0.1 Definitions
Positions: , with
and
;
Interparticle unit vector:
Directions (unit vectors): ,
Width:
(side-by-side),
Length: (end-to-end).
Then
|
(1) |
where the generalized diameter and well depth parameters are given by
|
(2) |
and
|
(3) |
with
|
(4) |
|
(5) |
and
|
(6) |
A widely studied system is defined by the length-to-width ratio
= 3. In this case the usual choice for the
parameters , and
is
|
(7) |
It should be noted that these parameters were identified by an optimal fit
to a site-site potential in which 4 LJ centers were placed along a line
at distances
; in other words, the distance between
the outer LJ centers was .
For molecules of other l/w ratios other choices of the parameters would
be appropriate. However, model simulations are often done with the same
, and even
.
For
the model should become
identical to the simple LJ model; it does so only if the parameter
is also modified so as to approach .
A simple linear interpolation formula would be
|
(8) |
The problem with this formula is that for lengths
larger than it proceeds to unphysical
negative values of
. In fact, this ratio
should, for longer and longer molecules, asymptotically tend to zero, since
the negative side-by-side potential energy increases while the end-to-end
energy remains finite. An interpolation formula that accounts for this is
|
(9) |
F. J. Vesely / University of Vienna