Hello, in this video we'll
just say a few things about determining the radial
distribution function from molecular dynamics. G of r can be determined
experimentally but it is quite easy to obtain it
for molecular dynamics. One can show that the radial
distribution function can be calculated with the expression
that's showing there, n of r comma delta r is the number of
molecules that are in this little annular
region that shows purple in the cartoon and delta are being
width of that region. So the expression is that the
average of that is divided by n over 2 times rho times the volume of
that annular region, which of course is just
a geometric factor and the numerator is
averaged over all molecules. So we can calculate g of r in
this fashion assuming that we've run the MD
simulation and we know where all the molecules
are as a function of time. We can also obtain the pressure. Pressure in an equilibrium
environment is caused by atomic motion and by the effect of
inter-molecular forces. So by summing over
all of the gradients of potential energy
as a function of r and adding this term into the ideal gas portion we can actually
calculate the pressure. This is an example from a numerical simulation
that I ran, it assumes spherical particles, they are argon with
Lennard-Jones potential. This shows the radial
distribution function and you can see it's pretty nicely done that there isn't
too much noise. The longer I run this simulation, the less noise I get and
the smoother the curve will be because I'm averaging over more and more trajectories. So where can you get MD software? There are commercial
systems out there. They tend to be expensive and the ones that
are open source are probably better in many
ways because you can get access to the code, you can modify the code and
all that sort of thing. The ones I've worked on
mostly are the first two, that's Tinker and that was
developed and was published by the group of
Professor Jay Ponder at Saint Louis University. It was really developed for
bio-molecule simulations. Most of the big work on MD
was developed either for that or for materials purposes. DL_ POLY is another
good open source. What I like about DL_POLY is that it has wonderful documentation, just really detailed explanation
of how everything works. Tinker is easy-to-use,
DL_POLY is a little less easy to use but
not significantly. So either one of
them are just fine. LAMMPS was produced by
Sandia National Laboratory, is maintained by Sandia. It was developed mainly
for materials but it can be used for liquids
and gas phase as well. Then NAMD is another open
source molecular dynamics code that is also available
for your users pleasure. So that is it. I think that it is interesting to do
these MD calculations. I personally have done
a lot of calculations studying ionic liquids
for which I've had to modify both Tinker and DL_POLY because
neither one accounted for pure ionic type
electrostatic interactions. I should say, I take that back, they accounted for electrostatic interaction but what
they didn't account for was imposed electric fields which is the problem
that I was studying. But nonetheless, these are great codes and one can
do a lot with them. So that's it for this
video in this module. Have a great day.
Thanks for listening.