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Re: [ccp4bb] Program to fill unitcell randomly |
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CCP4bb navigationCCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999Subject: Re: Program to fill unitcell randomly From: Ethan Merritt merritt {- at -} U {- dot -} WASHINGTON {- dot -} EDU Date: 2008-12-01 On Monday 01 December 2008 10:28:34 Edward A. Berry wrote: > Ethan A Merritt wrote: > > On Friday 28 November 2008, Mueller, Juergen-Joachim wrote: > >> Dear all, > >> does anybody know a program to > >> fill an unit cell a,b,c randomly by an arbitrary number > >> of spheres (atoms)? > > > > First you would need to define "random". > > Uniform density throughout the lattice? > > Uniform distribution of neighbor-neighbor distances? > > Uniform fractional coodinates? > > Must the placement conform to space group symmetry? > > > Although I am sure it was not intended, this might suggest > to some that uniform is equivalent to random- > actually they are the opposite: a random distribution would > have large areas with nothing and other places where two or > three spheres are almost on top of each other. > A uniform distribution is, well, uniform. I fear you are muddying the waters rather than clarifying. What you refer to as "random distribution" is better described as random sampling from a uniform distribution. > Most programming languages have a function to generate a random > number evenly distributed between 0 and 1. My point was that simple random sampling is not correct in the context of crystallographic symmetry. If you use this procedure to "fill the unit cell", as originally requested, you will violate the crystal symmetry. If you use it to fill the asymmetric unit, then the distribution that describes placement within the full unit cell is no longer the same distribution as you sampled from, since it is now perturbed by the additional placements generated by crystallographic symmetric rather than by random sampling. That may be acceptable, or it may not, depending on the intended application. > Decide how many atoms > you want, get three random numbers for each atom, and those are > your fractional coordinates of your random spheres. Coordconv will > convert to orthogonal angstroms given your cell parameters. That was the "uniform fractional coordinates" case that I listed. It is unlikely to be the correct choice (although as always it depends on the question). This problem is that since it is based on fractional coordinates rather than the true cartesian coordinates, the resulting density of atomic centers will be strongly anisotropic. The density along each axis will be inversely proportional to the cell edge. You would do better to define a cartesian coordinate grid that fills the region of interest, and then assign an atom to each grid point with probability 1/N. This produces artifacts of its own, of course, since the distribution of interatomic distances is now discrete rather than continuous. The question "what is random?" is very deep, and the answer depends strongly on the intended application. -- Ethan A Merritt Biomolecular Structure Center University of Washington, Seattle 98195-7742 CCP4bb navigationCCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999 |
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