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.(adsbygoogle = window.adsbygoogle || []).push({});

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:

[tex]E = 4\epsilon\left[\left(\frac{\sigma}{R}\right)^{12} - \left(\frac{\sigma}{R}\right)^6\right][/tex]

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

With that in mind, I was told this:

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. 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.

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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# Atomic simulation and lots of questions

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