AMBER Archive (2007)

Subject: Re: AMBER: Deriving constraint forces on water molecules based on SETTLE moves

From: Steven Winfield (saw44_at_cam.ac.uk)
Date: Thu Feb 15 2007 - 07:28:00 CST

Hello David,

Have you tried just considering a water molecule moving in the x-y
plane? That gives you 3 force/velocity/position components you know must
always be zero... hence if you get non-zero answers for these at any
point you know there's a problem with your maths somewhere.

Steve

David Cerutti wrote:
> Hello again,
>
> I've been making some headway on this constraint virial problem, and
> I now know that my error involves the computation of constraint forces
> for SETTLE'd water molecules.
>
> Does anyone know where I can find formula that tell you the forces to
> apply along each of the three constrained bonds to reproduce the
> accelerations that the SETTLE routine applies to the water? The problem
> can be phrased fairly simply: SETTLE is considered to have applied
> forces along each of the constrained bonds to return the molecule to its
> original shape after a Verlet-integration (half) step deformed the water
> molecule slightly. But, at the end of the SETTLE calculation, all we
> have are the new velocities, from which we derive the net accelerations
> and thus the net forces on each atom. Ww must account for these force
> vectors with a unique set of forces acting along each of the bonds.
> Three constrained bonds, three atoms and one net force on each atom
> resulting from the SETTLE calculation.
>
> But, when I try to write down these equations and then solve for the
> magnitude of the force along each bond, I run into all sorts of trouble
> and I can't figure out why. It would seem that the system is
> over-determined; I can write nine different equations relating each of
> the three components of the three net atomic forces computed by SETTLE
> to two other terms involving the forces applied along each of the bonds
> ending at each of the three atoms. I can pick three of the equations
> and solve them for the magnitude of the force along each bond, but for
> some resaon I get different results depending on which three equations I
> pick--they don't even seem to be self-consist when I look closely at the
> equations.
>
> But, at the same time, it seems that there are three unknowns (the
> magnitudes of the forces along each bond) and three knowns (the net
> force on each atom applied by SETTLE) so there should be a fairly
> concise solution to these equations...
>
> Thanks!
>
> Dave
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