# Re: Potentials of mean force using ABF

From: Jerome Henin (jhenin_at_cmm.chem.upenn.edu)
Date: Sat Sep 08 2007 - 18:09:28 CDT

Hello Vaithee,
For the distance and distance-com coordinates, the implementation
assumes spherical symmetry, essentially because the choice of those
coordinates assumes spherical symmetry in the first place.
In a system with cylindrical symmetry, the best approach would
probably to use another coordinate, namely xyDistance or a modified
version thereof if the cylindrical symmetry axis does not coincide
with the z-axis.
If you have collected data using one of the isotropic coordinates and
want to obtain (non-normalized) P(r), the Jacobian correction
-2kT*ln(r) should be added. Not that since the symmetry of the
coordinate does not match that of the system, it is likely that no
kind of normalization will result in a 'conventional' PMF that levels
off at long distances.
Jerome

On 9/8/07, Subramanian Vaitheeswaran <vaithee_at_umd.edu> wrote:
> I have a question regarding the use of NAMD's ABF module to calculate PMFs, where the reaction coordinate is the distance between the centers of mass of two molecules solvated in water.
>
> In a periodically replicated system, it is clear that the PMF written to the "abf outFile" is properly scaled by r^2. i.e. this quantity is -kT log g(r), where k is Boltzmann's constant and g(r) is the radial distribution function. The PMF therefore tends to a constant value for large r and this constant can then be subtracted off as is conventionally done.
>
> But what about systems that are not spherically symmetric - e.g. with cylindrical geometry where the solute molecules are near the boundaries? Since g(r) cannot be defined, is it correct to interpret the data in the 2nd column of "abf outFile" as -kT log P(r) (_without_ the r^2 normalization), where P(r) is the probability of occurrence of r?
>
> I looked carefully at the original reference (Henin and Chipot, J. Chem. Phys., v121, 2904-2914, 2004), but it is not clear how the Jacobian correction is calculated in the absence of spherical symmetry in the NAMD implementation.
>
> thanks,
> S. Vaitheeswaran
> (Vaithee)

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