VMD-L Mailing List

From: Axel Kohlmeyer (akohlmey_at_cmm.chem.upenn.edu)
Date: Mon Aug 25 2008 - 15:14:35 CDT

On Mon, 25 Aug 2008, Maxim Paliy wrote:

MP> Hi All

hi maxim,

MP> I've a couple of quick questions about "measure gofr" command
MP>
MP> 1) how exactly the unnormalised histogram (last output list) is
MP> normalised to the second output list?
MP> i.e. what is the density rho ?

is the "pair-particle" density formed by both selections averaged
over either the volume of the simulation cell - in case of pbc aware
calculations - or else assuming the particle density of water (without
PBC the density is not a well defined entity anyways). this density
excludes "self-pairing". the resulting graph does not need to
be corrected for finite size effects, i.e. it approaches 1.0 instead
of (n-1)/n in the case of n particles of the same type.

MP> 2) In the manuals, the factor 4pi seems to be missing from the formula
MP> for the third output list
MP> (runnig coordination number n(r) = int( rho*g(r)*r^2*dr ).. Is this a
MP> typo in the manuals?

well, as it is scaling factor one could claim it is included
in "rho". in any case, the integral is computed directly from
taking the sum over the averaged histogram bins, like in:

n(r) = Sum_i=0..k <h(i)>, with k = r/delta (delta=bin width).

as this is the only way to correctly compute this value from
simulations where the number of particles in the selections
changes over time.

in case you observed any (minor?) inconsistencies, please note
that a couple of bugs that were mostly (but not completely)
compensating each other have been found and fixed recently in
the measure gofr code and that the vmd alpha releases are commended
to use for any application that depends on accurate numerical results.

cheers,
   axel.

MP>
MP> thank you advance for clarifications,
MP> Maxim
MP> 

-- 
=======================================================================
Axel Kohlmeyer   akohlmey_at_cmm.chem.upenn.edu   http://www.cmm.upenn.edu
   Center for Molecular Modeling   --   University of Pennsylvania
Department of Chemistry, 231 S.34th Street, Philadelphia, PA 19104-6323
tel: 1-215-898-1582,  fax: 1-215-573-6233,  office-tel: 1-215-898-5425
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If you make something idiot-proof, the universe creates a better idiot.