A Mathematica Algorithm for Calculating the Energy Transition Paths of Molecules
Document Type
Oral Presentation
Campus where you would like to present
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