Title

A Mathematica Algorithm for Calculating the Energy Transition Paths of Molecules

Presenter Information

Garret Bolton

Document Type

Oral Presentation

Location

SURC Ballroom C/D

Start Date

16-5-2013

End Date

16-5-2013

Abstract

Many equations in the applied sciences can be realized as critical points of a function. For example, one goal in computational chemistry is to determine the amount of energy necessary to transition a molecule from one stable state to another. Determining the amount of energy necessary to transition between stable states is analogous to finding a mountain pass connecting two valleys. Finding mountain passes is also of interest for other fields. In economics, a mountain pass may arise as a equilibrium in a game with multiple players. In physics, a mountain pass may arise as an unstable motion of a mechanical system. In this research, we look at finding these mountains passes using a computer algorithm implemented in Mathematica. The algorithm begins by designating a discrete path that connects the two states, and then iteratively deforms the path. We are further refining this algorithm, and discretizing the method, which is a challenge because the path lies on a continuous landscape. The purpose of this research project is to find mountain passes using Mathematica which could have numerous applications in other fields.

Poster Number

56

Faculty Mentor(s)

James Bisgard, Filip Jagodzinski

Additional Mentoring Department

Mathematics

Additional Mentoring Department

Computer Science

This document is currently not available here.

Share

COinS
 
May 16th, 8:20 AM May 16th, 10:50 AM

A Mathematica Algorithm for Calculating the Energy Transition Paths of Molecules

SURC Ballroom C/D

Many equations in the applied sciences can be realized as critical points of a function. For example, one goal in computational chemistry is to determine the amount of energy necessary to transition a molecule from one stable state to another. Determining the amount of energy necessary to transition between stable states is analogous to finding a mountain pass connecting two valleys. Finding mountain passes is also of interest for other fields. In economics, a mountain pass may arise as a equilibrium in a game with multiple players. In physics, a mountain pass may arise as an unstable motion of a mechanical system. In this research, we look at finding these mountains passes using a computer algorithm implemented in Mathematica. The algorithm begins by designating a discrete path that connects the two states, and then iteratively deforms the path. We are further refining this algorithm, and discretizing the method, which is a challenge because the path lies on a continuous landscape. The purpose of this research project is to find mountain passes using Mathematica which could have numerous applications in other fields.