By way of history I am just another madcap attempting to fold protein… in real time.  The problem seems simple enough to solve were it not for the missing shelf in the library.  Go to any library and you will find astronomy, cosmology, particle physics and empirical chemistry books.  What seems missing is the shelf of books, or the book, or even one simple equation describing simple molecular dynamics, or terms that work well in a computer program.

All I want is a simple equation that says what the force of attraction or repulsion is between two atoms at a known distance. 

My goal is not to solve all known cosmological and particle problems in one equation.  I just want to move little atoms around in a manner that mimics real life using my laptop.  You would think this easy but the common force field equations that commonly describe such atomic interaction are generally inefficient, unwieldy and crude at best.  Even if you swap some of the steps around in a Monte Carlo simulator, reducing the number of calculations required by many, many orders of magnitude, you still have a problem with the force field calculation consuming vast amounts of computing power.

So, enters the joke;

For the Apollo project the Americans spent millions developing a pen that would work in zero gravity and wildly fluctuating temperatures.  The Russians used a pencil. 

So, think like a Russian. 

The conventional interatomic force calculation is the Lennard Jones curve.  This curve is depicted below.  This is the graph that says two atoms are attracted to each other a little bit at a great distance, then as they get closer the attraction gets stronger until at one point they start pushing against each other.  In summary they’re attracted to each other enough to touch but don’t want to overlap.  Things fall down but don’t keep going.