Ask A Scientist Chemistry Archive

Question:
Hi, I am interested in doing a project for the Superquest computational
competition dealing with the precursor film advancing ahead of a droplet
dropped onto a solid surface.  From the little information that I currently
have (I just started my research), I understand that Leonard-Jones potential
is used for making computational models in Molecular Dynamics.  Could you
provide me with some information about Leonard-Jones potential, as well as
some sources where I could find detailed information.
Thank you very much
-------------Larry(lmel)

Answer 1:  It'll probably be too hard to explain here.  You may want to check a
physical chemistry book, or better yet, a quantum chemistry book for a more 
detailed explanation.
-Joe Schultz
 
Answer 2:  Well, I really am on my way out, but I saw this note, and 
being a computational chemist myself, I couldn't resist....I can tell 
you a little about the Lennard-Jones potential. This potential is 
typically used to represent the interaction between two atoms which 
are NOT chemically bonded to one another. The form of the potential 
is V(r) = 4*eps*[ (sig/r)^12 - (sig/r)^6 ] where sig is a "collision 
diameter (units of length) and eps is the dissociation energy. Here is 
the internuclear distance between two atoms. The parameters eps and sig 
are adjusted so that simulations will give reasonable agreement with experiment.
 
Actually, there is a little bit of physical meaning to this potential.  When 
two neutral (uncharged) atoms are a long distance apart, the potential 
energy decreases approximately as C/r^^6, where C is a constant. This comes 
from a combination of classical electrostatics and some quantum fluctuations 
of the electron distributions.  However, the D/r^^12 part of the potential has 
no physical origin.  It is merely a quickly diverging function, which is 
convenient, and it is equal to the square of the C/r^^6 term, which is 
computationally efficient. Actually, quantum mechanics says that the repulsive 
part of the potential should diverge exponentially [A*exp(-a*r)], but it's 
computationally more expensive to exponentiate than it is to square. A GREAT 
reference is Allen and Tildesley's "Computer Simulation of Liquids," Oxford 
Press. Good luck! - dr topper

Oh, one more VERY good reference which may be a little
more elementary and have more details is Karplus and Porter's
text "Atoms and Molecules: An Introduction for Students
of Physical Chemistry." Also, there is the classic reference by
Hirschfelder, Curtiss, and Bird, "Molecular Theory of Gases
and Liquids." Finally, there's a new book out by J.M. Haile
called "Molecular Dynamics Simulation: Elementary Methods" which
I think you will find helpful(1992, John Wiley and Sons).
But definitely look at Allen and Tildesley too!

-dr topper