## Overview of Computational Nanoscience: a UC Berkeley Course

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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.

Specific examples of topics the course will cover are:

- The central ideas behind a wide range of nanomaterials simulations methods
- How to break down a nanoscale problem into its “simulatable” constituents, and then piece it back together
- How to simulate the same thing in two different ways
- How to know what you’re doing and why thinking is still important
- The importance of connecting simulation directly with experiment
- What to do with all of that data, and how to judge its accuracy and validity
- Why the “multi-scale” modeling picture is critically important and also nonsense

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

Online simulation tools: Berkeley Computational Nanoscience Class Tools

#### Credits

University of California, Berkeley

#### References

*Understanding Molecular Simulation,*Frenkel and Smit, 2002.

Good For: Molecular Dynamics, Monte Carlo*Monte Carlo Simulations in Statistical Physics,*Landau and Binder, 2000.

Good For: Statistical methods, Monte Carlo*Electronic Structure,*Martin 2004.

Good For: Quantum methods, especially DFT*Introduction to Computational Chemistry,*Jensen, 2007.

Good For: Quantum Chemistry, Molecular Orbitals, Basis Sets, Hartree and Hartree-based methods, etc.- Computational Nanoscience Do It Yourself Lecture Notes.

Good For: lots of things, a great set of introductory lecture notes on many topics - Generally a good resource: http://freescience.info.

Under the category "Physics", then "Condensed Matter"

Lots of references on Monte Carlo, Quantum Monte Carlo, Correlated systems, DFT, ... Many by very seminal authors!

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Lecture Number/Topic | Online Lecture | Video | Lecture Notes | Supplemental Material | Suggested Exercises |
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Computational Nanoscience, Lecture 1: Introduction to Computational Nanoscience | Notes | ||||

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 … |
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Computational Nanoscience, Lecture 2: Introduction to Molecular Dynamics | Notes | ||||

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 … |
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Computational Nanoscience, Homework Assignment 1: Averages and Statistical Uncertainty | Notes | ||||

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 … |
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Computational Nanoscience, Lecture 3: Computing Physical Properties | Notes | ||||

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

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

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

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

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

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 … |
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Computational Nanoscience, Lecture 7: Monte Carlo Simulation Part I | Notes | ||||

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 … |
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Computational Nanoscience, Lecture 8: Monte Carlo Simulation Part II | Notes | ||||

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

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

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

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

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 … |
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Computational Nanoscience, Homework Assignment 4: Hard-Sphere Monte Carlo and Ising Model | Notes | ||||

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. … |
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Computational Nanoscience, Lecture 13: Introduction to Computational Quantum Mechanics | Notes | ||||

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 | Notes | ||||

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 | Notes | ||||

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 | Notes | ||||

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

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

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 … |
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Computational Nanoscience, Lecture 18.5: A Little More, and Lots of Repetition, on Solids | Notes | ||||

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 | Notes | ||||

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 … |
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Computational Nanoscience, Lecture 20: Quantum Monte Carlo, part I | Notes | ||||

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 … |
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Computational Nanoscience, Lecture 21: Quantum Monte Carlo, part II | Notes | ||||

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 … |
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Computational Nanoscience, Pop-Quiz | Notes | ||||

This quiz summarizes the most important concepts which have covered in class so far related to Molecular Dynamics, Classical Monte Carlo Methods, and Quantum Mechanical Methods.University of … |
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Computational Nanoscience, Pop-Quiz Solutions | Notes | ||||

The solutions to the pop-quiz are given in this handout.University of California, Berkeley |
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Computational Nanoscience, Lecture 23: Modeling Morphological Evolution | Notes | ||||

In this lecture, we present an introduction to modeling the morphological evolution of materials systems. We introduce concepts of coarsening, particle-size distributions, the … |
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Computational Nanoscience, Lecture 26: Life Beyond DFT -- Computational Methods for Electron Correlations, Excitations, and Tunneling Transport | Notes | ||||

In this lecture, we provide a brief introduction to "beyond DFT" methods for studying excited state properties, optical properties, and transport properties. We discuss how the GW approximation to … |
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Computational Nanoscience, Lecture 27: Simulating Water and Examples in Computational Biology | Notes | ||||

In this lecture, we describe the challenges in simulating water and introduce both explicit and implicit approaches. We also briefly describe protein structure, the Levinthal paradox, and … |
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Computational Nanoscience, Lecture 28: Wish-List, Reactions, and X-Rays. | Notes | ||||

After a brief interlude for class feedback on the course content and suggestions for next semester, we turn to modeling chemical reactions. We describe chain-of-state methods such as the Nudged … |
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Computational Nanoscience, Lecture 29: Verification, Validation, and Some Examples | Notes | ||||

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 … |