# Re: Orientation colvar + metadynamics questions

From: Jérôme Hénin (jerome.henin_at_ibpc.fr)
Date: Thu Feb 21 2013 - 09:21:43 CST

----- Original Message -----
> Thanks for the answers Jérôme. One last question, if I may - in
> quaternion
> space, is the biasing Gaussian function 'isotropic' (ie, same width
> applied to all 4 dimensions), or are the scalar and vector parts
> treated
> differently?

The four components are treated in a symmetric way, but not as a Euclidean distance: since the orientation quaternions are always unit, their distance is defined as the geodesic distance on the unit sphere (4D hypersphere). More precisely, the distance between Q1 and Q2 is the min of d(Q1, Q2) and d(Q1, -Q2), as Q2 and -Q2 have the same meaning in terms of rotations. So unless I am mistaken, it should be between 0 and pi/2.

Best,
Jerome

> On Thu, 21 Feb 2013 13:53:28 +0100, Jérôme Hénin
> <jerome.henin_at_ibpc.fr>
> wrote:
>
> > Hi Benjamin,
> >
> > ----- Original Message -----
> >> Hello all,
> >>
> >> I'm attempting to use quaternions (colvar 'orientation') as a
> >> biasing
> >> coordinate for a metadynamics simulation, to control the
> >> orientation
> >> of a
> >> molecule with respect to another. I have a few questions that
> >> neither
> >> the
> >> documentation nor my first results have completely answered:
> >>
> >> - Am I correct in assuming that the 'orientation' colvar is
> >> affected
> >> by
> >> the overall rotation of the system, meaning that if I want to
> >> control
> >> the
> >> orientation of B relative to A, I have to restrain the rotation of
> >> A
> >> (using, e.g., another 'orientation' colvar and a 'harmonic'
> >> restraint)?
> >
> > You are correct that the 'orientation' colvar is, in general,
> > sensitive
> > to overall rotations of the system, but incorrect in concluding
> > that you
> > need restraints. As with all colvars, you can define this
> > orientation
> > based on rotated coordinates, in the frame of reference of group A.
> > to
> > that effect, use the rotateReference and refPositionsGroup
> > keywords,
> > providing group A as the the refPositionsGroup.
> >
> >
> >> - How exactly is the width of the hill Gaussians (in R^4) defined
> >> from the
> >> scalar 'width' parameter? I could find no trivial relationship
> >> between
> >> this parameter and the width of the hills (also scalar) given in
> >> the
> >> colvars.state file.
> >
> > The width of each Gaussian is considered to be twice its standard
> > deviation, and it is obtained as the hillWidth parameter of
> > metadynamics, times that colvar's width parameter. So the std. dev.
> > is:
> > 1/2 * hillWidth * colvar->width
> >
> >
> >> - Since 'orientation' is not grid-compatible, PMF output seems
> >> disabled.
> >> Is there a utility program to convert the hills file to a PMF, or
> >> should I
> >> write my own (which would require me to understand the
> >> aforementioned
> >> hill-width thing...)?
> >
> > I don't think there is such a utility at this point, but I hope the
> > info
> > above is enough for you to compute the PMF.
> >
> > Best,
> > Jerome
>

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