Francisco Garcia wrote:
Dear users,
I wish to ask a question regarding the maximum cut-off in the minimum
image convention (MIC).
According to my understanding, MIC ensures that the separation
between two particles i and j along each coordinate axes, namely,
xi- xj, yi-yj, and zi-zj, is in the interval (-0.5L, 0.5L), where L is the box
length (assumed the box to be cubic). This implies that
distance rij can vary between 0 and 0.5L*sqrt(3).
In order words the maximum separation should be less than half the diagonal:
for example if i is located at (0,0,0) and j is located at the corner
(0.49L, 0.49L, 0.49L).
However, I read a couple of text books and online notes that claim
that if r > 0.5L, then MIC is violated.
Specifically, this means that 0.5L < rij < 0.5L*sqrt(3) violates MIC.
I find this confusing. I have been grinding hard to understand this
point but I just
cannot figure it out.
In short my claim is that in MIC, rij can be at most half the diagonal
length whereas
the textbook says that rij can be at most half the box length.
If I am wrong, can someone explain the flaw in my argument?
The box diagonal is the longest dimension across the unit cell, so indeed it
would seem that you can have r > 0.5L. Simplify your problem to 2 dimensions
and the answer becomes very clear. If you have a particle in the center of this
2-D lattice, and you have a cutoff > 0.5L, then you are counting interactions
with other particles within the central unit cell and duplicating at least some
of these interactions in the periodic image. See, for instance:
http://cmt.dur.ac.uk/sjc/thesis_dlc/node60.html
Extend the radius in that image ever so slightly, and particle 1 is going to
interact with *both* particles 4 and 7, the latter being the periodic image of
the same particle. Several textbooks also discuss this phenomenon in depth.
-Justin
Thanks!
--
========================================
Justin A. Lemkul
Ph.D. Candidate
ICTAS Doctoral Scholar
MILES-IGERT Trainee
Department of Biochemistry
Virginia Tech
Blacksburg, VA
jalemkul[at]vt.edu | (540) 231-9080
http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin
========================================
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