# Trajectories on the Müller-Brown Potential Energy Surface

Trajectories on the Müller-Brown Potential Energy Surface

The Müller–Brown potential energy surface is a canonical example of a potential surface used in theoretical chemistry. The analytic form for this surface is given by

V(x,y)=expx-+x-y-+y-

4

∑

k=1

A

k

2

a

k

0

x

k

b

k

0

x

k

0

y

k

2

c

k

0

y

k

with

A=(-200,-100,-170,15),a=(-1,-1,-6.5,0.7),b=(0,0,11,0.6),c=(-10,-10,-6.5,0.7),=(1,0,-0.5,-1),=(0,0.5,1.5,1).

0

x

0

y

There are three minima and two saddle points. This model is often used for testing algorithms that find transition states and for exploring minimum-energy pathways. In this Demonstration, you can explore the trajectories generated by this potential and superimpose them on the surface itself. You can set the initial position of the trajectory using one of the controls. By advancing the "time" slider, you can view the dynamical evolution of the system as either a 2D contour plot or a 3D surface. You can observe interesting dynamical events, including surmounting the energy barriers, quasi-periodic orbits, and trajectories that recross the transition-state dividing surface.