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> Alternative origins are documented in:
> http://www.ccp4.ac.uk/dist/html/alternate_origins.html

Note that this list makes no distinction between alternate origins and
symmetry-equivalent origins.  In principle, for any space group, any
completely arbitrary alternate origin is permissible, all you need to do
is expand the structure to P1, shift the co-ords to any arbitrary origin
and off you go.  It will of course mean that the symmetry elements are
no longer where you expect them to be from ITC-A!  In many cases the
structure factor program does a partial expansion to a sub-group (maybe
P1) because the SF formulae that it has coded are for a limited
selection of space groups (I'm thinking specifically about SFALL,
possibly other programs have a much more complete set of SF formulae
coded).  We try to avoid doing the full expansion because we want to
take advantage of the symmetry as far as possible to minimise the
computation time (though that's hardly an issue with modern computers).

What this means is that only the alternate origins listed are consistent
with the SF formula that the program is using for the specific space
group that it uses for the calculation.  However in addition, for
centred space groups (A,B,C,F,I,R) some of the alternate origins will be
equivalent, in that the SFs calculated using those origin shifts will be
identical in both amplitude and phase so that the electron density maps
will be identical, and no origin shift is needed if you want to overlay
them (it may be that you still need to apply a space-group symmetry
operator in order to overlay the atomic co-ordinates, but this won't
change the SFs).  For non-equivalent alternate origins only the
calculated amplitudes are invariant, the phases are not, so that the
maps will look completely different unless you apply the appropriate
origin shift.

For example in P212121 (0,0,0) and (1/2,1/2,1/2) are non-equivalent
alternate origins (there are 8 in all) if the program uses the standard
factorised SF formula for P212121, whereas in I222 these two are
equivalent (so there are only 4 non-equivalent).  Similar considerations
apply to C222 (4 non-equivalent origins) and F222 (2) but the table
above makes no such distinction.

Cheers

-- Ian


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