Day 4

Overview

Today, we return to Monte Carlo methods. In previous days, we learned about simple Monte Carlo integration. Then, we learned about the Lennard Jones equation, an empirical model that is often used to model the potential energy of non-bonded atoms. Today, we will combine Monte Carlo and the Lennard Jones equation in order to create a molecular Monte Carlo simulation. Our molecular Monte Carlo simulation will generate configurations of our system, which then can be analyzed to get molecular properties. Because MC simulation of a molecular system is more complicated than our original Monte Carlo problem (one dimensional integration of a function), we will have to change some of the ways our MC is performed.

Lessons

Lesson Title	Objectives	Questions
Total Energy Comparison	Apply a cut-off and periodic boundaries to the energy calculation and compare it to values reported by NIST.	Does my total energy agree with the values reported from NIST?
Monte Carlo for a Lennard Jones Fluid	Use the Metropolis algorithm to sample configurations of LJ particles	How do I write a Monte Carlo simulation?

Discussions and Assignments

• Class Warm Up
• Group Homework Assignment Day 4