**From:** Jérôme Hénin (*jhenin_at_ifr88.cnrs-mrs.fr*)

**Date:** Tue Jan 19 2010 - 01:56:34 CST

**Next message:**ipsita basu: "starting namd"**Previous message:**Axel Kohlmeyer: "Re: Center of Mass Harmonic Potentials"**In reply to:**Axel Kohlmeyer: "Re: Center of Mass Harmonic Potentials"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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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