# Re: CCL:MD/MM combination

*From*: Konrad Hinsen <hinsen.,at,.ibs.ibs.fr>
*Subject*: Re: CCL:MD/MM combination
*Date*: Wed, 6 Nov 96 20:13:26 +0100

> There seems to be some confusion here with understanding of the
> equipartition theorm. The classical equipartition theorem assigns a total
> energy (note not just kinetic energy) of kT/2 per each term in the system's
> Hamiltonian (momentum or position) that is quadratic. Only for ideal gases
> is the total energy kinetic, for other molecules this is not true. Also,
> non quadratic terms will contibute to the energy of the system but not
> necessarily in the simple kT/2 way. For empirical potential energy
I don't see the problem. The equipartition theorem says that there
will be kT/2 of (kinetic) energy for each degree of freedom whose
momentum enters quadratically into the Hamiltonian, and kT/2 of
(potential) energy for each degree of freedom whose coordinate enters
quadratically into the Hamiltonian. The first part remains true even
if the second part can't be applied. As far as I know, the equipartition
theorem is used in MD only for the momenta, not for the coordinates.
The form of the potential energy function is therefore irrelevant.
For those who want it precisely, here's the equipartition theorem
for the kinetic energy in its exact form:
/ d H \ kT
< p ------- > = ----
\ i d p / 2
i
(Of course it's a partial derivative, but ASCII didn't provide for this!)
--
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Konrad Hinsen | E-Mail: hinsen.,at,.ibs.ibs.fr
Laboratoire de Dynamique Moleculaire | Tel.: +33-76.88.99.28
Institut de Biologie Structurale | Fax: +33-76.88.54.94
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