Simulation: MD of Carbon Nanostructures

13 Feb 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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 …

Computational Nanoscience, Lecture 4: Geometry Optimization and Seeing What You're Doing

13 Feb 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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 …

Computational Nanoscience, Lecture 2: Introduction to Molecular Dynamics

30 Jan 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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 …

Computational Nanoscience, Lecture 9: Hard-Sphere Monte Carlo In-Class Simulation

19 Feb 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

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 …

Computational Nanoscience, Lecture 21: Quantum Monte Carlo, part II

15 May 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

This is our second lecture in a series on Quantum Monte Carlo methods. We describe the Diffusion Monte Carlo approach here, in which the approximation to the solution is not restricted by choice of a functional form for the wavefunction. The DMC approach is explained, and the fixed node …

Computational Nanoscience, Lecture 10: Brief Review, Kinetic Monte Carlo, and Random Numbers

25 Feb 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

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 …

Computational Nanoscience, Lecture 17: Tight-Binding, and Moving Towards Density Functional Theory

21 Mar 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

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 …

Computational Nanoscience, Lecture 18: Density Functional Theory and some Solid Modeling

21 Mar 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

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 …

Computational Nanoscience, Lecture 8: Monte Carlo Simulation Part II

14 Feb 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

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 …

Computational Nanoscience, Homework Assignment 3: Molecular Dynamics Simulation of Carbon Nanotubes

14 Feb 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

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 …

Computational Nanoscience, Lecture 3: Computing Physical Properties

11 Feb 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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 …

Computational Nanoscience, Lecture 6: Pair Distribution Function and More on Potentials

13 Feb 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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 …

Computational Nanoscience, Lecture 20: Quantum Monte Carlo, part I

15 May 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

This lecture provides and introduction to Quantum Monte Carlo methods. We review the concept of electron correlation and introduce Variational Monte Carlo methods as an approach to going beyond the mean field approximation. We describe briefly the Slater-Jastrow expansion of the wavefunction, and …

Computational Nanoscience, Pop-Quiz Solutions

15 May 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

The solutions to the pop-quiz are given in this handout.University of California, Berkeley

Computational Nanoscience, Lecture 13: Introduction to Computational Quantum Mechanics

30 Apr 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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.

Computational Nanoscience, Homework Assignment 1: Averages and Statistical Uncertainty

30 Jan 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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

Computational Nanoscience, Lecture 14: Hartree-Fock Calculations

30 Apr 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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.

Computational Nanoscience, Lecture 16: More and Less than Hartree-Fock

30 Apr 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

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 …

Computational Nanoscience, Homework Assignment 2: Molecular Dynamics Simulation of a Lennard-Jones Liquid

14 Feb 2008 | Teaching Materials | Contributor(s): Elif Ertekin, Jeffrey C Grossman

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 …

Computational Nanoscience, Lecture 29: Verification, Validation, and Some Examples

16 May 2008 | Teaching Materials | Contributor(s): Jeffrey C Grossman, Elif Ertekin

We conclude our course with a lecture of verification, and validation. We describe what each of these terms means, and provide a few recent examples of nanoscale simulation in terms of these concepts.University of California, Berkeley