Introduction To Molecular dynamics

Molecular dynamics is a way to calculate the behavior of molecules as they interact. The general idea to treat molecules like billiard balls which obey Newtons equation of motion. One then numerically integrates the equations of motion to calculate the molecular behavior.

Recall back to your first semester of freshman physics when you discussed Newton's equations of motion. (i.e.F=m a). Newton's equations of motion describe how particles move in the presence of an external field, and when particles collide. For example, you can use Newton's equations of motion of describe how a cannonball moves under the influence of gravity. You can also use Newton's equation of motion to describe what happens when two billiard balls collide.

Well, in the same way one can use Newton's equations of motion to describe when molecules collide. Consider a simple reaction, where A collides with BC to produce products.

A+BC ==>AB + C

Atoms A, B, and C obey

dxA
dt
= vA  (1)
dxB
dt
= vB  (2)
dxC
dt
= vC  (3)
mAdvA
dt
= FA  (4)
mBdvB
dt
= FB  (5)
mCdvC
dt
= FC  (6)

where xA, xB and xC are the position vectors for atoms A, B and C and vA, vA, and vc are their velocity vectors, FA, FB, and FC are the forces on the atoms, and mA, mB and mC are the masses of atoms A, B and C.

Notice that you can calculate how atoms A B and C move as a function of time by numerically integrating equations (1) through (6)

The hard part is determining the forces. Generally, people use quantum mechanics to calculate the E(xA, xB, xC ), the total energy of the system as a function of the positions of atoms A, B, C. The force on A is then given by:

FA =  -
d E(xA, xB, xC )
d xA
 (7)

Note the derivative in equation 7 is a gradient because xA is a vector. If one knows E(xA, xB, xC ), one can calculate the position of the atoms as a function of time. There is a good description of the calculation of E(xA, xB, xC ) in chapter 11 of Masel, Kinetics and Catalysis, Wiley to appear.

In order to use MD to calculate rates you:

You can then average to calculate a reaction rate.


Click here for instructions about how to use ReactMD to simulate A + BC ==> AB + C


There is more information on the ReactMD website.
Click here to visit the ReactMD website

Click here for updates to the documentation

For further information about applications of this program please look in Chapter 9 of R. I. Masel, Principles of Adsorption and Reaction on Solid Surfaces, Wiley 1996 or Chapter 8 of R. I. Masel, Kinetics and Catalysis, Wiley 2000