Re: Center of Mass Harmonic Potentials

From: Jérôme Hénin (jhenin_at_ifr88.cnrs-mrs.fr)
Date: Tue Jan 19 2010 - 01:56:34 CST

Hi Keith,
Let me just add to Axel's reply with a word about the mathematical
logic behind that, i.e. a simple chain rule.

If you apply a biasing potential V(C(R)), where R = {r_i}, i<=N and
the center of mass
C(R) = 1/M Sum (m_i * r_i)
(M the total mass, etc.).
The total force on the group is F = -dV/dC
The force on a given atom i should be F_i = -dV / dr_i
then (chain rule) F_i = (m_i / M) * F

I hope that made things clearer.

Jerome

2010/1/19 Axel Kohlmeyer <akohlmey_at_gmail.com>:
> On Mon, 2010-01-18 at 18:59 -0600, Keith Battle wrote:
>> Hi NAMD users,
>
> hi keith,
>
>> Our group has been performing potential of mean force calculations
>> using a variety of techniques for some time now. Our systems are
>> rather large so we use center of mass harmonic potentials to define
>> the desired reaction coordinate. Our results have been encouraging,
>> but we have never fully been able to understand how the force applied
>> by the harmonic potential is distributed between atoms in a molecule
>> during a free energy calculation. It’s quite easy to understand the
>> concept when applied between two atoms of a molecule, but not so easy
>> to understand when the force is applied to the center of mass. Any
>> insight would be appreciated.
>
> it is quite easy for center of mass restraints as well. ;)
>
> the force vector on the individual atoms is the force vector
> on the center of mass scaled by the mass fraction of the
> individual atom in the molecule or group.
>
> cheers,
>   axel.
>
>>
>> Best,
>>
>>
>>
>>
>>
>> Keith Battle
>>
>> Research Assistant
>>
>> Department of Chemistry
>>
>> University of South Alabama
>>
>> 251-214-6877
>>
>>
>>
>>
>
> --
> Dr. Axel Kohlmeyer  akohlmey_at_gmail.com
> Institute for Computational Molecular Science
> College of Science and Technology
> Temple University, Philadelphia PA, USA.
>
>

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