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Leonard-Jones Potential in Computational Models
Name: Larry(lmel)
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: 1999
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
Replies:
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
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
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