# Reparametrization

Hello,
Can we reparametrize parameters A, B, C in Buckingham potential form from Lennard-Jonnes potential? Could you suggest some paper who did this kind of conversion if you don't mind?
Thanks.

Hello,
Can we reparametrize parameters A, B, C in Buckingham potential form
from Lennard-Jonnes potential? Could you suggest some paper who did this
kind of conversion if you don't mind?

technically, yes. practically, no.

you can fairly easily rationalize the process with a bit of analysis
(i.e. the kind of math people usually learn in middle school).

1: write out the functional form for both potentials
2: determine the first and second derivative and identify "important"
points (e,g, location of the minimum, depth of the minimum)

then you can equate their respective expressions for the potential
function and its derivatives, and derive expressions for the
parameters in one potential from the parameters of the other
potentials. if the potentials could be directly converted, then those
expressions would be independent of the distance between the two
atoms. but since this is not the case, they are not, so now you can
only create an approximation and you have to choose, where you want
this approximation to be good and where you can allow it to be bad.
for that you can rationalize the use of extrema, e.g. the potential
should have the same minimum in both cases or should have the same
dissociation energy. but for the most part the shape will not match
well, and thus your will quickly have (arbitrary) differences. BTW:
using an automated least squares fit without any additional
constraints will usually result in a really bad fit (= conversion).

when i taught computational chemistry classes in the past, i often
included a two part exercise, where people first do a potential energy
scan with a quantum chemistry code and then get to program a two atom
oscillator using a harmonic potential, a morse potential, an N-M
Lennard-Jones potential and a linearly tabulated potential. at the end
the assignment, people then have to do a least squares fit of the
quantum chemistry data for all potentials. then compare the result
with the tabulated potential. only the morse gives a good match, but
the harmonic potential is easily generated from using the position of
the minimum and its curvature (which can also be extracted
analytically from the fitted morse potential through doing a second
order taylor-maclaurin expansion).

so if you don't believe me, i suggest you do exactly that assignment
for, say, a hydrogen molecule (keep in mind that you need to do a
CASSCF calculation if you want to scan the potential in its entirety
until dissociation. but otherwise you can just scan around the minimum
and then take the energy of two single isolated hydrogen atoms) and
see for yourself. it is very instructive.

ciao,
axel.