# [gmx-users] Re: Simulation of 2D lattice model

Bogdan Costescu bcostescu at gmail.com
Sun Jan 6 15:15:34 CET 2013

```On Sun, Jan 6, 2013 at 1:44 PM, James Starlight <jmsstarlight at gmail.com> wrote:
> I mean absence of exponential factor in the C6 term :)
>
> So to change the vdw radius of the specified atom I should to varry
> both c6 and c12 shouldn't it ?

Hmm, to me these look like very basic force field questions. Did you
try to look the Lennard-Jones potential in a good MD book ? Or in the
vast amount of resources available for free online ? Or, even better,
in the GROMACS manual ? That would take surely less than an hour,
while your questions on the subject have stretched over several days.

The 6-12 LJ potential is composed of an attractive and repulsive term.
The 6-12 combination is often used because of computational
efficiency, as the 12-term can be obtained by multiplying the 6-term
with itself. Each of these terms has a constant, typically called C6
and C12, which tells how much each term contributes to the total
potential. For example, to have only the 6-term, C12 can be set to
zero - this is useful when one knows how much attractive and how much
repulsive the potential should be. Most often though, one thinks of
the LJ potential in terms of equilibrium distance (obtained through a
combination rule) and potential well, expressed through the sigma and
epsilon constants. The two pairs (C6/C12 and sigma/epsilon) are
interrelated. The relation is given in the GROMACS manual, on the
Wikipedia page related to the LJ potential and in many other places.
GROMACS also comes with a tool (g_sigeps) which allows an easy
transformation between them. As you can see from the formulas, sigma
depends on both C6 and C12 and epsilon depends on both C6 and C12. So,
(sigma) you need to vary both C6 and C12. It's only partly answered
because you need to read about combination rules in the GROMACS manual
to see how to get from the atom radius to LJ potential sigma...

Please note that a particular force field uses only one of the pairs
(C6/C12 or sigma/epsilon) - you can't mix and match. If you want to
use f.e. OPLS-AA, all LJ interactions are expressed using the
sigma/epsilon pair. If you want to introduce in this force field a new
type of interaction based on another force field which is defined
using the C6/C12 pair, you have to perform the conversion to
sigma/epsilon. If, on the other hand, you design your own force field,
you are free to use either of the two pairs but, once chosen, you have
to be consistent and use that pair for all LJ interactions.

Cheers,
Bogdan

```