Dear Jorge,

what you write makes sense to me, and I cannot answer your questions. This is 
just to say that the situation you encounter is not completely uncommon, 
although most crystallographers would abandon such a crystal form, I guess.
The technical term that describes this 4-fold twinning is "tetartohedral 
twinning" (in contrast to merohedral twinning, which involves two twin 
domains); maybe this helps to find additional pointers.

best wishes,
Kay

On Wed, 20 Jul 2022 11:10:04 -0300, Jorge Iulek <jiu...@gmail.com> wrote:

>Dear all,
>
>
>      We had some data collections at a Synchrotron. Crystals are a kind
>of brush like (lattice strains, to use a term by Dr. Bergfors, though we
>employed good effort for purification), but we took advantage of the
>Synchrotron microfocus.
>
>     Some of the datasets (images) clearly shows more than one lattice
>(maybe more than two) that, struggling, we managed to process a get a
>dataset which allowed molecular replacement and then (initial) refinement.
>
>     But, in a second Synchrotron travel (and after efforts for
>improving crystals), we got in some cases images with spots "well
>separated'  "unique lattice" at some of the target spots (radiation on
>the crystal) in the crystal.
>
>     We processed these happily to P212121 (though some strange points
>by pointless and/or xtriage, namely that " the L-test suggests that the
>data may be twinned,  so the indicated Laue symmetry may be too high"). 
>Systematic absences seem to be OK for lower resolution reflections, but
>at higher resolution there seems to be more of a modulation (if a look
>at a P222 processing).
>
>     Anyway, we took, initially, refinement at P212121, nevertheless (I
>should say not surprisingly), it stuck at 30/31 % R-free, model close
>(if not at all) to completion. Data resolution is 2.31 A.
>
>     We went to process these images in P1, and in the three possible
>P21  (named P21_45, P21_122 and P21_155 - according to approx. axis
>dimensions) sg's. Then we went to refine (refmac, twin option) the
>current model (and then due "symmetry copies" produced with pdbset and
>added to the model to be refined,) in all possible space groups, and
>*care was taken* to  inherit the former r-free set *and* make the then
>corresponding twin related reflections to be in the r-free set (to be
>close to 5% of reflections, but "independent" reflections). It turned
>out that the R/Rfree values dropped around to ~19/25% for P1 and one
>(namely, P21_b151) of the P21; higher values for other P21's. As
>expected, twin domains refine more or less close to 25 (P1) and 50% (any
>P21), respectively.
>
>     To mess up a bit more, I made the same study with "another dataset"
>(another illuminated spot on the - same - crystal). In this case, only
>the dataset processed in P1 presented "good" R values.
>
>     I think these observations might correlate to what the "crystal "
>physically is... a mix of portions genuinely P212121 but mixed, more or
>less, that in some places with twins in one or more other types,
>depending on where I focus my beam.
>
>     Should I look at anything else to establish twin P1 is the best way
>to refine this structure?
>
>
>     Related, and a question I mentioned before in this forum: what if a
>genuine 2 axis (say , P222 to P2, or even to P1) (I do not mean this is
>the case here) is ignored such that one would have doubled the number of
>observations but also doubled the number of parameters to be refined
>(suppose to exclude NCS in any case). Would one expect R/Rfree values to
>be similar in both P222 and P2 (or even P1)? How much extra freedom
>would one have besides the twin domain fractions to refine?
>
>
>     Yours,
>
>
>Jorge
>
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