Help for Atomic Simulation

From: Zach (zachary_at_tong-web-dot-com.no-spam.invalid)
Date: 09/22/04 

Date: 21 Sep 2004 19:35:48 -0500

First, hi. This is my first post, and after careful perusing of the
forum I *think* this post is in the correct place. Feel free to move
it around if not, apologies.

The meat of my questions. I'm a High School student that would like to
simulate atoms on the computer. I've been getting help from alot of
various sources, and therefore have a real hodgepodge of information.
I'm not quite sure how it all fits together. And to top it off, I
think there may be some math needed that I don't know yet (calculus,
which I have next trimester). But I'm willing to learn :)

I have been corresponding with a few chemistry professors. They have
told me to start off small using the Lennard Jones potential. I
understand the theory behind the potential quite well now (at medium
distance, the two atoms in question are mildly attractive, and at
short distances they are extremely repulsive. As the distance
increases, the attraction rapidly drops off to about nothing). The LJ
potential is as follows:

http://www.fisica.uniud.it/~ercolessi/md/md/img20.gif

Where E is the energy in joules/mol, epsilon is the depth of the well
in joules/mol, sigma is the distance in angstroms for the interaction
to occur. R is distance in angstroms between the two atoms. Both and
are constants

With that in mind, I was told this:

>
> The basic way to use the L-J potential, any potential really, is to
take the derivative of it with respect to the distance between the
atoms to get the force between the atoms. Since you know the mass of
the atoms, you can then determine the acceleration acting on them.
>From the acceleration and current velocity you can get their new
velocity and ultimately the new position of the atoms some amount of
time later.
>

And from here my questions start. Do I need to differentiate that
equation? I don't know calculus, so I'm not sure if that is needed.
Or does that merely mean plug in the distance to get the energy.

>From there, I know the mass, as the quote says. Finding the
acceleration is trivial (F=ma). The next part of my questions has to
deal with the "ultimately finding the new positions" part. I have
been told by a few people I will need to "integrate with respect to
time". I've also been told by someone else that I don't need
classical calculus, but instead need to use Euler's Integration, as
that is the only way to do such a thing on the computer (I believe I
understand this. Calculus is continuous, while the Euler integration
assumes a constant value in between timesteps. If I were to use
classical calc, I would have to reduce my timestep infintely to
achive the results). But again, I have no idea, and could be talking
out of my rear.

Thanks, any help would be greatly appreciated. I am swimming in a sea
of knowledge, but no real way to piece it together.

BTW, this LaTex math function stuff is extremely cool :)

EDIT: I forgot to mention, I've also heard of using the Verlet
Algorithm for integratin instead of the others. Again, no idea if
this is what I should aim for or not. Thanks again.

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