(I don't remember the motivation for the original question.)
Shake-and-Bake used to generate random atoms in an asymmetric unit, and
the program kept the atoms spaced by at least a bond length. Since
PDB entry 2erl, I am not up to date on Shake-and-Bake's current set of
tricks.
The crystal for 2erl was so densely packed that random atoms spaced by
1.5A produced very good starting phase sets. (but I still don't know
what's the motivation underlying the current discussion.)
Did that help?,
Dan
On Mon, 1 Dec 2008, Ethan Merritt wrote:
> 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.
>
>
--
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