-----Original Message-----
From: Lijun Liu [mailto:[email protected]]
Sent: 15 December 2008 18:10
To: Ian Tickle
Cc: [email protected]
Subject: Re: [ccp4bb] About system absence in P4222?
Ian,
Your examples may cause more confusion, especially for those
beginners with symmetry.
In your P222 and P3 cases, an exact "NCS" (0, 0, 1/2) turns
to be an exact crystallographic
translation, which reduces the unit cell to a half while the
reciprocal unit cell gets doubled. A
half of reflection were absent, including those listed as (0,
0, 2n+1). This rule applies generally
to all non-centrosymmetric space groups (P1, P2, P3, P4, and
P6) with P-lattice when only having
one rotational symmetric element other than P1, and some
other space groups like P222.
(Pseudo) translational NCS' role in systematic
absences(weakness) is complicated. However,
to do the math with
--------------
Plug the coordinates (x,y,z) and x+tx, Y+ty,
z+tz) into the
SF equation.
--------------
is exactly the only way to test it.
Lijun
On Dec 15, 2008, at 5:04 AM, Ian Tickle wrote:
But that only means that the SF contribution from that
pair of molecules in the unit cell is zero for (00l) l=odd
reflections. Depending on the crystallographic symmetry
(e.g. if it were 3-fold or higher order) there may be other
pairs for which the SF contribution is non-zero for all (00l)
(but zero for the the odd orders in some other line that is
symmetry-equivalent to (00l)).
So for example I did a test with 2 mols in the a.u.
related by an exact (0,0,1/2) NCS translation in P222:
h k l Fcalc phicalc
0 0 1 0.00 180.00
0 0 2 5120.88 180.00
0 0 3 0.00 180.00
0 0 4 1273.09 0.00
0 0 5 0.01 0.00
0 0 6 260.21 180.00
0 0 7 0.00 180.00
0 0 8 39.42 180.00
0 0 9 0.01 0.00
0 0 10 43.19 0.00
0 0 11 0.00 180.00
0 0 12 118.59 180.00
0 0 13 0.01 0.00
0 0 14 120.89 180.00
0 0 15 0.01 0.00
(00l) l odd are definitely absent here! - because none
of the crystallographic 2-folds affect the (0,0,1/2) translation.
Then I generated 2 mols in the a.u. related by the
(1/2,0,0) NCS translation in P4 to get the (h00) line (note
that the 4-fold along c would not affect a c-axis translation):
1 0 0 25189.10 0.00
2 0 0 200.09 0.00
3 0 0 14404.46 180.00
4 0 0 12608.60 180.00
5 0 0 4669.64 180.00
6 0 0 748.81 0.00
7 0 0 3184.06 0.00
8 0 0 3858.87 0.00
9 0 0 2578.38 0.00
10 0 0 382.61 0.00
11 0 0 683.43 180.00
12 0 0 444.89 180.00
13 0 0 236.65 180.00
14 0 0 352.46 180.00
15 0 0 5.62 0.00
No absences! The 4-fold generates a pair of molecules
related by the (0,1/2,0), not the (1/2,0,0) translation. So
Eleanor is right only in specific cases, Ronald is right in
the general case.
As an aside, while I was verifying this, I think I
found a problem with the P3 specific SF calculation in SFALL.
Here's what I get for 2 mols in the a.u. related by an exact
(0,0,1/2) NCS translation in P3 using the default P3 specific routine:
0 0 1 8.24 -175.63
0 0 2 7339.05 121.46
0 0 3 27.32 125.92
0 0 4 949.76 -10.37
0 0 5 39.10 -103.39
0 0 6 461.79 -115.99
0 0 7 19.18 61.53
0 0 8 219.72 -96.80
0 0 9 66.51 -174.45
0 0 10 288.25 -86.65
Now if I use the P1 routine (SFSG 1):
0 0 1 0.00 165.96
0 0 2 7343.28 121.51
0 0 3 0.00 -24.58
0 0 4 974.19 -13.35
0 0 5 0.00 -155.29
0 0 6 438.79 -115.60
0 0 7 0.01 133.49
0 0 8 226.07 -97.44
0 0 9 0.01 -101.82
0 0 10 291.15 -83.96
The 3-fold along c should not generate any pairs not
related by the (0,0,1/2) NCS translation, so there should be
(00l) l odd absences in this case. So something wrong here!
Personally I always use the P1 routines, why take a chance
just to shave a few secs off the run time? (note that ccp4i
uses the default, i.e. the space-group specific routines).
Cheers
-- Ian
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf
Of Eleanor Dodson
Sent: 15 December 2008 09:56
To: Ronald E Stenkamp
Cc: [email protected]
Subject: Re: [ccp4bb] About system absence in P4222?
Plug the coordinates (x,y,z) and x+tx, Y+ty,
z+tz) into the
SF equation.
If the translation component along c is 0.5
say, then all the 00l
reflections for l=2n+1 will be absent.
Eleanor
Ronald E Stenkamp wrote:
Hi.
Non-crystallographic symmetry (NCS)
doesn't apply to the entire
crystal, so how can it give rise to
systematic absences? I know it
can give rise to systematically weak classes of
reflections, but they
aren't entirely absent.
Ron
On Thu, 11 Dec 2008, Winter, G (Graeme) wrote:
One of the many facilities in
pointless is to search for
absences and
provide a list of likely
spacegroup choices based on the
results. It
includes adjustments for
neighbouring spots to address one of
Eleanor's concerns. NCS can
cause reflections to be systematically
absent too.
The program can be found on the
ccp4 prerelease pages or on the
pointless ftp site.
Cheers,
Graeme
-----Original Message-----
From: CCP4 bulletin board
[mailto:[email protected]]
On Behalf Of
Eleanor Dodson
Sent: 11 December 2008 09:41
To: [email protected]
Subject: Re: [ccp4bb] About
system absence in P4222?
劉家欣(NTHU) wrote:
Dear All:
We have a crystl with P4222 sg.
All statistics look fine.
However, there is a
system absense in l axis.
Any body have
experiences on that?
Any suggestions would
be high appreciated.
jaishin
can you give more details, eg
all reflections along the particular
axis..
Things like ice rings or
overlapping intensity from a next
neighbour
getting integrated
inapropriately can cause anomalies..
Eleanor
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Lijun Liu, PhD
Institute of Molecular Biology
HHMI & Department of Physics
University of Oregon
Eugene, OR 97403
541-346-5176
http://www.uoregon.edu/~liulj/
