#### Title

A Mathematica Algorithm for Calculating the Energy Transition Paths of Molecules

#### 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.

#### Recommended Citation

Bolton, Garret, "A Mathematica Algorithm for Calculating the Energy Transition Paths of Molecules" (2013). *Symposium Of University Research and Creative Expression (SOURCE)*. 7.

https://digitalcommons.cwu.edu/source/2013/posters/7

#### Poster Number

56

#### Additional Mentoring Department

Mathematics

#### Additional Mentoring Department

Computer Science

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.

## Faculty Mentor(s)

James Bisgard, Filip Jagodzinski